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3x3_inst25_var1_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst25/assembly/3x3_inst25assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst25/assembly/3x3_inst25assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst25/assembly/3x3_inst25assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst25/assembly/3x3_inst25assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1)."], "valid": true, "config": [{"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.3682140433334865, 0.08970897647428389, 0.502425376239822], "cell_center": [1.6830127018922196, 6.147114317029974]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.5344029398630591, 0.9891697464278887, 0.21703088700988227], "cell_center": [5.049038105676659, 6.147114317029974]}, {"index": 2, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.04014975225319073, 0.7060719947405601, 0.7632273797026523], "cell_center": [1.6830127018922196, 2.049038105676658]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n11\n11\n\nPiece C:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst15_var3_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst15/assembly/4x4_inst15assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/assembly/4x4_inst15assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/assembly/4x4_inst15assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/assembly/4x4_inst15assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/assembly/4x4_inst15assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/assembly/4x4_inst15assembly_step_5.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).", "Place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 2)."], "valid": true, "config": [{"index": 0, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.4523784950258848, 0.5966474216563278, 0.4209460701703134], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 2, 4], "color": [0.38174873155304245, 0.8750272159825754, 0.7170741611088424], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 3, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [2, 4, 1, 2], "color": [0.4240667615814787, 0.7222327073498909, 0.6054485127949952], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 2, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 0, 1], "color": [0.13557809727733983, 0.7545597463569302, 0.3732963496374987], "cell_center": [9.330127018922195, 5.598076211353316]}, {"index": 4, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.29106684612422073, 0.3972090277120738, 0.0043544742627775745], "cell_center": [5.598076211353316, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nPiece D:\n1\n1\n\nPiece E:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst12_var2_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 2: Place piece D with its upper-left corner at (x, y) = (0, 1).
Step 3: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).
Step 4: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst12/perturbed_part/4x4_inst12perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst12/perturbed_part/4x4_inst12perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst12/perturbed_part/4x4_inst12perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst12/perturbed_part/4x4_inst12perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst12/perturbed_part/4x4_inst12perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece D with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "", "Overlap", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 60, "orig_width": 4, "orig_height": 3, "w": 4.598076211353316, "h": 4.964101615137755, "label": "4x3", "piece": [0, 3, 0, 4], "color": [0.8269286759639897, 0.28853959708119414, 0.11506735623330777]}, {"index": 3, "angle": 60, "orig_width": 4, "orig_height": 1, "w": 2.8660254037844393, "h": 3.9641016151377544, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.8799540670390662, 0.016815702542142485, 0.6851494150554925]}, {"index": 1, "angle": 0, "orig_width": 1, "orig_height": 3, "w": 1.0, "h": 3.0, "label": "1x3", "piece": [0, 3, 3, 4], "color": [0.6933282349034623, 0.28464064197742567, 0.5984440934517744]}, {"index": 2, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [2, 3, 0, 3], "color": [0.49483518787283254, 0.25660426038958584, 0.4007459306539174]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1111\n1111\n1111\n\nPiece B:\n1\n1\n1\n\nPiece C:\n1\n1\n1\n\nPiece D:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps | [
"yes",
"no"
] |
|
4x4_inst16_var3_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst16/irregular_assembly/4x4_inst16invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/irregular_assembly/4x4_inst16invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/irregular_assembly/4x4_inst16invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/irregular_assembly/4x4_inst16invalid_irregular_assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 2).", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 4).", "Place piece C with its upper-left corner at (x,y) = (3, 4)."], "results": ["", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 1, 4], "angle": 90, "flip": "none", "color": [0.2906409364547665, 0.18966064628256707, 0.16656066606481745], "is_merged": false}, {"index": 1, "shape": [2, 4, 3, 4], "angle": 90, "flip": "none", "color": [0.6455578112263359, 0.04059609907027828, 0.9406976161672972], "is_merged": true}, {"index": 2, "shape": [[0, 2, 0, 1], [2, 4, 0, 3]], "angle": 0, "flip": "none", "color": [0.10552732137168419, 0.7961088453102383, 0.6833810431216795], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n11\n\nPiece B:\n1100\n1111\n1100\n\nPiece C:\n111\n111\n100\n100\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"yes",
"no"
] |
|
4x4_inst27_var4_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 2: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).
Step 3: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).
Step 4: Place piece B with its upper-left corner at (x, y) = (1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/perturbed_part/4x4_inst27perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).", "Place piece B with its upper-left corner at (x, y) = (1, 4)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 60, "orig_width": 1, "orig_height": 3, "w": 3.098076211353316, "h": 2.3660254037844393, "label": "1x3", "piece": [0, 3, 0, 1], "color": [0.7760512609454071, 0.23147233408575651, 0.09518146844402253]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [1, 2, 1, 3], "color": [0.24455951613028104, 0.36845158724774063, 0.3057028634543797]}, {"index": 3, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.9816281227015189, 0.5664740351314982, 0.6376532394833729]}, {"index": 1, "angle": 60, "orig_width": 3, "orig_height": 3, "w": 4.098076211353316, "h": 4.098076211353316, "label": "3x3", "piece": [0, 3, 1, 4], "color": [0.3199404465463558, 0.3203558624653322, 0.7504705648122028]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n111\n111\n111\n\nPiece C:\n11\n\nPiece D:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst27_var1_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst27/irregular_assembly/3x3_inst27invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/irregular_assembly/3x3_inst27invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/irregular_assembly/3x3_inst27invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (-1, 3).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 2)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 0, 1]], "angle": 30, "flip": "vertical", "color": [0.604000330200972, 0.6770340247405751, 0.5551674092714912], "is_merged": true}, {"index": 0, "shape": [0, 2, 1, 3], "angle": 90, "flip": "none", "color": [0.17203857926331845, 0.4970169511811482, 0.5662534091810973], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n010\n010\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"yes",
"no"
] |
|
4x4_inst19_var2_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).
Step 2: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).
Step 3: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 4: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).
Step 5: Place piece D with its upper-left corner at (x, y) = (0, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/perturbed_part/4x4_inst19perturbed_part_assembly_step_5.png"], "instructions": ["", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).", "Place piece D with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 2, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 2, 4], "color": [0.9646222808065529, 0.17286663433434668, 0.9197129911831481]}, {"index": 4, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.15548994568154517, 0.5175640932286619, 0.924036957862598]}, {"index": 0, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.952951108351252, 0.41844418587893295, 0.20783217104778784]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [0, 1, 2, 4], "color": [0.2136068442754907, 0.9077636730804951, 0.008593383588581083]}, {"index": 3, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [2, 4, 0, 3], "color": [0.8421463017266881, 0.998579446834601, 0.828081664466033]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n11\n\nPiece C:\n11\n11\n\nPiece D:\n11\n11\n11\n\nPiece E:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst3_var3_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece A with its upper-left corner at (x,y) = (1, 1).
Step 2: Place piece B with its upper-left corner at (x,y) = (0, 3).
Step 3: Rotate piece C by about 60 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst3/irregular_assembly/3x3_inst3irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/irregular_assembly/3x3_inst3irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/irregular_assembly/3x3_inst3irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/irregular_assembly/3x3_inst3irregular_assembly_step_3.png"], "instructions": ["", "Place piece A with its upper-left corner at (x,y) = (1, 1).", "Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece C by about 60 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (2, 3)."], "valid": true, "config": [{"index": 0, "shape": [1, 3, 2, 3], "angle": 0, "flip": "none", "color": [0.3390410963415108, 0.7053312771029449, 0.11207793212756367], "is_merged": false}, {"index": 1, "shape": [0, 1, 1, 3], "angle": 0, "flip": "none", "color": [0.17413619213984544, 0.539393258896573, 0.7469777807902688], "is_merged": true}, {"index": 2, "shape": [[1, 3, 0, 2], [0, 1, 0, 1]], "angle": 60, "flip": "none", "color": [0.39620311885379433, 0.3597929969599728, 0.413678806220555], "is_merged": false}], "results": ["", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n10\n\nPiece C:\n11\n11\n10\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps | [
"no",
"yes"
] |
|
3x3_inst1_var3_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst1/assembly/3x3_inst1assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst1/assembly/3x3_inst1assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst1/assembly/3x3_inst1assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst1/assembly/3x3_inst1assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst1/assembly/3x3_inst1assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 1)."], "valid": true, "config": [{"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.256800880301729, 0.03751904073714318, 0.9621217613176958], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [2, 3, 0, 2], "color": [0.6560169554382161, 0.08892499875961357, 0.2746181042425252], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.4502474416941842, 0.8486047097331468, 0.005901795236425311], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 3, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [2, 3, 2, 3], "color": [0.14881909049605957, 0.9309150666944223, 0.2473442019032891], "cell_center": [5.598076211353316, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"yes",
"no"
] |
|
3x3_inst5_var3_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst5/assembly/3x3_inst5assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst5/assembly/3x3_inst5assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst5/assembly/3x3_inst5assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst5/assembly/3x3_inst5assembly_step_3.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).", "Place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 1, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 2, 3], "color": [0.445111390892756, 0.16653115882702152, 0.8213500363599643], "cell_center": [6.0, 4.848076211353316]}, {"index": 2, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.2058943173019785, 0.3076399768831918, 0.506910472590548], "cell_center": [2.0, 1.6160254037844386]}, {"index": 0, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.07357053851548412, 0.9733870202483494, 0.6618987325140707], "cell_center": [2.0, 4.848076211353316]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n1\n1\n\nPiece C:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst3_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_7.png", "output_dir/Tangram_puzzle_v2/4x4_inst3/perturbed_part/4x4_inst3perturbed_part_assembly_step_8.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece G by about 60 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (2, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Place piece D with its upper-left corner at (x, y) = (1, 3).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece H by about 30 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (0, 1).", "Place piece E with its upper-left corner at (x, y) = (3, 3).", "Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (1, 2)."], "results": ["", "", "Over board", "Over board", "Over board", "Over board", "Over board", "Over board", "Over board"], "valid": false, "config": [{"index": 0, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.54590476492727, 0.8017288265026836, 0.19702177212746563]}, {"index": 6, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [2, 3, 2, 6], "color": [0.6703174692655477, 0.09045368054856773, 0.1109174370728383]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 0, 1], "color": [0.9449625741817751, 0.10699177732051413, 0.906832733107004]}, {"index": 3, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [1, 2, 1, 3], "color": [0.09413549272860999, 0.7680476368577523, 0.4128776322048002]}, {"index": 1, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [0, 1, 1, 4], "color": [0.7422122588815101, 0.7551189736163385, 0.9234718311827813]}, {"index": 7, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [3, 4, 0, 1], "color": [0.713590518367683, 0.3036182518548164, 0.1397252722702369]}, {"index": 4, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [1, 2, 3, 4], "color": [0.6840121753279651, 0.8419883108103203, 0.07133341675213412]}, {"index": 5, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [2, 4, 1, 2], "color": [0.4972346165255138, 0.8906984233290346, 0.7562452955907089]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n111\n\nPiece C:\n11\n\nPiece D:\n11\n\nPiece E:\n1\n\nPiece F:\n1\n1\n\nPiece G:\n1111\n\nPiece H:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q_only | [
"no",
"yes"
] |
|
4x4_inst8_var4_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).
Step 2: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
Step 3: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 4: Place piece F with its upper-left corner at (x, y) = (3, 2).
Step 5: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
Step 6: Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (0, 1).
Step 7: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst8/assembly/4x4_inst8assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/assembly/4x4_inst8assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/assembly/4x4_inst8assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/assembly/4x4_inst8assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/assembly/4x4_inst8assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/assembly/4x4_inst8assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/assembly/4x4_inst8assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/assembly/4x4_inst8assembly_step_7.png"], "instructions": ["", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece F with its upper-left corner at (x, y) = (3, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (0, 1).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3)."], "valid": true, "config": [{"index": 4, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [1, 2, 3, 4], "color": [0.7918351590524052, 0.539204813032439, 0.47469005514533036], "cell_center": [6.147114317029974, 6.0]}, {"index": 1, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [0, 1, 1, 4], "color": [0.43734772906443453, 0.7140607992935755, 0.5214252728488368], "cell_center": [6.147114317029974, 10.0]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.6104741962438478, 0.7105984792563446, 0.35533199360146306], "cell_center": [2.049038105676658, 10.0]}, {"index": 5, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.17104429060676052, 0.31991486174124684, 0.7751148512375546], "cell_center": [10.24519052838329, 6.0]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.2306122657446259, 0.821394282823099, 0.040689723719669946], "cell_center": [10.24519052838329, 10.0]}, {"index": 6, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [3, 4, 0, 3], "color": [0.8441902472414256, 0.8605058939309127, 0.9086859759671123], "cell_center": [2.049038105676658, 2.0]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 2, 3], "color": [0.4434074109775199, 0.09519571468722166, 0.1803872345266927], "cell_center": [2.049038105676658, 6.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n1\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n11\n\nPiece E:\n1\n\nPiece F:\n1\n1\n\nPiece G:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"yes",
"no"
] |
|
4x4_inst18_var0_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
Step 2: Place piece G with its upper-left corner at (x, y) = (2, 1).
Step 3: Place piece A with its upper-left corner at (x, y) = (0, 4).
Step 4: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).
Step 5: Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (0, 1).
Step 6: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
Step 7: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_7.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Place piece G with its upper-left corner at (x, y) = (2, 1).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).", "Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (0, 1).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3)."], "results": ["", "", "", "", "", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [0, 1, 1, 4], "color": [0.9869982514704612, 0.32281939344324206, 0.8306345483609714]}, {"index": 6, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [3, 4, 2, 3], "color": [0.20448500268098213, 0.7476839464016675, 0.4118171950672438]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.1356106596338602, 0.9006559215808044, 0.9720273788893483]}, {"index": 4, "angle": 60, "orig_width": 1, "orig_height": 3, "w": 3.098076211353316, "h": 2.3660254037844393, "label": "1x3", "piece": [1, 4, 3, 4], "color": [0.19883839915334045, 0.19820963751580922, 0.4332106091628175]}, {"index": 5, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [3, 4, 0, 3], "color": [0.6952002937385011, 0.5451393144090627, 0.3598069443124001]}, {"index": 2, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.3429060563864845, 0.9039302662351224, 0.4769621469089005]}, {"index": 3, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.8949499330157833, 0.9775042345165299, 0.9215521124499638]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n111\n\nPiece C:\n11\n11\n\nPiece D:\n1\n1\n\nPiece E:\n1\n1\n1\n\nPiece F:\n111\n\nPiece G:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst76_var1_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst76/irregular_assembly/4x4_inst76invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst76/irregular_assembly/4x4_inst76invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst76/irregular_assembly/4x4_inst76invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst76/irregular_assembly/4x4_inst76invalid_irregular_assembly_step_3.png"], "instructions": ["", "Rotate piece C by about 60 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 4).", "Rotate piece A by about 90 degrees clockwise. Flip piece A horizontally. Place piece A with its upper-left corner at (x,y) = (0, 4).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 3)."], "results": ["", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 2, "shape": [[0, 3, 0, 1], [0, 2, 1, 4]], "angle": 60, "flip": "none", "color": [0.8729652561213695, 0.4670473594081451, 0.3827853734975395], "is_merged": false}, {"index": 0, "shape": [3, 4, 0, 4], "angle": 90, "flip": "horizontal", "color": [0.7144190865779325, 0.1269941874659385, 0.47721963270875234], "is_merged": true}, {"index": 1, "shape": [2, 3, 1, 4], "angle": 30, "flip": "none", "color": [0.7121854587320088, 0.6924932948073018, 0.6144529363650728], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1110\n0011\n0011\n0011\n\nPiece B:\n111\n\nPiece C:\n1000\n1111\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst30_var4_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).
Step 2: Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (1, 4).
Step 3: Place piece D with its upper-left corner at (x,y) = (0, 4).
Step 4: Rotate piece A by about 60 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (0, 4).
Step 5: Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/irregular_assembly/4x4_inst30irregular_assembly_step_5.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (1, 4).", "Place piece D with its upper-left corner at (x,y) = (0, 4).", "Rotate piece A by about 60 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3)."], "valid": true, "config": [{"index": 1, "shape": [1, 3, 1, 3], "angle": 90, "flip": "none", "color": [0.16483746954885847, 0.051758929606153026, 0.12492630379800751], "is_merged": false}, {"index": 4, "shape": [[0, 3, 3, 4], [0, 1, 0, 3]], "angle": 30, "flip": "none", "color": [0.3656083002105275, 0.47581511365521845, 0.6183891885528554], "is_merged": false}, {"index": 3, "shape": [3, 4, 1, 4], "angle": 0, "flip": "none", "color": [0.8519142300537066, 0.5805075864102989, 0.9259830837764971], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 1], "angle": 60, "flip": "horizontal", "color": [0.9035591471762607, 0.11970560100617034, 0.4855676628213387], "is_merged": true}, {"index": 2, "shape": [3, 4, 0, 1], "angle": 30, "flip": "none", "color": [0.868250353967598, 0.8718178531170512, 0.8044667206493435], "is_merged": false}], "results": ["", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1000\n1000\n1111\n\nPiece B:\n11\n11\n\nPiece C:\n1\n\nPiece D:\n111\n\nPiece E:\n0001\n0001\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst27_var0_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 3).
Step 2: Rotate piece B by about 60 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (-1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst27/irregular_assembly/4x4_inst27invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/irregular_assembly/4x4_inst27invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst27/irregular_assembly/4x4_inst27invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 3).", "Rotate piece B by about 60 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (-1, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 3, 1, 4], "angle": 30, "flip": "none", "color": [0.7760512609454071, 0.23147233408575651, 0.09518146844402253], "is_merged": false}, {"index": 1, "shape": [[3, 4, 0, 4], [0, 3, 0, 1]], "angle": 60, "flip": "horizontal", "color": [0.3199404465463558, 0.3203558624653322, 0.7504705648122028], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n111\n\nPiece B:\n1111\n0010\n0010\n0010\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps | [
"no",
"yes"
] |
|
3x3_inst30_var4_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece A with its upper-left corner at (x, y) = (0, 3).
Step 2: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).
Step 3: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst30/assembly/3x3_inst30assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/assembly/3x3_inst30assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/assembly/3x3_inst30assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/assembly/3x3_inst30assembly_step_3.png"], "instructions": ["", "Place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3)."], "valid": true, "config": [{"index": 0, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.3898459914352054, 0.015125501920735585, 0.9748770770994594], "cell_center": [1.8660254037844388, 6.0]}, {"index": 2, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [2, 3, 0, 3], "color": [0.8886986770755988, 0.16381677715556997, 0.3911952313182817], "cell_center": [1.8660254037844388, 2.0]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.9881484609812746, 0.3578709672961633, 0.9546513187032589], "cell_center": [5.598076211353316, 6.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"yes",
"no"
] |
|
4x4_inst7_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst7/assembly/4x4_inst7assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/assembly/4x4_inst7assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/assembly/4x4_inst7assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/assembly/4x4_inst7assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst7/assembly/4x4_inst7assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 2).", "Place piece B with its upper-left corner at (x, y) = (1, 4)."], "valid": true, "config": [{"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.0038464181562460897, 0.5456025205471018, 0.8316288348193334], "cell_center": [2.299038105676658, 6.348076211353315]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [2, 4, 0, 1], "color": [0.18526689525137774, 0.6222333081082303, 0.3116245006929087], "cell_center": [2.299038105676658, 2.1160254037844384]}, {"index": 3, "angle": 30, "orig_width": 3, "orig_height": 2, "w": 3.598076211353316, "h": 3.232050807568877, "label": "3x2", "piece": [2, 4, 1, 4], "color": [0.19476840970141396, 0.68707522398946, 0.14366332946109706], "cell_center": [6.897114317029974, 2.1160254037844384]}, {"index": 1, "angle": 0, "orig_width": 3, "orig_height": 2, "w": 3.0, "h": 2.0, "label": "3x2", "piece": [0, 2, 1, 4], "color": [0.5883107006707854, 0.8743059263428191, 0.51136848550568], "cell_center": [6.897114317029974, 6.348076211353315]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n111\n111\n\nPiece C:\n11\n\nPiece D:\n111\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"no",
"yes"
] |
|
3x3_inst26_var4_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst26/assembly/3x3_inst26assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/assembly/3x3_inst26assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/assembly/3x3_inst26assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/assembly/3x3_inst26assembly_step_3.png"], "instructions": ["", "Place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.8601757328506661, 0.8373920802150087, 0.4098927320047637], "cell_center": [6.147114317029974, 5.049038105676658]}, {"index": 2, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.769985114119021, 0.6023151000208017, 0.43905466192464926], "cell_center": [2.049038105676658, 1.6830127018922192]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.1762969342918307, 0.2700538547336413, 0.9959210428826512], "cell_center": [2.049038105676658, 5.049038105676658]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"yes",
"no"
] |
|
4x4_inst28_var3_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 2: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
Step 3: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).
Step 4: Place piece B with its upper-left corner at (x, y) = (2, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst28/perturbed_part/4x4_inst28perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst28/perturbed_part/4x4_inst28perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst28/perturbed_part/4x4_inst28perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst28/perturbed_part/4x4_inst28perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst28/perturbed_part/4x4_inst28perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Place piece B with its upper-left corner at (x, y) = (2, 4)."], "results": ["", "", "", "", "Over board"], "valid": false, "config": [{"index": 0, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.31870027151465274, 0.9820788726257209, 0.8550947462305866]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [2, 4, 0, 2], "color": [0.9709321163056576, 0.9638050814682778, 0.48474678634569257]}, {"index": 3, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.2615618203446515, 0.30219545939699477, 0.7851313753013661]}, {"index": 1, "angle": 30, "orig_width": 4, "orig_height": 1, "w": 3.964101615137755, "h": 2.8660254037844384, "label": "4x1", "piece": [0, 1, 2, 6], "color": [0.3088457752297562, 0.9442534400895921, 0.6030597092417792]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n1111\n\nPiece C:\n11\n11\n\nPiece D:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst23_var2_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 4).
Step 2: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 3: Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2).
Step 4: Place piece B with its upper-left corner at (x, y) = (1, 4).
Step 5: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).
Step 6: Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst23/assembly/4x4_inst23assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/assembly/4x4_inst23assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/assembly/4x4_inst23assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/assembly/4x4_inst23assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/assembly/4x4_inst23assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/assembly/4x4_inst23assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/assembly/4x4_inst23assembly_step_6.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 4).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2)."], "valid": true, "config": [{"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 2, 4], "color": [0.5175730479893074, 0.7209008156630139, 0.8339774749798693], "cell_center": [7.5, 4.848076211353316]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.25815493806589496, 0.2761207462023175, 0.2168904413637872], "cell_center": [1.5, 4.848076211353316]}, {"index": 5, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.9313701131443723, 0.8577776822629893, 0.1914255443977304], "cell_center": [7.5, 1.6160254037844386]}, {"index": 1, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 1, 2], "color": [0.6716820917008354, 0.3773450251007877, 0.850605988039298], "cell_center": [4.5, 4.848076211353316]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [2, 4, 0, 1], "color": [0.2475030415730417, 0.8334016992404263, 0.08403143743189156], "cell_center": [1.5, 1.6160254037844386]}, {"index": 4, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [2, 4, 1, 3], "color": [0.5986403619608208, 0.29107166733029166, 0.30497019909230927], "cell_center": [4.5, 1.6160254037844386]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n11\n\nPiece E:\n11\n11\n\nPiece F:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst18_var4_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst18/irregular_assembly/4x4_inst18irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/irregular_assembly/4x4_inst18irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/irregular_assembly/4x4_inst18irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/irregular_assembly/4x4_inst18irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/irregular_assembly/4x4_inst18irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/irregular_assembly/4x4_inst18irregular_assembly_step_5.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (3, 4).", "Rotate piece D by about 90 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 3).", "Rotate piece B by about 90 degrees clockwise. Flip piece B vertically. Place piece B with its lower-left corner at (x,y) = (1, 4).", "Rotate piece E by about 30 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (0, 4).", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1)."], "valid": true, "config": [{"index": 2, "shape": [1, 3, 0, 2], "angle": 90, "flip": "none", "color": [0.3429060563864845, 0.9039302662351224, 0.4769621469089005], "is_merged": false}, {"index": 3, "shape": [0, 1, 0, 1], "angle": 90, "flip": "none", "color": [0.8949499330157833, 0.9775042345165299, 0.9215521124499638], "is_merged": false}, {"index": 1, "shape": [3, 4, 0, 3], "angle": 90, "flip": "vertical", "color": [0.9869982514704612, 0.32281939344324206, 0.8306345483609714], "is_merged": true}, {"index": 4, "shape": [[1, 3, 2, 3], [0, 1, 1, 4]], "angle": 30, "flip": "none", "color": [0.19883839915334045, 0.19820963751580922, 0.4332106091628175], "is_merged": false}, {"index": 0, "shape": [1, 4, 3, 4], "angle": 60, "flip": "none", "color": [0.1356106596338602, 0.9006559215808044, 0.9720273788893483], "is_merged": false}], "results": ["", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n100\n111\n100\n\nPiece C:\n11\n11\n\nPiece D:\n1\n\nPiece E:\n010\n010\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q_only | [
"yes",
"no"
] |
|
3x3_inst2_var1_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 2).
Step 2: Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (-1, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst2/irregular_assembly/3x3_inst2invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/irregular_assembly/3x3_inst2invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/irregular_assembly/3x3_inst2invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 2).", " Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (-1, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 1, 3], "angle": 90, "flip": "none", "color": [0.12351699744789202, 0.5664729497490351, 0.624512595749913], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 0, 1]], "angle": 0, "flip": "vertical", "color": [0.12655138063137172, 0.33097078814054737, 0.7001299158222172], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n010\n010\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps | [
"yes",
"no"
] |
|
4x4_inst16_var4_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
Step 2: Place piece C with its upper-left corner at (x, y) = (0, 2).
Step 3: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 4: Place piece D with its upper-left corner at (x, y) = (3, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst16/assembly/4x4_inst16assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/assembly/4x4_inst16assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/assembly/4x4_inst16assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/assembly/4x4_inst16assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/assembly/4x4_inst16assembly_step_4.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece D with its upper-left corner at (x, y) = (3, 2)."], "valid": true, "config": [{"index": 1, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [0, 2, 1, 4], "color": [0.6455578112263359, 0.04059609907027828, 0.9406976161672972], "cell_center": [6.0, 6.0]}, {"index": 2, "angle": 0, "orig_width": 3, "orig_height": 2, "w": 3.0, "h": 2.0, "label": "3x2", "piece": [2, 4, 0, 3], "color": [0.10552732137168419, 0.7961088453102383, 0.6833810431216795], "cell_center": [2.0, 2.0]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.2906409364547665, 0.18966064628256707, 0.16656066606481745], "cell_center": [2.0, 6.0]}, {"index": 3, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.28731779180264194, 0.03647956859760171, 0.15648045527389287], "cell_center": [6.0, 2.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n11\n\nPiece C:\n111\n111\n\nPiece D:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst8_var1_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece C with its upper-left corner at (x, y) = (0, 1).
Step 2: Place piece B with its upper-left corner at (x, y) = (1, 3).
Step 3: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 1).
Step 4: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst8/assembly/3x3_inst8assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst8/assembly/3x3_inst8assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst8/assembly/3x3_inst8assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst8/assembly/3x3_inst8assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst8/assembly/3x3_inst8assembly_step_4.png"], "instructions": ["", "Place piece C with its upper-left corner at (x, y) = (0, 1).", "Place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (1, 1).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 2, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.42736045177487814, 0.8513826938670388, 0.8750119894026337], "cell_center": [1.5, 1.6160254037844386]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.20247270312835763, 0.14681033333288918, 0.039265900955547495], "cell_center": [4.5, 4.848076211353316]}, {"index": 3, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [2, 3, 1, 3], "color": [0.9743504876400423, 0.8767773860180708, 0.6725336937906906], "cell_center": [4.5, 1.6160254037844386]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.9121940999636362, 0.4658006204694346, 0.5093386252677216], "cell_center": [1.5, 4.848076211353316]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n11\n11\n\nPiece C:\n1\n\nPiece D:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"yes",
"no"
] |
|
4x4_inst5_var4_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_7.png", "output_dir/Tangram_puzzle_v2/4x4_inst5/perturbed_part/4x4_inst5perturbed_part_assembly_step_8.png"], "instructions": ["", "Place piece D with its upper-left corner at (x, y) = (0, 3).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 3).", "Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 3).", "Rotate piece H by about 90 degrees clockwise, and place piece H with its upper-left corner at (x, y) = (2, 1).", "Place piece C with its upper-left corner at (x, y) = (2, 4).", "Place piece G with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4)."], "results": ["", "", "", "", "Over board", "Over board", "Over board", "Over board", "Over board"], "valid": false, "config": [{"index": 3, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.9240533250960073, 0.9819349600532725, 0.6747134014128692]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.7349991584173213, 0.6699660472482647, 0.43315305080703437]}, {"index": 4, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 1, 2], "color": [0.22291133685432907, 0.48383465028816663, 0.5699125213630748]}, {"index": 5, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [1, 2, 2, 6], "color": [0.5397844496723473, 0.05872496894813528, 0.15399180068950846]}, {"index": 7, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [3, 4, 2, 4], "color": [0.48160700821724445, 0.60931785491179, 0.22992601917545952]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [0, 1, 2, 4], "color": [0.6297825243848936, 0.49093541919773, 0.6669745716275061]}, {"index": 6, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.6662381683077349, 0.4371576487638136, 0.8074652784518175]}, {"index": 1, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 1, 2], "color": [0.26612579155187954, 0.07055091126826107, 0.08305000539925333]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n1\n\nPiece C:\n11\n\nPiece D:\n1\n1\n\nPiece E:\n11\n\nPiece F:\n1111\n\nPiece G:\n11\n\nPiece H:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q_only | [
"yes",
"no"
] |
|
3x3_inst48_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst48/irregular_assembly/3x3_inst48invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst48/irregular_assembly/3x3_inst48invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst48/irregular_assembly/3x3_inst48invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 3).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (2, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 3, 2, 3], "angle": 30, "flip": "none", "color": [0.5435938558033044, 0.035507830349890024, 0.4401982331145228], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 0, 2]], "angle": 30, "flip": "none", "color": [0.30153112752842937, 0.6867856503031506, 0.39580797040893645], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1100\n1100\n0111\n\nPiece B:\n110\n110\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst20_var4_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).
Step 2: Place piece C with its upper-left corner at (x, y) = (1, 2).
Step 3: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
Step 4: Place piece A with its upper-left corner at (x, y) = (2, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_step/4x4_inst20perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_step/4x4_inst20perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_step/4x4_inst20perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_step/4x4_inst20perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_step/4x4_inst20perturbed_step_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).", "Place piece C with its upper-left corner at (x, y) = (1, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Place piece A with its upper-left corner at (x, y) = (2, 2)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 90, "orig_width": 4, "orig_height": 1, "w": 1.0000000000000002, "h": 4.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.5744625311503513, 0.40604309103934255, 0.6755080869563523], "cell_center": [2.0, 7.5]}, {"index": 2, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [2, 3, 1, 4], "color": [0.18485780995210122, 0.8265364443197515, 0.6214626335028112], "cell_center": [6.0, 7.5]}, {"index": 1, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "3x2", "piece": [0, 2, 1, 4], "color": [0.6495522933888194, 0.5813963139566096, 0.8481586539915731], "cell_center": [2.0, 2.5]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 3, "w": 1.0, "h": 3.0, "label": "1x3", "piece": [0, 3, 0, 1], "color": [0.29966205358997233, 0.09697437710727908, 0.8636883692270556], "cell_center": [6.0, 2.5]}], "variant": "perturbed_step"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst6_var1_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst6/assembly/3x3_inst6assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/assembly/3x3_inst6assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/assembly/3x3_inst6assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/assembly/3x3_inst6assembly_step_3.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 2, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [2, 3, 0, 3], "color": [0.1586208137251468, 0.12393853736495797, 0.8716693278560734], "cell_center": [1.8660254037844386, 2.0]}, {"index": 1, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 2, 3], "color": [0.6512655327908536, 0.8401929301826332, 0.8460989766654483], "cell_center": [5.598076211353316, 6.0]}, {"index": 0, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.10309243167421278, 0.24076261322195902, 0.2100689922963226], "cell_center": [1.8660254037844386, 6.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n1\n1\n\nPiece C:\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"no",
"yes"
] |
|
3x3_inst69_var4_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece B with its upper-left corner at (x,y) = (0, 3).
Step 2: Rotate piece A by about 30 degrees clockwise. Flip piece A vertically. Place piece A with its lower-left corner at (x,y) = (1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst69/irregular_assembly/3x3_inst69invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst69/irregular_assembly/3x3_inst69invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst69/irregular_assembly/3x3_inst69invalid_irregular_assembly_step_2.png"], "instructions": ["", "Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 30 degrees clockwise. Flip piece A vertically. Place piece A with its lower-left corner at (x,y) = (1, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 2, 3]], "angle": 0, "flip": "none", "color": [0.8289271958121602, 0.2874252866675162, 0.18696413859663752], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 2], "angle": 30, "flip": "vertical", "color": [0.8091960335687763, 0.16612470580039684, 0.5513661647674789], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n111\n010\n010\n\nPiece B:\n001\n001\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst3_var0_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
Step 2: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
Step 3: Place piece D with its upper-left corner at (x, y) = (2, 2).
Step 4: Place piece A with its upper-left corner at (x, y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst3/assembly/3x3_inst3assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/assembly/3x3_inst3assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/assembly/3x3_inst3assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/assembly/3x3_inst3assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/assembly/3x3_inst3assembly_step_4.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Place piece D with its upper-left corner at (x, y) = (2, 2).", "Place piece A with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 1, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [0, 1, 1, 3], "color": [0.17413619213984544, 0.539393258896573, 0.7469777807902688], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.39620311885379433, 0.3597929969599728, 0.413678806220555], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 3, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.16349340438282878, 0.21139582589822659, 0.2570028333453004], "cell_center": [5.598076211353316, 1.8660254037844388]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.3390410963415108, 0.7053312771029449, 0.11207793212756367], "cell_center": [1.8660254037844388, 5.598076211353316]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n11\n\nPiece C:\n11\n11\n\nPiece D:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst15_var2_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 4).
Step 2: Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 2).
Step 3: Rotate piece B by about 30 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (0, 4).
Step 4: Rotate piece D by about 90 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (2, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst15/irregular_assembly/4x4_inst15irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/irregular_assembly/4x4_inst15irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/irregular_assembly/4x4_inst15irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/irregular_assembly/4x4_inst15irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst15/irregular_assembly/4x4_inst15irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 4).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 2).", "Rotate piece B by about 30 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (0, 4).", "Rotate piece D by about 90 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (2, 4)."], "valid": true, "config": [{"index": 2, "shape": [2, 4, 2, 4], "angle": 30, "flip": "none", "color": [0.13557809727733983, 0.7545597463569302, 0.3732963496374987], "is_merged": false}, {"index": 0, "shape": [0, 2, 2, 4], "angle": 30, "flip": "none", "color": [0.4523784950258848, 0.5966474216563278, 0.4209460701703134], "is_merged": false}, {"index": 1, "shape": [2, 4, 1, 2], "angle": 30, "flip": "vertical", "color": [0.38174873155304245, 0.8750272159825754, 0.7170741611088424], "is_merged": true}, {"index": 3, "shape": [[0, 2, 0, 2], [2, 4, 0, 1]], "angle": 90, "flip": "none", "color": [0.4240667615814787, 0.7222327073498909, 0.6054485127949952], "is_merged": false}], "results": ["", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n11\n11\n10\n10\n\nPiece C:\n11\n11\n\nPiece D:\n0011\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst21_var1_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).
Step 2: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).
Step 3: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst21/perturbed_step/3x3_inst21perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst21/perturbed_step/3x3_inst21perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst21/perturbed_step/3x3_inst21perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst21/perturbed_step/3x3_inst21perturbed_step_assembly_step_3.png"], "instructions": ["", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "results": ["", "Over board", "", "Over board"], "valid": false, "config": [{"index": 2, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.5750109852621413, 0.4718251861047962, 0.07260160357926093], "cell_center": [2.049038105676658, 5.049038105676658]}, {"index": 1, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.6140362933411411, 0.9726156360309749, 0.23541658483033545], "cell_center": [6.147114317029974, 5.049038105676658]}, {"index": 0, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.6165348490517608, 0.47248907820449537, 0.17394439876786527], "cell_center": [2.049038105676658, 1.6830127018922192]}], "variant": "perturbed_step"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst24_var3_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Step 2: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).
Step 3: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst24/assembly/3x3_inst24assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst24/assembly/3x3_inst24assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst24/assembly/3x3_inst24assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst24/assembly/3x3_inst24assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 2)."], "valid": true, "config": [{"index": 0, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [0, 1, 0, 3], "color": [0.7128663156774877, 0.20321597181862183, 0.6465282105669317], "cell_center": [1.8660254037844386, 6.0]}, {"index": 1, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.3668565042280403, 0.7544321568579433, 0.022670156613330716], "cell_center": [5.598076211353316, 6.0]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 2, 3], "color": [0.2714532942394723, 0.8400670830912441, 0.3547580632505397], "cell_center": [1.8660254037844386, 2.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst22_var4_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece C with its upper-left corner at (x,y) = (0, 3).
Step 2: Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 1).
Step 3: Flip piece B vertically. Place piece B with its lower-left corner at (x,y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst22/irregular_assembly/3x3_inst22irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst22/irregular_assembly/3x3_inst22irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst22/irregular_assembly/3x3_inst22irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst22/irregular_assembly/3x3_inst22irregular_assembly_step_3.png"], "instructions": ["", "Place piece C with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 1).", " Flip piece B vertically. Place piece B with its lower-left corner at (x,y) = (0, 3)."], "valid": true, "config": [{"index": 2, "shape": [[1, 3, 1, 3], [0, 1, 0, 2]], "angle": 0, "flip": "none", "color": [0.7857756960096848, 0.6067251586117914, 0.34088809144427157], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 1], "angle": 90, "flip": "none", "color": [0.8710687100386045, 0.541800756938831, 0.8463220295003806], "is_merged": false}, {"index": 1, "shape": [0, 1, 2, 3], "angle": 0, "flip": "vertical", "color": [0.7625957197009988, 0.9880404381427733, 0.37197914191274184], "is_merged": true}], "results": ["", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n110\n011\n011\n\nPiece C:\n011\n011\n110\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps | [
"yes",
"no"
] |
|
4x4_inst20_var0_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst20/irregular_assembly/4x4_inst20irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/irregular_assembly/4x4_inst20irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/irregular_assembly/4x4_inst20irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/irregular_assembly/4x4_inst20irregular_assembly_step_3.png"], "instructions": ["", " Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 4).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 2)."], "valid": true, "config": [{"index": 1, "shape": [0, 2, 1, 4], "angle": 0, "flip": "horizontal", "color": [0.6495522933888194, 0.5813963139566096, 0.8481586539915731], "is_merged": true}, {"index": 2, "shape": [[0, 3, 0, 1], [2, 3, 1, 4]], "angle": 90, "flip": "none", "color": [0.18485780995210122, 0.8265364443197515, 0.6214626335028112], "is_merged": false}, {"index": 0, "shape": [3, 4, 0, 4], "angle": 30, "flip": "none", "color": [0.29966205358997233, 0.09697437710727908, 0.8636883692270556], "is_merged": false}], "results": ["", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1111\n\nPiece B:\n1111\n0001\n0001\n\nPiece C:\n100\n100\n100\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst38_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst38/irregular_assembly/4x4_inst38invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst38/irregular_assembly/4x4_inst38invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst38/irregular_assembly/4x4_inst38invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst38/irregular_assembly/4x4_inst38invalid_irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst38/irregular_assembly/4x4_inst38invalid_irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).", " Flip piece C horizontally. Place piece C with its upper-left corner at (x,y) = (0, 4).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 2)."], "results": ["", "", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 3, "shape": [[2, 4, 1, 4], [0, 2, 2, 4]], "angle": 30, "flip": "none", "color": [0.12093478898180199, 0.6866466715293956, 0.13252558682790772], "is_merged": false}, {"index": 0, "shape": [0, 2, 0, 1], "angle": 60, "flip": "none", "color": [0.2834887826212631, 0.8656741309640128, 0.6531975744498982], "is_merged": false}, {"index": 2, "shape": [0, 2, 1, 2], "angle": 0, "flip": "horizontal", "color": [0.9282782748507362, 0.48858656271077405, 0.05954200460972181], "is_merged": true}, {"index": 1, "shape": [2, 4, 0, 1], "angle": 30, "flip": "none", "color": [0.16003991378313354, 0.02014673951971968, 0.3479685371859973], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n1\n1\n\nPiece C:\n0111\n0111\n1100\n1100\n\nPiece D:\n111\n111\n011\n011\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst23_var4_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
Step 2: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 3: Place piece D with its upper-left corner at (x, y) = (0, 2).
Step 4: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2).
Step 5: Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2).
Step 6: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (3, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_step/4x4_inst23perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_step/4x4_inst23perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_step/4x4_inst23perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_step/4x4_inst23perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_step/4x4_inst23perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_step/4x4_inst23perturbed_step_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst23/perturbed_step/4x4_inst23perturbed_step_assembly_step_6.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2).", "Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (3, 2)."], "results": ["", "", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 1, 2], "color": [0.6716820917008354, 0.3773450251007877, 0.850605988039298], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.25815493806589496, 0.2761207462023175, 0.2168904413637872], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 3, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 0, 1], "color": [0.2475030415730417, 0.8334016992404263, 0.08403143743189156], "cell_center": [9.330127018922195, 5.598076211353316]}, {"index": 4, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 1, 3], "color": [0.5986403619608208, 0.29107166733029166, 0.30497019909230927], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 5, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.9313701131443723, 0.8577776822629893, 0.1914255443977304], "cell_center": [5.598076211353316, 1.8660254037844388]}, {"index": 2, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 2, 4], "color": [0.5175730479893074, 0.7209008156630139, 0.8339774749798693], "cell_center": [9.330127018922195, 1.8660254037844388]}], "variant": "perturbed_step"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst22_var2_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).
Step 2: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).
Step 3: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 3).
Step 4: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 5: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst22/perturbed_part/4x4_inst22perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst22/perturbed_part/4x4_inst22perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst22/perturbed_part/4x4_inst22perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst22/perturbed_part/4x4_inst22perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst22/perturbed_part/4x4_inst22perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst22/perturbed_part/4x4_inst22perturbed_part_assembly_step_5.png"], "instructions": ["", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 3).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.11193829003358746, 0.30617434738153293, 0.40388324801152764]}, {"index": 4, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.23279928245104486, 0.8588011204766025, 0.7142789177710182]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.5252542307964176, 0.9142936793495643, 0.8624907593395256]}, {"index": 0, "angle": 90, "orig_width": 4, "orig_height": 1, "w": 1.0000000000000002, "h": 4.0, "label": "1x4", "piece": [0, 1, 0, 4], "color": [0.482618038040181, 0.6865131363274936, 0.7698501288262459]}, {"index": 2, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [1, 3, 2, 5], "color": [0.9444237233564657, 0.633971880646935, 0.9884764278637307]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n11\n11\n\nPiece D:\n11\n11\n\nPiece E:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps | [
"yes",
"no"
] |
|
4x4_inst24_var2_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 2).
Step 2: Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3).
Step 3: Rotate piece B by about 60 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (0, 4).
Step 4: Rotate piece D by about 60 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24invalid_irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24invalid_irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 2).", "Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3).", "Rotate piece B by about 60 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (0, 4).", "Rotate piece D by about 60 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4)."], "results": ["", "", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [3, 4, 0, 4], "angle": 30, "flip": "none", "color": [0.34673327216917005, 0.3823052678152453, 0.04807869538996756], "is_merged": false}, {"index": 2, "shape": [0, 2, 3, 4], "angle": 90, "flip": "none", "color": [0.3941478645364662, 0.07242735131670541, 0.6221981028733828], "is_merged": false}, {"index": 1, "shape": [2, 3, 1, 4], "angle": 60, "flip": "vertical", "color": [0.34499076168116316, 0.3941488900507818, 0.035379367870832845], "is_merged": true}, {"index": 3, "shape": [[0, 3, 0, 1], [0, 2, 1, 3]], "angle": 60, "flip": "none", "color": [0.667451459773487, 0.609690672977065, 0.9690305764874845], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1111\n\nPiece B:\n011\n111\n100\n100\n\nPiece C:\n11\n\nPiece D:\n100\n111\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst13_var4_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 2: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).
Step 3: Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 1).
Step 4: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3).
Step 5: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
Step 6: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst13/assembly/4x4_inst13assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/assembly/4x4_inst13assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/assembly/4x4_inst13assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/assembly/4x4_inst13assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/assembly/4x4_inst13assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/assembly/4x4_inst13assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst13/assembly/4x4_inst13assembly_step_6.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 1).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4)."], "valid": true, "config": [{"index": 0, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [0, 1, 0, 2], "color": [0.08091420612656075, 0.9562651224873678, 0.23051757819828445], "cell_center": [1.8660254037844386, 5.598076211353316]}, {"index": 4, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.7966424419178151, 0.9680914967906663, 0.866954291693426], "cell_center": [5.598076211353316, 1.8660254037844386]}, {"index": 5, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 2, 4], "color": [0.29384131363027277, 0.3163325797949277, 0.007829642754902055], "cell_center": [9.330127018922193, 1.8660254037844386]}, {"index": 3, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 2, 4], "color": [0.13663939469484443, 0.7631849020052232, 0.6462586504062603], "cell_center": [1.8660254037844386, 1.8660254037844386]}, {"index": 2, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.2805251122858946, 0.9715538225079458, 0.3810974789090861], "cell_center": [9.330127018922193, 5.598076211353316]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [0, 1, 2, 4], "color": [0.9400983497113293, 0.32605090347507637, 0.5045925067978794], "cell_center": [5.598076211353316, 5.598076211353316]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n\nPiece C:\n11\n11\n\nPiece D:\n11\n11\n\nPiece E:\n11\n\nPiece F:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst17_var3_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).
Step 2: Place piece A with its upper-left corner at (x, y) = (0, 4).
Step 3: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
Step 4: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 2).
Step 5: Place piece C with its upper-left corner at (x, y) = (3, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_5.png"], "instructions": ["", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 2).", "Place piece C with its upper-left corner at (x, y) = (3, 4)."], "valid": true, "config": [{"index": 3, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 0, 2], "color": [0.9578521580074713, 0.8815921980787345, 0.19295089472973515], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.3209357623770135, 0.4919116750200321, 0.05254088833875614], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.06114350981419958, 0.30119771230277814, 0.1293300317914955], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 4, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.09830256447954788, 0.3396191061459677, 0.9867290956314256], "cell_center": [5.598076211353316, 1.8660254037844388]}, {"index": 2, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.8024254343287276, 0.5212933415712149, 0.6519422431117098], "cell_center": [9.330127018922195, 5.598076211353316]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nPiece D:\n11\n11\n\nPiece E:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"yes",
"no"
] |
|
4x4_inst19_var4_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece E with its upper-left corner at (x, y) = (0, 1).
Step 2: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).
Step 3: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).
Step 4: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 5: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst19/assembly/4x4_inst19assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/assembly/4x4_inst19assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/assembly/4x4_inst19assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/assembly/4x4_inst19assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/assembly/4x4_inst19assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/assembly/4x4_inst19assembly_step_5.png"], "instructions": ["", "Place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2)."], "valid": true, "config": [{"index": 4, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.15548994568154517, 0.5175640932286619, 0.924036957862598], "cell_center": [7.5, 1.8660254037844386]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [0, 1, 2, 4], "color": [0.2136068442754907, 0.9077636730804951, 0.008593383588581083], "cell_center": [7.5, 5.598076211353316]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 2, 4], "color": [0.9646222808065529, 0.17286663433434668, 0.9197129911831481], "cell_center": [12.5, 5.598076211353316]}, {"index": 0, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.952951108351252, 0.41844418587893295, 0.20783217104778784], "cell_center": [2.5, 5.598076211353316]}, {"index": 3, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [2, 3, 0, 2], "color": [0.8421463017266881, 0.998579446834601, 0.828081664466033], "cell_center": [2.5, 1.8660254037844386]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n1\n1\n\nPiece E:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"no",
"yes"
] |
|
3x3_inst46_var0_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst46/irregular_assembly/3x3_inst46invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst46/irregular_assembly/3x3_inst46invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst46/irregular_assembly/3x3_inst46invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).", "Rotate piece B by about 90 degrees clockwise. Flip piece B horizontally. Place piece B with its upper-left corner at (x,y) = (-1, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 0, 1], "angle": 60, "flip": "none", "color": [0.3729218927568879, 0.31290847144958933, 0.3203892891755481], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 1, 3]], "angle": 90, "flip": "horizontal", "color": [0.9286877744394081, 0.0842528242268854, 0.49084544991398305], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n100\n100\n111\n011\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"yes",
"no"
] |
|
4x4_inst2_var4_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst2/irregular_assembly/4x4_inst2irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/irregular_assembly/4x4_inst2irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/irregular_assembly/4x4_inst2irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/irregular_assembly/4x4_inst2irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/irregular_assembly/4x4_inst2irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/irregular_assembly/4x4_inst2irregular_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst2/irregular_assembly/4x4_inst2irregular_assembly_step_6.png"], "instructions": ["", "Rotate piece E by about 90 degrees clockwise. Place piece E with its upper-left corner at (x,y) = (1, 4).", "Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 3).", "Rotate piece F by about 30 degrees clockwise. Place piece F with its upper-left corner at (x,y) = (2, 4).", "Rotate piece D by about 30 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).", "Place piece B with its upper-left corner at (x,y) = (2, 3).", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2)."], "valid": true, "config": [{"index": 4, "shape": [3, 4, 2, 4], "angle": 90, "flip": "none", "color": [0.4062185845144768, 0.82080352213676, 0.12435592468962808], "is_merged": false}, {"index": 2, "shape": [3, 4, 0, 1], "angle": 90, "flip": "none", "color": [0.5214964160883804, 0.14197386071806894, 0.6150886066496369], "is_merged": false}, {"index": 5, "shape": [[0, 2, 0, 2], [0, 1, 2, 4]], "angle": 30, "flip": "none", "color": [0.09465920484769241, 0.5230886510184202, 0.29886511441981023], "is_merged": false}, {"index": 3, "shape": [3, 4, 1, 2], "angle": 30, "flip": "none", "color": [0.6355020062380002, 0.8225754659177894, 0.9905175449642316], "is_merged": false}, {"index": 1, "shape": [1, 3, 2, 4], "angle": 0, "flip": "none", "color": [0.6569014157009531, 0.2313466861102611, 0.010872417072518958], "is_merged": false}, {"index": 0, "shape": [2, 3, 0, 2], "angle": 60, "flip": "none", "color": [0.4909418154450287, 0.8295599853485568, 0.8848537987406436], "is_merged": true}], "results": ["", "", "", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1100\n1111\n\nPiece B:\n11\n11\n\nPiece C:\n1\n\nPiece D:\n1\n\nPiece E:\n1\n1\n\nPiece F:\n1100\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst8_var2_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
Step 2: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 3).
Step 3: Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2).
Step 4: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 5: Rotate piece G by about 60 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (0, 1).
Step 6: Place piece D with its upper-left corner at (x, y) = (2, 3).
Step 7: Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_step/4x4_inst8perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_step/4x4_inst8perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_step/4x4_inst8perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_step/4x4_inst8perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_step/4x4_inst8perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_step/4x4_inst8perturbed_step_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_step/4x4_inst8perturbed_step_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst8/perturbed_step/4x4_inst8perturbed_step_assembly_step_7.png"], "instructions": ["", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 3).", "Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (3, 2).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece G by about 60 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (0, 1).", "Place piece D with its upper-left corner at (x, y) = (2, 3).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3)."], "results": ["", "", "Overlap", "", "Over board", "Overlap", "", "Overlap"], "valid": false, "config": [{"index": 2, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.2306122657446259, 0.821394282823099, 0.040689723719669946], "cell_center": [1.8660254037844386, 10.24519052838329]}, {"index": 1, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "3x1", "piece": [0, 1, 1, 4], "color": [0.43734772906443453, 0.7140607992935755, 0.5214252728488368], "cell_center": [5.598076211353316, 10.24519052838329]}, {"index": 5, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.17104429060676052, 0.31991486174124684, 0.7751148512375546], "cell_center": [9.330127018922193, 10.24519052838329]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.6104741962438478, 0.7105984792563446, 0.35533199360146306], "cell_center": [1.8660254037844386, 6.147114317029974]}, {"index": 6, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [3, 4, 0, 3], "color": [0.8441902472414256, 0.8605058939309127, 0.9086859759671123], "cell_center": [5.598076211353316, 6.147114317029974]}, {"index": 3, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.4434074109775199, 0.09519571468722166, 0.1803872345266927], "cell_center": [9.330127018922193, 6.147114317029974]}, {"index": 4, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [1, 2, 3, 4], "color": [0.7918351590524052, 0.539204813032439, 0.47469005514533036], "cell_center": [1.8660254037844386, 2.049038105676658]}], "variant": "perturbed_step"} | q+steps | [
"no",
"yes"
] |
|
3x3_inst20_var2_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Flip piece B vertically. Place piece B with its lower-left corner at (x,y) = (0, 3).
Step 2: Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 2).
Step 3: Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst20/irregular_assembly/3x3_inst20irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst20/irregular_assembly/3x3_inst20irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst20/irregular_assembly/3x3_inst20irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst20/irregular_assembly/3x3_inst20irregular_assembly_step_3.png"], "instructions": ["", " Flip piece B vertically. Place piece B with its lower-left corner at (x,y) = (0, 3).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 2).", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 3)."], "valid": true, "config": [{"index": 1, "shape": [2, 3, 0, 1], "angle": 0, "flip": "vertical", "color": [0.2188625865501932, 0.3982672040489632, 0.24949930857585112], "is_merged": true}, {"index": 0, "shape": [0, 2, 2, 3], "angle": 30, "flip": "none", "color": [0.21514705147792568, 0.4919973529353018, 0.7207131866942781], "is_merged": false}, {"index": 2, "shape": [[0, 2, 0, 2], [2, 3, 1, 3]], "angle": 30, "flip": "none", "color": [0.11933639623212677, 0.6534312470367666, 0.34450218937820265], "is_merged": false}], "results": ["", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n110\n110\n011\n\nPiece C:\n011\n110\n110\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst25_var0_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 2).
Step 2: Rotate piece B by about 90 degrees clockwise. Place piece B with its lower-left corner at (x,y) = (0, 4).
Step 3: Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst25/irregular_assembly/4x4_inst25irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/irregular_assembly/4x4_inst25irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/irregular_assembly/4x4_inst25irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/irregular_assembly/4x4_inst25irregular_assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 2).", "Rotate piece B by about 90 degrees clockwise. Place piece B with its lower-left corner at (x,y) = (0, 4).", "Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 4)."], "valid": true, "config": [{"index": 0, "shape": [0, 2, 3, 4], "angle": 90, "flip": "none", "color": [0.46767221164754547, 0.4767504561709347, 0.15453668427780887], "is_merged": false}, {"index": 1, "shape": [2, 4, 0, 2], "angle": 90, "flip": "none", "color": [0.2200316360246839, 0.16174837472242654, 0.08603563855101859], "is_merged": true}, {"index": 2, "shape": [[0, 2, 0, 3], [2, 4, 2, 4]], "angle": 90, "flip": "none", "color": [0.25574162196635564, 0.51986659658632, 0.7369240379748156], "is_merged": false}], "results": ["", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n1100\n1111\n0011\n0011\n\nPiece C:\n1100\n1111\n0011\n0011\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps | [
"no",
"yes"
] |
|
3x3_inst3_var3_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst3/irregular_assembly/3x3_inst3irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/irregular_assembly/3x3_inst3irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/irregular_assembly/3x3_inst3irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst3/irregular_assembly/3x3_inst3irregular_assembly_step_3.png"], "instructions": ["", "Place piece A with its upper-left corner at (x,y) = (1, 1).", "Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece C by about 60 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (2, 3)."], "valid": true, "config": [{"index": 0, "shape": [1, 3, 2, 3], "angle": 0, "flip": "none", "color": [0.3390410963415108, 0.7053312771029449, 0.11207793212756367], "is_merged": false}, {"index": 1, "shape": [0, 1, 1, 3], "angle": 0, "flip": "none", "color": [0.17413619213984544, 0.539393258896573, 0.7469777807902688], "is_merged": true}, {"index": 2, "shape": [[1, 3, 0, 2], [0, 1, 0, 1]], "angle": 60, "flip": "none", "color": [0.39620311885379433, 0.3597929969599728, 0.413678806220555], "is_merged": false}], "results": ["", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n10\n\nPiece C:\n11\n11\n10\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q_only | [
"yes",
"no"
] |
|
3x3_inst2_var1_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst2/irregular_assembly/3x3_inst2invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/irregular_assembly/3x3_inst2invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/irregular_assembly/3x3_inst2invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 2).", " Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (-1, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 1, 3], "angle": 90, "flip": "none", "color": [0.12351699744789202, 0.5664729497490351, 0.624512595749913], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 0, 1]], "angle": 0, "flip": "vertical", "color": [0.12655138063137172, 0.33097078814054737, 0.7001299158222172], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n010\n010\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"yes",
"no"
] |
|
3x3_inst23_var4_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst23/assembly/3x3_inst23assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/assembly/3x3_inst23assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/assembly/3x3_inst23assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/assembly/3x3_inst23assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/assembly/3x3_inst23assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 1).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1)."], "valid": true, "config": [{"index": 3, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [2, 3, 2, 3], "color": [0.16858591960978841, 0.08544656496515068, 0.11494367118197413], "cell_center": [5.598076211353316, 1.8660254037844388]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.6294248924659861, 0.3328326929596823, 0.09034406811739082], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.02981754658528879, 0.27867823105972955, 0.046516018756367794], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 2, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [2, 3, 0, 2], "color": [0.9963442161344365, 0.11387330077903723, 0.2799037066005946], "cell_center": [1.8660254037844388, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"yes",
"no"
] |
|
4x4_inst24_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24invalid_irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst24/irregular_assembly/4x4_inst24invalid_irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 2).", "Rotate piece C by about 90 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (1, 3).", "Rotate piece B by about 60 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (0, 4).", "Rotate piece D by about 60 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4)."], "results": ["", "", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [3, 4, 0, 4], "angle": 30, "flip": "none", "color": [0.34673327216917005, 0.3823052678152453, 0.04807869538996756], "is_merged": false}, {"index": 2, "shape": [0, 2, 3, 4], "angle": 90, "flip": "none", "color": [0.3941478645364662, 0.07242735131670541, 0.6221981028733828], "is_merged": false}, {"index": 1, "shape": [2, 3, 1, 4], "angle": 60, "flip": "vertical", "color": [0.34499076168116316, 0.3941488900507818, 0.035379367870832845], "is_merged": true}, {"index": 3, "shape": [[0, 3, 0, 1], [0, 2, 1, 3]], "angle": 60, "flip": "none", "color": [0.667451459773487, 0.609690672977065, 0.9690305764874845], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1111\n\nPiece B:\n011\n111\n100\n100\n\nPiece C:\n11\n\nPiece D:\n100\n111\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"no",
"yes"
] |
|
3x3_inst28_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst28/irregular_assembly/3x3_inst28irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/irregular_assembly/3x3_inst28irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/irregular_assembly/3x3_inst28irregular_assembly_step_2.png"], "instructions": ["", "Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its lower-left corner at (x,y) = (0, 3)."], "valid": true, "config": [{"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 2, 3]], "angle": 0, "flip": "none", "color": [0.5629568688202203, 0.21307617484959096, 0.3881604215827764], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 2], "angle": 90, "flip": "none", "color": [0.24874432956275316, 0.10459104781785566, 0.290015710844736], "is_merged": true}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n111\n001\n001\n\nPiece B:\n001\n001\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst19_var3_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 1).
Step 2: Rotate piece C by about 60 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 3).
Step 3: Rotate piece D by about 90 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).
Step 4: Place piece B with its lower-left corner at (x,y) = (0, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst19/irregular_assembly/4x4_inst19irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/irregular_assembly/4x4_inst19irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/irregular_assembly/4x4_inst19irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/irregular_assembly/4x4_inst19irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst19/irregular_assembly/4x4_inst19irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 1).", "Rotate piece C by about 60 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 3).", "Rotate piece D by about 90 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).", "Place piece B with its lower-left corner at (x,y) = (0, 4)."], "valid": true, "config": [{"index": 0, "shape": [3, 4, 0, 4], "angle": 60, "flip": "none", "color": [0.952951108351252, 0.41844418587893295, 0.20783217104778784], "is_merged": false}, {"index": 2, "shape": [0, 1, 2, 4], "angle": 60, "flip": "none", "color": [0.9646222808065529, 0.17286663433434668, 0.9197129911831481], "is_merged": false}, {"index": 3, "shape": [[0, 2, 0, 2], [1, 3, 2, 4]], "angle": 90, "flip": "none", "color": [0.8421463017266881, 0.998579446834601, 0.828081664466033], "is_merged": false}, {"index": 1, "shape": [2, 3, 0, 2], "angle": 0, "flip": "none", "color": [0.2136068442754907, 0.9077636730804951, 0.008593383588581083], "is_merged": true}], "results": ["", "", "", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1111\n\nPiece B:\n0011\n1111\n1100\n\nPiece C:\n11\n\nPiece D:\n110\n110\n011\n011\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q+steps | [
"no",
"yes"
] |
|
3x3_inst20_var0_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst20/assembly/3x3_inst20assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst20/assembly/3x3_inst20assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst20/assembly/3x3_inst20assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst20/assembly/3x3_inst20assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst20/assembly/3x3_inst20assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Place piece D with its upper-left corner at (x, y) = (1, 1).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 2, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.11933639623212677, 0.6534312470367666, 0.34450218937820265], "cell_center": [1.5, 1.6160254037844386]}, {"index": 3, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [2, 3, 1, 3], "color": [0.12249492574431531, 0.29714219616431337, 0.07666461362276034], "cell_center": [4.5, 1.6160254037844386]}, {"index": 1, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 2, 3], "color": [0.2188625865501932, 0.3982672040489632, 0.24949930857585112], "cell_center": [4.5, 4.848076211353316]}, {"index": 0, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.21514705147792568, 0.4919973529353018, 0.7207131866942781], "cell_center": [1.5, 4.848076211353316]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n1\n1\n\nPiece C:\n1\n\nPiece D:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"yes",
"no"
] |
|
3x3_inst25_var4_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst25/irregular_assembly/3x3_inst25invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst25/irregular_assembly/3x3_inst25invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst25/irregular_assembly/3x3_inst25invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (-1, 3).", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 2)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 0, 1]], "angle": 60, "flip": "none", "color": [0.5344029398630591, 0.9891697464278887, 0.21703088700988227], "is_merged": true}, {"index": 0, "shape": [0, 2, 1, 3], "angle": 30, "flip": "none", "color": [0.3682140433334865, 0.08970897647428389, 0.502425376239822], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n111\n010\n010\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"yes",
"no"
] |
|
3x3_inst12_var0_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_part/3x3_inst12perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_part/3x3_inst12perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_part/3x3_inst12perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_part/3x3_inst12perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst12/perturbed_part/3x3_inst12perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3)."], "results": ["", "", "", "Overlap", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.7158111525953443, 0.3144750396327004, 0.9033798732112359]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.4602759030241912, 0.5263411433589661, 0.5878592840681638]}, {"index": 0, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.9103403361123941, 0.38267590340608304, 0.7632217986287583]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [0, 1, 1, 3], "color": [0.946796380694129, 0.7835046474330913, 0.11945153897003868]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q_only | [
"yes",
"no"
] |
|
4x4_inst11_var3_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).
Step 2: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 3: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst11/perturbed_part/4x4_inst11perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/perturbed_part/4x4_inst11perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/perturbed_part/4x4_inst11perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/perturbed_part/4x4_inst11perturbed_part_assembly_step_3.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "", "Over board"], "valid": false, "config": [{"index": 1, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.2617125427976732, 0.3180100977057472, 0.9938777587600973]}, {"index": 0, "angle": 60, "orig_width": 3, "orig_height": 2, "w": 3.2320508075688776, "h": 3.598076211353316, "label": "3x2", "piece": [0, 2, 0, 3], "color": [0.590194494564307, 0.8146086514121477, 0.17186877412793822]}, {"index": 2, "angle": 90, "orig_width": 2, "orig_height": 4, "w": 4.0, "h": 2.0000000000000004, "label": "4x2", "piece": [2, 6, 0, 2], "color": [0.21016152453789094, 0.9415963033779045, 0.8255857971856693]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n\nPiece B:\n1\n1\n\nPiece C:\n1111\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps | [
"no",
"yes"
] |
|
3x3_inst26_var3_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst26/perturbed_part/3x3_inst26perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/perturbed_part/3x3_inst26perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/perturbed_part/3x3_inst26perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/perturbed_part/3x3_inst26perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst26/perturbed_part/3x3_inst26perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1)."], "results": ["", "", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 2, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [0, 1, 1, 3], "color": [0.769985114119021, 0.6023151000208017, 0.43905466192464926]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.8601757328506661, 0.8373920802150087, 0.4098927320047637]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.1762969342918307, 0.2700538547336413, 0.9959210428826512]}, {"index": 3, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [2, 3, 0, 3], "color": [0.7902874398047327, 0.9053459516385535, 0.6109399886078966]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q_only | [
"yes",
"no"
] |
|
4x4_inst30_var0_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (1, 1).
Step 2: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
Step 3: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 3).
Step 4: Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 3).
Step 5: Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (0, 1).
Step 6: Place piece B with its upper-left corner at (x, y) = (3, 4).
Step 7: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_part/4x4_inst30perturbed_part_assembly_step_7.png"], "instructions": ["", "Rotate piece G by about 30 degrees clockwise, and place piece G with its upper-left corner at (x, y) = (1, 1).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 3).", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 3).", "Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (0, 1).", "Place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4)."], "results": ["", "", "", "Overlap", "Overlap", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 6, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [3, 4, 1, 4], "color": [0.3925122716097921, 0.08314977817411329, 0.23188307859675394]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.868250353967598, 0.8718178531170512, 0.8044667206493435]}, {"index": 3, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.8519142300537066, 0.5805075864102989, 0.9259830837764971]}, {"index": 4, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.3656083002105275, 0.47581511365521845, 0.6183891885528554]}, {"index": 5, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [3, 4, 0, 1], "color": [0.05693842955173811, 0.9065171787135644, 0.309832012336156]}, {"index": 1, "angle": 30, "orig_width": 1, "orig_height": 3, "w": 2.3660254037844384, "h": 3.098076211353316, "label": "1x3", "piece": [0, 3, 3, 4], "color": [0.16483746954885847, 0.051758929606153026, 0.12492630379800751]}, {"index": 0, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.9035591471762607, 0.11970560100617034, 0.4855676628213387]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n\nPiece B:\n1\n1\n1\n\nPiece C:\n1\n1\n\nPiece D:\n1\n1\n\nPiece E:\n11\n11\n\nPiece F:\n1\n\nPiece G:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst2_var4_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Step 2: Place piece C with its upper-left corner at (x, y) = (0, 1).
Step 3: Place piece B with its upper-left corner at (x, y) = (1, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst2/perturbed_part/3x3_inst2perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/perturbed_part/3x3_inst2perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/perturbed_part/3x3_inst2perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/perturbed_part/3x3_inst2perturbed_part_assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece C with its upper-left corner at (x, y) = (0, 1).", "Place piece B with its upper-left corner at (x, y) = (1, 3)."], "results": ["", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.12351699744789202, 0.5664729497490351, 0.624512595749913]}, {"index": 2, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.20573163102149872, 0.7110069434915763, 0.3696499764946295]}, {"index": 1, "angle": 0, "orig_width": 3, "orig_height": 3, "w": 3.0, "h": 3.0, "label": "3x3", "piece": [0, 3, 1, 4], "color": [0.12655138063137172, 0.33097078814054737, 0.7001299158222172]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n111\n111\n111\n\nPiece C:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps | [
"yes",
"no"
] |
|
4x4_inst42_var1_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (3, 3).
Step 2: Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (-1, 2).
Step 3: Place piece F with its upper-left corner at (x,y) = (3, 4).
Step 4: Rotate piece D by about 90 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).
Step 5: Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1).
Step 6: Place piece E with its upper-left corner at (x,y) = (1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst42/irregular_assembly/4x4_inst42invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst42/irregular_assembly/4x4_inst42invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst42/irregular_assembly/4x4_inst42invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst42/irregular_assembly/4x4_inst42invalid_irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst42/irregular_assembly/4x4_inst42invalid_irregular_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst42/irregular_assembly/4x4_inst42invalid_irregular_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst42/irregular_assembly/4x4_inst42invalid_irregular_assembly_step_6.png"], "instructions": ["", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (3, 3).", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (-1, 2).", "Place piece F with its upper-left corner at (x,y) = (3, 4).", "Rotate piece D by about 90 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (0, 4).", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 1).", "Place piece E with its upper-left corner at (x,y) = (1, 4)."], "results": ["", "", "", "", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 2, "shape": [0, 1, 0, 1], "angle": 30, "flip": "none", "color": [0.9524278181594674, 0.6518896749874769, 0.7240333247338142], "is_merged": false}, {"index": 1, "shape": [2, 4, 1, 3], "angle": 90, "flip": "none", "color": [0.6644427750389728, 0.5522085718688583, 0.4053814571504184], "is_merged": true}, {"index": 5, "shape": [[1, 2, 0, 3], [0, 1, 1, 4]], "angle": 0, "flip": "none", "color": [0.8508983564043737, 0.8925002048281677, 0.871218180639155], "is_merged": false}, {"index": 3, "shape": [1, 3, 3, 4], "angle": 90, "flip": "none", "color": [0.1835895328909921, 0.24110342593319922, 0.9822734709131831], "is_merged": false}, {"index": 0, "shape": [2, 4, 0, 1], "angle": 90, "flip": "none", "color": [0.615535860392779, 0.5385634227720585, 0.8595055225835873], "is_merged": false}, {"index": 4, "shape": [3, 4, 3, 4], "angle": 0, "flip": "none", "color": [0.9570031788748194, 0.5793073704228564, 0.3085590884080971], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n01\n01\n11\n10\n10\n\nPiece C:\n1\n\nPiece D:\n11\n\nPiece E:\n1\n\nPiece F:\n1110\n0111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst22_var1_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).
Step 2: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 3).
Step 3: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).
Step 4: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 5: Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst22/assembly/4x4_inst22assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst22/assembly/4x4_inst22assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst22/assembly/4x4_inst22assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst22/assembly/4x4_inst22assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst22/assembly/4x4_inst22assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst22/assembly/4x4_inst22assembly_step_5.png"], "instructions": ["", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1)."], "valid": true, "config": [{"index": 3, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.11193829003358746, 0.30617434738153293, 0.40388324801152764], "cell_center": [1.9330127018922196, 2.482050807568877]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.5252542307964176, 0.9142936793495643, 0.8624907593395256], "cell_center": [5.799038105676659, 7.446152422706632]}, {"index": 2, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [1, 2, 2, 4], "color": [0.9444237233564657, 0.633971880646935, 0.9884764278637307], "cell_center": [9.665063509461099, 7.446152422706632]}, {"index": 0, "angle": 60, "orig_width": 4, "orig_height": 1, "w": 2.8660254037844393, "h": 3.9641016151377544, "label": "4x1", "piece": [0, 1, 0, 4], "color": [0.482618038040181, 0.6865131363274936, 0.7698501288262459], "cell_center": [1.9330127018922196, 7.446152422706632]}, {"index": 4, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.23279928245104486, 0.8588011204766025, 0.7142789177710182], "cell_center": [5.799038105676659, 2.482050807568877]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1111\n\nPiece B:\n11\n11\n\nPiece C:\n11\n\nPiece D:\n11\n11\n\nPiece E:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst18_var0_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_6.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/perturbed_part/4x4_inst18perturbed_part_assembly_step_7.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Place piece G with its upper-left corner at (x, y) = (2, 1).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).", "Rotate piece F by about 60 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (0, 1).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3)."], "results": ["", "", "", "", "", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [0, 1, 1, 4], "color": [0.9869982514704612, 0.32281939344324206, 0.8306345483609714]}, {"index": 6, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [3, 4, 2, 3], "color": [0.20448500268098213, 0.7476839464016675, 0.4118171950672438]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.1356106596338602, 0.9006559215808044, 0.9720273788893483]}, {"index": 4, "angle": 60, "orig_width": 1, "orig_height": 3, "w": 3.098076211353316, "h": 2.3660254037844393, "label": "1x3", "piece": [1, 4, 3, 4], "color": [0.19883839915334045, 0.19820963751580922, 0.4332106091628175]}, {"index": 5, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [3, 4, 0, 3], "color": [0.6952002937385011, 0.5451393144090627, 0.3598069443124001]}, {"index": 2, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.3429060563864845, 0.9039302662351224, 0.4769621469089005]}, {"index": 3, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.8949499330157833, 0.9775042345165299, 0.9215521124499638]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n111\n\nPiece C:\n11\n11\n\nPiece D:\n1\n1\n\nPiece E:\n1\n1\n1\n\nPiece F:\n111\n\nPiece G:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q_only | [
"yes",
"no"
] |
|
3x3_inst30_var4_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst30/assembly/3x3_inst30assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/assembly/3x3_inst30assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/assembly/3x3_inst30assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst30/assembly/3x3_inst30assembly_step_3.png"], "instructions": ["", "Place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3)."], "valid": true, "config": [{"index": 0, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.3898459914352054, 0.015125501920735585, 0.9748770770994594], "cell_center": [1.8660254037844388, 6.0]}, {"index": 2, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [2, 3, 0, 3], "color": [0.8886986770755988, 0.16381677715556997, 0.3911952313182817], "cell_center": [1.8660254037844388, 2.0]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.9881484609812746, 0.3578709672961633, 0.9546513187032589], "cell_center": [5.598076211353316, 6.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"yes",
"no"
] |
|
4x4_inst25_var1_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 2).
Step 2: Place piece C with its upper-left corner at (x,y) = (0, 4).
Step 3: Flip piece B horizontally. Place piece B with its lower-left corner at (x,y) = (1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst25/irregular_assembly/4x4_inst25invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/irregular_assembly/4x4_inst25invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/irregular_assembly/4x4_inst25invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/irregular_assembly/4x4_inst25invalid_irregular_assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 2).", "Place piece C with its upper-left corner at (x,y) = (0, 4).", " Flip piece B horizontally. Place piece B with its lower-left corner at (x,y) = (1, 4)."], "results": ["", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 3, 4], "angle": 90, "flip": "none", "color": [0.46767221164754547, 0.4767504561709347, 0.15453668427780887], "is_merged": false}, {"index": 2, "shape": [[0, 2, 0, 3], [2, 4, 2, 4]], "angle": 0, "flip": "none", "color": [0.25574162196635564, 0.51986659658632, 0.7369240379748156], "is_merged": false}, {"index": 1, "shape": [2, 4, 0, 2], "angle": 0, "flip": "horizontal", "color": [0.2200316360246839, 0.16174837472242654, 0.08603563855101859], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n110\n110\n111\n111\n\nPiece C:\n0011\n0011\n1110\n1110\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps | [
"no",
"yes"
] |
|
3x3_inst55_var4_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece A with its lower-left corner at (x,y) = (1, 4).
Step 2: Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst55/irregular_assembly/3x3_inst55invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst55/irregular_assembly/3x3_inst55invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst55/irregular_assembly/3x3_inst55invalid_irregular_assembly_step_2.png"], "instructions": ["", "Place piece A with its lower-left corner at (x,y) = (1, 4).", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 3, 0, 2], "angle": 0, "flip": "none", "color": [0.9123528570556101, 0.7630357217740212, 0.9404631597785433], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 2, 3]], "angle": 60, "flip": "none", "color": [0.23979007488546733, 0.8736367172923079, 0.6619995780562954], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n010\n010\n111\n\nPiece B:\n001\n001\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst7_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst7/perturbed_part/3x3_inst7perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst7/perturbed_part/3x3_inst7perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst7/perturbed_part/3x3_inst7perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst7/perturbed_part/3x3_inst7perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst7/perturbed_part/3x3_inst7perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 1).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).", "Place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 2, 3], "color": [0.10779093077082336, 0.9663519770282707, 0.08719575355451004]}, {"index": 1, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 2, 3], "color": [0.8890167433678454, 0.8396728997385756, 0.6423378141699023]}, {"index": 2, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [2, 3, 0, 2], "color": [0.5214492117729866, 0.6446553823041661, 0.06936597519800336]}, {"index": 0, "angle": 30, "orig_width": 4, "orig_height": 1, "w": 3.964101615137755, "h": 2.8660254037844384, "label": "4x1", "piece": [0, 1, 0, 4], "color": [0.73843051684633, 0.04893125943557952, 0.5781887360388885]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1111\n\nPiece B:\n11\n\nPiece C:\n11\n\nPiece D:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q_only | [
"yes",
"no"
] |
|
4x4_inst25_var1_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst25/irregular_assembly/4x4_inst25invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/irregular_assembly/4x4_inst25invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/irregular_assembly/4x4_inst25invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/irregular_assembly/4x4_inst25invalid_irregular_assembly_step_3.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (3, 2).", "Place piece C with its upper-left corner at (x,y) = (0, 4).", " Flip piece B horizontally. Place piece B with its lower-left corner at (x,y) = (1, 4)."], "results": ["", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 3, 4], "angle": 90, "flip": "none", "color": [0.46767221164754547, 0.4767504561709347, 0.15453668427780887], "is_merged": false}, {"index": 2, "shape": [[0, 2, 0, 3], [2, 4, 2, 4]], "angle": 0, "flip": "none", "color": [0.25574162196635564, 0.51986659658632, 0.7369240379748156], "is_merged": false}, {"index": 1, "shape": [2, 4, 0, 2], "angle": 0, "flip": "horizontal", "color": [0.2200316360246839, 0.16174837472242654, 0.08603563855101859], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n110\n110\n111\n111\n\nPiece C:\n0011\n0011\n1110\n1110\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"yes",
"no"
] |
|
4x4_inst4_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst4/assembly/4x4_inst4assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/assembly/4x4_inst4assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/assembly/4x4_inst4assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/assembly/4x4_inst4assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/assembly/4x4_inst4assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/assembly/4x4_inst4assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst4/assembly/4x4_inst4assembly_step_6.png"], "instructions": ["", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Rotate piece F by about 30 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (2, 1).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece C with its upper-left corner at (x, y) = (2, 3).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 4).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2)."], "valid": true, "config": [{"index": 4, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 0, 2], "color": [0.9516920847941206, 0.09192754978443096, 0.034011632485778764], "cell_center": [4.848076211353316, 1.5]}, {"index": 5, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [3, 4, 2, 4], "color": [0.5159597562042038, 0.7332772521875923, 0.7847260582105081], "cell_center": [8.080127018922193, 1.5]}, {"index": 0, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.1486163972137372, 0.09099753565850044, 0.9804276633019189], "cell_center": [1.6160254037844386, 4.5]}, {"index": 2, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 2, 4], "color": [0.6633151367722326, 0.05563697103144172, 0.996308043298854], "cell_center": [8.080127018922193, 4.5]}, {"index": 1, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [0, 1, 2, 4], "color": [0.3298784267001694, 0.4254879586883913, 0.8323218982811694], "cell_center": [4.848076211353316, 4.5]}, {"index": 3, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [2, 3, 0, 2], "color": [0.7873704671604125, 0.6920579729169158, 0.06370548134717746], "cell_center": [1.6160254037844386, 1.5]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n1\n1\n\nPiece E:\n11\n\nPiece F:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst21_var0_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece B with its upper-left corner at (x, y) = (2, 4).
Step 2: Place piece C with its upper-left corner at (x, y) = (0, 1).
Step 3: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst21/assembly/4x4_inst21assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst21/assembly/4x4_inst21assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst21/assembly/4x4_inst21assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst21/assembly/4x4_inst21assembly_step_3.png"], "instructions": ["", "Place piece B with its upper-left corner at (x, y) = (2, 4).", "Place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4)."], "valid": true, "config": [{"index": 1, "angle": 0, "orig_width": 2, "orig_height": 3, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [0, 3, 2, 4], "color": [0.9226983536502249, 0.3780541609495376, 0.9449843452750281], "cell_center": [7.5, 6.348076211353316]}, {"index": 2, "angle": 0, "orig_width": 4, "orig_height": 1, "w": 4.0, "h": 1.0, "label": "4x1", "piece": [3, 4, 0, 4], "color": [0.13844656237050856, 0.09373377464750454, 0.41854255601994583], "cell_center": [2.5, 2.116025403784439]}, {"index": 0, "angle": 60, "orig_width": 2, "orig_height": 3, "w": 3.598076211353316, "h": 3.2320508075688776, "label": "2x3", "piece": [0, 3, 0, 2], "color": [0.4773278399576071, 0.4179807901546365, 0.3658306231917948], "cell_center": [2.5, 6.348076211353316]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n11\n\nPiece B:\n11\n11\n11\n\nPiece C:\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst27_var0_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Step 2: Place piece B with its upper-left corner at (x, y) = (1, 3).
Step 3: Place piece D with its upper-left corner at (x, y) = (0, 1).
Step 4: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst27/perturbed_part/3x3_inst27perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/perturbed_part/3x3_inst27perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/perturbed_part/3x3_inst27perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/perturbed_part/3x3_inst27perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst27/perturbed_part/3x3_inst27perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Place piece B with its upper-left corner at (x, y) = (1, 3).", "Place piece D with its upper-left corner at (x, y) = (0, 1).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2)."], "results": ["", "", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.17203857926331845, 0.4970169511811482, 0.5662534091810973]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.604000330200972, 0.6770340247405751, 0.5551674092714912]}, {"index": 3, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [2, 3, 0, 3], "color": [0.08831913378263734, 0.050174014729534866, 0.27620176775171223]}, {"index": 2, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.7341641971685425, 0.29244769077896215, 0.1293027898421113]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n11\n11\n\nPiece D:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst28_var3_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst28/irregular_assembly/3x3_inst28invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/irregular_assembly/3x3_inst28invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst28/irregular_assembly/3x3_inst28invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).", "Rotate piece A by about 60 degrees clockwise. Flip piece A horizontally. Place piece A with its lower-left corner at (x,y) = (1, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 2, 3]], "angle": 60, "flip": "none", "color": [0.5629568688202203, 0.21307617484959096, 0.3881604215827764], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 2], "angle": 60, "flip": "horizontal", "color": [0.24874432956275316, 0.10459104781785566, 0.290015710844736], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n010\n010\n111\n\nPiece B:\n001\n001\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst18_var3_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst18/assembly/4x4_inst18assembly_step_6.png"], "instructions": ["", "Place piece F with its upper-left corner at (x, y) = (0, 1).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 3).", "Rotate piece E by about 90 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (3, 3).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 5, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [3, 4, 0, 3], "color": [0.6952002937385011, 0.5451393144090627, 0.3598069443124001], "cell_center": [10.0, 1.8660254037844386]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 2, 3], "color": [0.8949499330157833, 0.9775042345165299, 0.9215521124499638], "cell_center": [2.0, 1.8660254037844386]}, {"index": 4, "angle": 90, "orig_width": 1, "orig_height": 3, "w": 3.0, "h": 1.0000000000000002, "label": "3x1", "piece": [1, 4, 3, 4], "color": [0.19883839915334045, 0.19820963751580922, 0.4332106091628175], "cell_center": [6.0, 1.8660254037844386]}, {"index": 1, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [0, 1, 1, 4], "color": [0.9869982514704612, 0.32281939344324206, 0.8306345483609714], "cell_center": [6.0, 5.598076211353316]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.1356106596338602, 0.9006559215808044, 0.9720273788893483], "cell_center": [2.0, 5.598076211353316]}, {"index": 2, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.3429060563864845, 0.9039302662351224, 0.4769621469089005], "cell_center": [10.0, 5.598076211353316]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n111\n\nPiece C:\n11\n11\n\nPiece D:\n11\n\nPiece E:\n111\n\nPiece F:\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"yes",
"no"
] |
|
4x4_inst25_var2_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
Step 2: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).
Step 3: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).
Step 4: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst25/assembly/4x4_inst25assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/assembly/4x4_inst25assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/assembly/4x4_inst25assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/assembly/4x4_inst25assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst25/assembly/4x4_inst25assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4)."], "valid": true, "config": [{"index": 2, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 0, 2], "color": [0.25574162196635564, 0.51986659658632, 0.7369240379748156], "cell_center": [1.8660254037844388, 2.0]}, {"index": 3, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.9690186633818382, 0.9996354505529929, 0.019142756554478946], "cell_center": [5.598076211353316, 2.0]}, {"index": 1, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.2200316360246839, 0.16174837472242654, 0.08603563855101859], "cell_center": [5.598076211353316, 6.0]}, {"index": 0, "angle": 90, "orig_width": 3, "orig_height": 2, "w": 2.0, "h": 3.0, "label": "2x3", "piece": [0, 2, 0, 3], "color": [0.46767221164754547, 0.4767504561709347, 0.15453668427780887], "cell_center": [1.8660254037844388, 6.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n11\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"no",
"yes"
] |
|
3x3_inst16_var3_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
Step 2: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).
Step 3: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Step 4: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst16/assembly/3x3_inst16assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/assembly/3x3_inst16assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/assembly/3x3_inst16assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/assembly/3x3_inst16assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/assembly/3x3_inst16assembly_step_4.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (2, 2).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2)."], "valid": true, "config": [{"index": 1, "angle": 90, "orig_width": 2, "orig_height": 1, "w": 1.0000000000000002, "h": 2.0, "label": "1x2", "piece": [0, 1, 1, 3], "color": [0.9048699719372921, 0.07001798964152184, 0.5974823649881674], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 3, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [1, 3, 2, 3], "color": [0.7676425093614947, 0.24713964046947057, 0.3655219928054467], "cell_center": [5.598076211353316, 1.8660254037844388]}, {"index": 0, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.9976490339368843, 0.4943065670172001, 0.5594239487418055], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 2, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.10823406854150919, 0.5033344127325038, 0.9895981043015385], "cell_center": [1.8660254037844388, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n\nPiece D:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst77_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst77/irregular_assembly/4x4_inst77invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst77/irregular_assembly/4x4_inst77invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst77/irregular_assembly/4x4_inst77invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst77/irregular_assembly/4x4_inst77invalid_irregular_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst77/irregular_assembly/4x4_inst77invalid_irregular_assembly_step_4.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise. Flip piece C vertically. Place piece C with its upper-left corner at (x,y) = (-1, 4).", "Rotate piece D by about 90 degrees clockwise. Place piece D with its upper-left corner at (x,y) = (3, 4).", "Rotate piece B by about 30 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (3, 2).", "Place piece A with its upper-left corner at (x,y) = (0, 2)."], "results": ["", "", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 2, "shape": [0, 2, 3, 4], "angle": 90, "flip": "vertical", "color": [0.9775751376273765, 0.14181368177438902, 0.7760015342851491], "is_merged": true}, {"index": 3, "shape": [[2, 4, 0, 3], [0, 2, 1, 3]], "angle": 90, "flip": "none", "color": [0.242227308657038, 0.4467724888479374, 0.9386828300316119], "is_merged": false}, {"index": 1, "shape": [2, 4, 3, 4], "angle": 30, "flip": "none", "color": [0.690871182237763, 0.5987108183857973, 0.4205523950952955], "is_merged": false}, {"index": 0, "shape": [0, 2, 0, 1], "angle": 0, "flip": "none", "color": [0.9126118143408732, 0.673204282995526, 0.908580732890369], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n1\n1\n\nPiece C:\n1100\n1111\n0011\n0011\n\nPiece D:\n1111\n1111\n1100\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"yes",
"no"
] |
|
4x4_inst20_var3_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst20/irregular_assembly/4x4_inst20invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/irregular_assembly/4x4_inst20invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/irregular_assembly/4x4_inst20invalid_irregular_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/irregular_assembly/4x4_inst20invalid_irregular_assembly_step_3.png"], "instructions": ["", "Place piece B with its upper-left corner at (x,y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise. Place piece C with its upper-left corner at (x,y) = (0, 4).", "Place piece A with its upper-left corner at (x,y) = (1, 2)."], "results": ["", "", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [0, 2, 1, 4], "angle": 0, "flip": "none", "color": [0.6495522933888194, 0.5813963139566096, 0.8481586539915731], "is_merged": true}, {"index": 2, "shape": [[0, 3, 0, 1], [2, 3, 1, 4]], "angle": 30, "flip": "none", "color": [0.18485780995210122, 0.8265364443197515, 0.6214626335028112], "is_merged": false}, {"index": 0, "shape": [3, 4, 0, 4], "angle": 0, "flip": "none", "color": [0.29966205358997233, 0.09697437710727908, 0.8636883692270556], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1111\n\nPiece B:\n1000\n1111\n1000\n\nPiece C:\n1111\n1000\n1000\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"no",
"yes"
] |
|
3x3_inst23_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/3x3_inst23/perturbed_part/3x3_inst23perturbed_part_assembly_step_5.png"], "instructions": ["", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 1).", "Place piece D with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 4, "angle": 90, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [2, 3, 2, 3], "color": [0.33940213919128803, 0.15148877406439698, 0.5222835237729154]}, {"index": 3, "angle": 60, "orig_width": 2, "orig_height": 1, "w": 1.8660254037844388, "h": 2.232050807568877, "label": "2x1", "piece": [2, 3, 0, 2], "color": [0.16858591960978841, 0.08544656496515068, 0.11494367118197413]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.6294248924659861, 0.3328326929596823, 0.09034406811739082]}, {"index": 2, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [1, 2, 1, 2], "color": [0.9963442161344365, 0.11387330077903723, 0.2799037066005946]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.02981754658528879, 0.27867823105972955, 0.046516018756367794]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n\nPiece D:\n11\n\nPiece E:\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q_only | [
"yes",
"no"
] |
|
3x3_inst21_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst21/irregular_assembly/3x3_inst21invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst21/irregular_assembly/3x3_inst21invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst21/irregular_assembly/3x3_inst21invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3).", " Flip piece A vertically. Place piece A with its lower-left corner at (x,y) = (-1, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 1, 3]], "angle": 90, "flip": "none", "color": [0.6140362933411411, 0.9726156360309749, 0.23541658483033545], "is_merged": false}, {"index": 0, "shape": [1, 3, 0, 1], "angle": 0, "flip": "vertical", "color": [0.6165348490517608, 0.47248907820449537, 0.17394439876786527], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1110\n0011\n0011\n\nPiece B:\n111\n111\n001\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"no",
"yes"
] |
|
3x3_inst2_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst2/irregular_assembly/3x3_inst2irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/irregular_assembly/3x3_inst2irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/irregular_assembly/3x3_inst2irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (1, 2).", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (0, 3)."], "valid": true, "config": [{"index": 0, "shape": [0, 2, 1, 3], "angle": 30, "flip": "none", "color": [0.12351699744789202, 0.5664729497490351, 0.624512595749913], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 0, 1]], "angle": 60, "flip": "none", "color": [0.12655138063137172, 0.33097078814054737, 0.7001299158222172], "is_merged": true}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n111\n100\n100\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q_only | [
"yes",
"no"
] |
|
3x3_inst24_var4_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).
Step 2: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 2).
Step 3: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst24/perturbed_step/3x3_inst24perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst24/perturbed_step/3x3_inst24perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst24/perturbed_step/3x3_inst24perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst24/perturbed_step/3x3_inst24perturbed_step_assembly_step_3.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (0, 2).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 2).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 2)."], "results": ["", "", "", "Overlap"], "valid": false, "config": [{"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.3668565042280403, 0.7544321568579433, 0.022670156613330716], "cell_center": [1.8660254037844388, 6.147114317029974]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.2714532942394723, 0.8400670830912441, 0.3547580632505397], "cell_center": [5.598076211353316, 6.147114317029974]}, {"index": 0, "angle": 60, "orig_width": 3, "orig_height": 1, "w": 2.3660254037844393, "h": 3.098076211353316, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.7128663156774877, 0.20321597181862183, 0.6465282105669317], "cell_center": [1.8660254037844388, 2.049038105676658]}], "variant": "perturbed_step"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst16_var1_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece D with its upper-left corner at (x, y) = (0, 2).
Step 2: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).
Step 3: Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 2).
Step 4: Place piece A with its upper-left corner at (x, y) = (0, 3).
Step 5: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst16/perturbed_part/3x3_inst16perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/perturbed_part/3x3_inst16perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/perturbed_part/3x3_inst16perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/perturbed_part/3x3_inst16perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/perturbed_part/3x3_inst16perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/3x3_inst16/perturbed_part/3x3_inst16perturbed_part_assembly_step_5.png"], "instructions": ["", "Place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 3).", "Rotate piece E by about 30 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 2).", "Place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 0, 2], "color": [0.7676425093614947, 0.24713964046947057, 0.3655219928054467]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [0, 1, 2, 3], "color": [0.10823406854150919, 0.5033344127325038, 0.9895981043015385]}, {"index": 4, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [1, 3, 2, 3], "color": [0.47356598896022406, 0.4025739472207259, 0.6326173695303007]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 1, "w": 1.0, "h": 1.0, "label": "1x1", "piece": [0, 1, 0, 1], "color": [0.9976490339368843, 0.4943065670172001, 0.5594239487418055]}, {"index": 1, "angle": 30, "orig_width": 2, "orig_height": 1, "w": 2.232050807568877, "h": 1.8660254037844386, "label": "2x1", "piece": [0, 1, 1, 3], "color": [0.9048699719372921, 0.07001798964152184, 0.5974823649881674]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n\nPiece B:\n11\n\nPiece C:\n1\n\nPiece D:\n11\n11\n\nPiece E:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps | [
"yes",
"no"
] |
|
4x4_inst78_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst78/irregular_assembly/4x4_inst78invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst78/irregular_assembly/4x4_inst78invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst78/irregular_assembly/4x4_inst78invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 90 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (2, 3).", "Rotate piece B by about 60 degrees clockwise. Flip piece B vertically. Place piece B with its upper-left corner at (x,y) = (-1, 4)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 3, 2, 4], "angle": 90, "flip": "none", "color": [0.3056860116971202, 0.043885788151956984, 0.4256561876414787], "is_merged": false}, {"index": 1, "shape": [[3, 4, 0, 4], [0, 3, 0, 2]], "angle": 60, "flip": "vertical", "color": [0.8762584141629572, 0.9179960185123505, 0.12890262591567792], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n\nPiece B:\n0110\n0110\n0110\n1111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"yes",
"no"
] |
|
3x3_inst24_var1_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst24/irregular_assembly/3x3_inst24irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst24/irregular_assembly/3x3_inst24irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst24/irregular_assembly/3x3_inst24irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (2, 3).", " Flip piece A vertically. Place piece A with its upper-left corner at (x,y) = (0, 3)."], "valid": true, "config": [{"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 0, 2]], "angle": 90, "flip": "none", "color": [0.3668565042280403, 0.7544321568579433, 0.022670156613330716], "is_merged": false}, {"index": 0, "shape": [1, 3, 2, 3], "angle": 0, "flip": "vertical", "color": [0.7128663156774877, 0.20321597181862183, 0.6465282105669317], "is_merged": true}], "results": ["", "", ""], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n111\n110\n110\n\nPiece B:\n001\n111\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_assembly"} | q_only | [
"yes",
"no"
] |
|
4x4_inst14_var0_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).
Step 2: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (3, 4).
Step 3: Place piece B with its upper-left corner at (x, y) = (1, 4).
Step 4: Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 5: Place piece F with its upper-left corner at (x, y) = (3, 2).
Step 6: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst14/assembly/4x4_inst14assembly_step_6.png"], "instructions": ["", "Rotate piece D by about 30 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (3, 4).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece F with its upper-left corner at (x, y) = (3, 2).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (1, 2)."], "valid": true, "config": [{"index": 3, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [2, 4, 0, 1], "color": [0.5631914090172505, 0.5804703370467916, 0.4790988214748605], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.15000823947344966, 0.4439607975953732, 0.1370434408981498], "cell_center": [9.330127018922195, 5.598076211353316]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.6561140073467281, 0.4764433888300178, 0.7238357704859639], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.25169887858646867, 0.6011267349617215, 0.9995531297392487], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 5, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.8928397408510584, 0.20487579654854826, 0.908916065600491], "cell_center": [9.330127018922195, 1.8660254037844388]}, {"index": 4, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 1, 3], "color": [0.23171741259592205, 0.12354035634812421, 0.9975313433534191], "cell_center": [5.598076211353316, 1.8660254037844388]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nPiece D:\n1\n1\n\nPiece E:\n11\n11\n\nPiece F:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"no",
"yes"
] |
|
4x4_inst20_var2_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).
Step 2: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Step 3: Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2).
Step 4: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_part/4x4_inst20perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_part/4x4_inst20perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_part/4x4_inst20perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_part/4x4_inst20perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst20/perturbed_part/4x4_inst20perturbed_part_assembly_step_4.png"], "instructions": ["", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 2).", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4)."], "results": ["", "", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 90, "orig_width": 4, "orig_height": 1, "w": 1.0000000000000002, "h": 4.0, "label": "1x4", "piece": [3, 4, 0, 4], "color": [0.5744625311503513, 0.40604309103934255, 0.6755080869563523]}, {"index": 0, "angle": 60, "orig_width": 2, "orig_height": 4, "w": 4.464101615137754, "h": 3.7320508075688776, "label": "2x4", "piece": [0, 4, 0, 2], "color": [0.29966205358997233, 0.09697437710727908, 0.8636883692270556]}, {"index": 2, "angle": 30, "orig_width": 3, "orig_height": 1, "w": 3.098076211353316, "h": 2.3660254037844384, "label": "3x1", "piece": [2, 3, 1, 4], "color": [0.18485780995210122, 0.8265364443197515, 0.6214626335028112]}, {"index": 1, "angle": 60, "orig_width": 3, "orig_height": 2, "w": 3.2320508075688776, "h": 3.598076211353316, "label": "3x2", "piece": [0, 2, 1, 4], "color": [0.6495522933888194, 0.5813963139566096, 0.8481586539915731]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n11\n11\n\nPiece B:\n111\n111\n\nPiece C:\n111\n\nPiece D:\n1\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst38_var0_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 3).
Step 2: Place piece A with its lower-left corner at (x,y) = (-1, 2).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst38/irregular_assembly/3x3_inst38invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst38/irregular_assembly/3x3_inst38invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst38/irregular_assembly/3x3_inst38invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 3).", "Place piece A with its lower-left corner at (x,y) = (-1, 2)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 0, 1]], "angle": 60, "flip": "none", "color": [0.2640373819201658, 0.23801220505274123, 0.0902448886427546], "is_merged": false}, {"index": 0, "shape": [1, 3, 1, 3], "angle": 0, "flip": "none", "color": [0.8335762701827948, 0.8840202519453446, 0.5496566700702556], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n010\n010\n111\n\nPiece B:\n100\n100\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps | [
"yes",
"no"
] |
|
4x4_inst16_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_part/4x4_inst16perturbed_part_assembly_step_5.png"], "instructions": ["", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Place piece E with its upper-left corner at (x, y) = (3, 2).", "Rotate piece C by about 30 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (1, 3).", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4)."], "results": ["", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 0, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.2906409364547665, 0.18966064628256707, 0.16656066606481745]}, {"index": 4, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.5772308670225175, 0.5432997569378035, 0.6895078587076925]}, {"index": 2, "angle": 30, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844386, "h": 1.3660254037844386, "label": "1x1", "piece": [1, 2, 1, 2], "color": [0.10552732137168419, 0.7961088453102383, 0.6833810431216795]}, {"index": 3, "angle": 60, "orig_width": 3, "orig_height": 2, "w": 3.2320508075688776, "h": 3.598076211353316, "label": "3x2", "piece": [2, 4, 0, 3], "color": [0.28731779180264194, 0.03647956859760171, 0.15648045527389287]}, {"index": 1, "angle": 0, "orig_width": 3, "orig_height": 2, "w": 3.0, "h": 2.0, "label": "3x2", "piece": [0, 2, 1, 4], "color": [0.6455578112263359, 0.04059609907027828, 0.9406976161672972]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n111\n111\n\nPiece C:\n1\n\nPiece D:\n111\n111\n\nPiece E:\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "perturbed_part"} | q_only | [
"no",
"yes"
] |
|
4x4_inst16_var1_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Place piece D with its upper-left corner at (x, y) = (3, 2).
Step 2: Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 2).
Step 3: Place piece B with its upper-left corner at (x, y) = (1, 4).
Step 4: Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_step/4x4_inst16perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_step/4x4_inst16perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_step/4x4_inst16perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_step/4x4_inst16perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst16/perturbed_step/4x4_inst16perturbed_step_assembly_step_4.png"], "instructions": ["", "Place piece D with its upper-left corner at (x, y) = (3, 2).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (2, 2).", "Place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece A by about 60 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4)."], "results": ["", "", "Overlap", "Overlap", "Overlap"], "valid": false, "config": [{"index": 3, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [2, 4, 3, 4], "color": [0.28731779180264194, 0.03647956859760171, 0.15648045527389287], "cell_center": [2.299038105676658, 6.348076211353315]}, {"index": 2, "angle": 30, "orig_width": 3, "orig_height": 2, "w": 3.598076211353316, "h": 3.232050807568877, "label": "3x2", "piece": [2, 4, 0, 3], "color": [0.10552732137168419, 0.7961088453102383, 0.6833810431216795], "cell_center": [6.897114317029974, 6.348076211353315]}, {"index": 1, "angle": 0, "orig_width": 3, "orig_height": 2, "w": 3.0, "h": 2.0, "label": "3x2", "piece": [0, 2, 1, 4], "color": [0.6455578112263359, 0.04059609907027828, 0.9406976161672972], "cell_center": [2.299038105676658, 2.1160254037844384]}, {"index": 0, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.2906409364547665, 0.18966064628256707, 0.16656066606481745], "cell_center": [6.897114317029974, 2.1160254037844384]}], "variant": "perturbed_step"} | q+steps | [
"yes",
"no"
] |
|
4x4_inst17_var3_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst17/assembly/4x4_inst17assembly_step_5.png"], "instructions": ["", "Rotate piece D by about 60 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (0, 2).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 4).", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (2, 2).", "Place piece C with its upper-left corner at (x, y) = (3, 4)."], "valid": true, "config": [{"index": 3, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 0, 2], "color": [0.9578521580074713, 0.8815921980787345, 0.19295089472973515], "cell_center": [1.8660254037844388, 1.8660254037844388]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.3209357623770135, 0.4919116750200321, 0.05254088833875614], "cell_center": [1.8660254037844388, 5.598076211353316]}, {"index": 1, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.06114350981419958, 0.30119771230277814, 0.1293300317914955], "cell_center": [5.598076211353316, 5.598076211353316]}, {"index": 4, "angle": 60, "orig_width": 2, "orig_height": 2, "w": 2.7320508075688776, "h": 2.7320508075688776, "label": "2x2", "piece": [2, 4, 2, 4], "color": [0.09830256447954788, 0.3396191061459677, 0.9867290956314256], "cell_center": [5.598076211353316, 1.8660254037844388]}, {"index": 2, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.8024254343287276, 0.5212933415712149, 0.6519422431117098], "cell_center": [9.330127018922195, 5.598076211353316]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n\nPiece D:\n11\n11\n\nPiece E:\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"no",
"yes"
] |
|
3x3_inst19_var2_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst19/assembly/3x3_inst19assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/assembly/3x3_inst19assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/assembly/3x3_inst19assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/assembly/3x3_inst19assembly_step_3.png", "output_dir/Tangram_puzzle_v2/3x3_inst19/assembly/3x3_inst19assembly_step_4.png"], "instructions": ["", "Place piece D with its upper-left corner at (x, y) = (1, 1).", "Place piece B with its upper-left corner at (x, y) = (1, 3).", "Rotate piece C by about 60 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece A by about 90 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 3, "angle": 0, "orig_width": 2, "orig_height": 1, "w": 2.0, "h": 1.0, "label": "2x1", "piece": [2, 3, 1, 3], "color": [0.8916148044641335, 0.3781423287870871, 0.36352922300777135], "cell_center": [4.5, 1.5]}, {"index": 1, "angle": 0, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.8415274483290549, 0.46286374035661404, 0.8797592115225641], "cell_center": [4.5, 4.5]}, {"index": 2, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [2, 3, 0, 1], "color": [0.3223902645479415, 0.8258414522110806, 0.3821764742442382], "cell_center": [1.5, 1.5]}, {"index": 0, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "2x1", "piece": [0, 2, 0, 1], "color": [0.4978586459293345, 0.5976559765313394, 0.14086452934263438], "cell_center": [1.5, 4.5]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n\nPiece B:\n11\n11\n\nPiece C:\n1\n\nPiece D:\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"yes",
"no"
] |
|
4x4_inst30_var3_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).
Step 2: Place piece A with its upper-left corner at (x, y) = (0, 4).
Step 3: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).
Step 4: Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (1, 1).
Step 5: Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).
Step 6: Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (3, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_step/4x4_inst30perturbed_step_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_step/4x4_inst30perturbed_step_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_step/4x4_inst30perturbed_step_assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_step/4x4_inst30perturbed_step_assembly_step_3.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_step/4x4_inst30perturbed_step_assembly_step_4.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_step/4x4_inst30perturbed_step_assembly_step_5.png", "output_dir/Tangram_puzzle_v2/4x4_inst30/perturbed_step/4x4_inst30perturbed_step_assembly_step_6.png"], "instructions": ["", "Rotate piece E by about 60 degrees clockwise, and place piece E with its upper-left corner at (x, y) = (0, 1).", "Place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 3).", "Rotate piece F by about 90 degrees clockwise, and place piece F with its upper-left corner at (x, y) = (1, 1).", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece D by about 90 degrees clockwise, and place piece D with its upper-left corner at (x, y) = (3, 3)."], "results": ["", "", "", "", "", "", "Overlap"], "valid": false, "config": [{"index": 4, "angle": 60, "orig_width": 1, "orig_height": 1, "w": 1.3660254037844388, "h": 1.3660254037844388, "label": "1x1", "piece": [3, 4, 0, 1], "color": [0.3656083002105275, 0.47581511365521845, 0.6183891885528554], "cell_center": [2.0, 6.147114317029974]}, {"index": 0, "angle": 0, "orig_width": 3, "orig_height": 1, "w": 3.0, "h": 1.0, "label": "3x1", "piece": [0, 1, 0, 3], "color": [0.9035591471762607, 0.11970560100617034, 0.4855676628213387], "cell_center": [6.0, 6.147114317029974]}, {"index": 2, "angle": 90, "orig_width": 1, "orig_height": 2, "w": 2.0, "h": 1.0000000000000002, "label": "1x2", "piece": [1, 3, 0, 1], "color": [0.868250353967598, 0.8718178531170512, 0.8044667206493435], "cell_center": [10.0, 6.147114317029974]}, {"index": 5, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "3x1", "piece": [3, 4, 1, 4], "color": [0.05693842955173811, 0.9065171787135644, 0.309832012336156], "cell_center": [2.0, 2.049038105676658]}, {"index": 1, "angle": 30, "orig_width": 1, "orig_height": 3, "w": 2.3660254037844384, "h": 3.098076211353316, "label": "1x3", "piece": [0, 3, 3, 4], "color": [0.16483746954885847, 0.051758929606153026, 0.12492630379800751], "cell_center": [6.0, 2.049038105676658]}, {"index": 3, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [1, 3, 1, 3], "color": [0.8519142300537066, 0.5805075864102989, 0.9259830837764971], "cell_center": [10.0, 2.049038105676658]}], "variant": "perturbed_step"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst6_var4_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst6/irregular_assembly/3x3_inst6invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/irregular_assembly/3x3_inst6invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/irregular_assembly/3x3_inst6invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Place piece A with its upper-left corner at (x,y) = (0, 2).", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (1, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [0, 2, 0, 2], "angle": 60, "flip": "none", "color": [0.10309243167421278, 0.24076261322195902, 0.2100689922963226], "is_merged": false}, {"index": 1, "shape": [[2, 3, 0, 3], [0, 2, 2, 3]], "angle": 60, "flip": "none", "color": [0.6512655327908536, 0.8401929301826332, 0.8460989766654483], "is_merged": true}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n111\n010\n010\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"no",
"yes"
] |
|
4x4_inst11_var0_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/4x4_inst11/assembly/4x4_inst11assembly_step_0.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/assembly/4x4_inst11assembly_step_1.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/assembly/4x4_inst11assembly_step_2.png", "output_dir/Tangram_puzzle_v2/4x4_inst11/assembly/4x4_inst11assembly_step_3.png"], "instructions": ["", "Rotate piece B by about 30 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (3, 4).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 4).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 2)."], "valid": true, "config": [{"index": 1, "angle": 30, "orig_width": 1, "orig_height": 2, "w": 1.8660254037844386, "h": 2.232050807568877, "label": "1x2", "piece": [0, 2, 3, 4], "color": [0.2617125427976732, 0.3180100977057472, 0.9938777587600973], "cell_center": [6.897114317029974, 7.5]}, {"index": 0, "angle": 30, "orig_width": 3, "orig_height": 2, "w": 3.598076211353316, "h": 3.232050807568877, "label": "3x2", "piece": [0, 2, 0, 3], "color": [0.590194494564307, 0.8146086514121477, 0.17186877412793822], "cell_center": [2.299038105676658, 7.5]}, {"index": 2, "angle": 90, "orig_width": 4, "orig_height": 2, "w": 2.0000000000000004, "h": 4.0, "label": "2x4", "piece": [2, 4, 0, 4], "color": [0.21016152453789094, 0.9415963033779045, 0.8255857971856693], "cell_center": [2.299038105676658, 2.5]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 4x4 square without overlaps or gaps?\n\nTarget board: a 4x4 grid\n\nAvailable pieces:\n\nPiece A:\n111\n111\n\nPiece B:\n1\n1\n\nPiece C:\n11\n11\n11\n11\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 4x4 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q_only | [
"no",
"yes"
] |
|
3x3_inst39_var3_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 60 degrees clockwise. Flip piece A horizontally. Place piece A with its upper-left corner at (x,y) = (0, 3).
Step 2: Place piece B with its upper-left corner at (x,y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst39/irregular_assembly/3x3_inst39invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst39/irregular_assembly/3x3_inst39invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst39/irregular_assembly/3x3_inst39invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Flip piece A horizontally. Place piece A with its upper-left corner at (x,y) = (0, 3).", "Place piece B with its upper-left corner at (x,y) = (2, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 3, 2, 3], "angle": 60, "flip": "horizontal", "color": [0.4889016189467239, 0.8044606918775942, 0.790149600882282], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 0, 2]], "angle": 0, "flip": "none", "color": [0.8739555335428091, 0.4336653277817235, 0.5821465473107338], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n0011\n0011\n1110\n\nPiece B:\n110\n110\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst39_var3_q_only | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Keep in mind that you can rotate or flip the pieces. Can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst39/irregular_assembly/3x3_inst39invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst39/irregular_assembly/3x3_inst39invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst39/irregular_assembly/3x3_inst39invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 60 degrees clockwise. Flip piece A horizontally. Place piece A with its upper-left corner at (x,y) = (0, 3).", "Place piece B with its upper-left corner at (x,y) = (2, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 3, 2, 3], "angle": 60, "flip": "horizontal", "color": [0.4889016189467239, 0.8044606918775942, 0.790149600882282], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 0, 2]], "angle": 0, "flip": "none", "color": [0.8739555335428091, 0.4336653277817235, 0.5821465473107338], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n0011\n0011\n1110\n\nPiece B:\n110\n110\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q_only | [
"no",
"yes"
] |
|
3x3_inst2_var3_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).
Step 2: Place piece A with its upper-left corner at (x, y) = (0, 3).
Step 3: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst2/assembly/3x3_inst2assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/assembly/3x3_inst2assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/assembly/3x3_inst2assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst2/assembly/3x3_inst2assembly_step_3.png"], "instructions": ["", "Rotate piece B by about 90 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (1, 3).", "Place piece A with its upper-left corner at (x, y) = (0, 3).", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1)."], "valid": true, "config": [{"index": 1, "angle": 90, "orig_width": 2, "orig_height": 2, "w": 2.0, "h": 2.0, "label": "2x2", "piece": [0, 2, 1, 3], "color": [0.12655138063137172, 0.33097078814054737, 0.7001299158222172], "cell_center": [4.5, 6.0]}, {"index": 0, "angle": 0, "orig_width": 1, "orig_height": 2, "w": 1.0, "h": 2.0, "label": "1x2", "piece": [0, 2, 0, 1], "color": [0.12351699744789202, 0.5664729497490351, 0.624512595749913], "cell_center": [1.5, 6.0]}, {"index": 2, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [2, 3, 0, 3], "color": [0.20573163102149872, 0.7110069434915763, 0.3696499764946295], "cell_center": [1.5, 2.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n1\n1\n\nPiece B:\n11\n11\n\nPiece C:\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"no",
"yes"
] |
|
3x3_inst6_var1_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).
Step 2: Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).
Step 3: Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | A | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst6/assembly/3x3_inst6assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/assembly/3x3_inst6assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/assembly/3x3_inst6assembly_step_2.png", "output_dir/Tangram_puzzle_v2/3x3_inst6/assembly/3x3_inst6assembly_step_3.png"], "instructions": ["", "Rotate piece C by about 90 degrees clockwise, and place piece C with its upper-left corner at (x, y) = (0, 1).", "Rotate piece B by about 60 degrees clockwise, and place piece B with its upper-left corner at (x, y) = (2, 3).", "Rotate piece A by about 30 degrees clockwise, and place piece A with its upper-left corner at (x, y) = (0, 3)."], "valid": true, "config": [{"index": 2, "angle": 90, "orig_width": 3, "orig_height": 1, "w": 1.0000000000000002, "h": 3.0, "label": "1x3", "piece": [2, 3, 0, 3], "color": [0.1586208137251468, 0.12393853736495797, 0.8716693278560734], "cell_center": [1.8660254037844386, 2.0]}, {"index": 1, "angle": 60, "orig_width": 1, "orig_height": 2, "w": 2.232050807568877, "h": 1.8660254037844388, "label": "1x2", "piece": [0, 2, 2, 3], "color": [0.6512655327908536, 0.8401929301826332, 0.8460989766654483], "cell_center": [5.598076211353316, 6.0]}, {"index": 0, "angle": 30, "orig_width": 2, "orig_height": 2, "w": 2.732050807568877, "h": 2.732050807568877, "label": "2x2", "piece": [0, 2, 0, 2], "color": [0.10309243167421278, 0.24076261322195902, 0.2100689922963226], "cell_center": [1.8660254037844386, 6.0]}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n11\n11\n\nPiece B:\n1\n1\n\nPiece C:\n1\n1\n1\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "assembly"} | q+steps | [
"yes",
"no"
] |
|
3x3_inst41_var1_q+steps | Check out an Tangram puzzle below. The left panel is an empty Tangram puzzle, while the right panel shows available pieces to complete the puzzle.
<image_0>Below are the steps to complete the Tangram puzzle:
Step 1: Rotate piece A by about 30 degrees clockwise. Flip piece A vertically. Place piece A with its upper-left corner at (x,y) = (0, 3).
Step 2: Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (2, 3).
Based on the above steps, can the Tangram puzzle be completed with the available pieces, yes or no? | B | {"images": ["output_dir/Tangram_puzzle_v2/3x3_inst41/irregular_assembly/3x3_inst41invalid_irregular_assembly_step_0.png", "output_dir/Tangram_puzzle_v2/3x3_inst41/irregular_assembly/3x3_inst41invalid_irregular_assembly_step_1.png", "output_dir/Tangram_puzzle_v2/3x3_inst41/irregular_assembly/3x3_inst41invalid_irregular_assembly_step_2.png"], "instructions": ["", "Rotate piece A by about 30 degrees clockwise. Flip piece A vertically. Place piece A with its upper-left corner at (x,y) = (0, 3).", "Rotate piece B by about 60 degrees clockwise. Place piece B with its upper-left corner at (x,y) = (2, 3)."], "results": ["", "", "Invalid irregular"], "valid": false, "config": [{"index": 0, "shape": [1, 3, 2, 3], "angle": 30, "flip": "vertical", "color": [0.5615163959144739, 0.8754968350575798, 0.9340271731662201], "is_merged": true}, {"index": 1, "shape": [[0, 1, 0, 3], [1, 3, 0, 2]], "angle": 60, "flip": "none", "color": [0.6566695133190994, 0.6035193980322114, 0.9422149247873488], "is_merged": false}], "text_question": "Tangram-Style Text Puzzle\n\nCan you use all of the following pieces\u2014rotating or flipping them as needed\u2014to exactly fill a 3x3 square without overlaps or gaps?\n\nTarget board: a 3x3 grid\n\nAvailable pieces:\n\nPiece A:\n0111\n1100\n1100\n\nPiece B:\n110\n110\n111\n\nFor each piece, the grid cells it occupies are marked with 1s and the rest with 0s.\n\nInstructions:\n\u2022 You must place every cell of each piece somewhere in the grid.\n\u2022 Pieces may be rotated in 90\u00b0 increments or flipped horizontally/vertically.\n\nQuestion: Is it possible to fill the 3x3 board exactly with these pieces? (Yes or No)", "variant": "irregular_invalid_assembly"} | q+steps | [
"yes",
"no"
] |
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