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You put a penny inside a glass with the opening facing up, then pick it up. You set the glass on a table with the opening facing down, then pick up the glass and put it on the floor opening facing up. Where is the penny? | The penny is on the table. | The penny fell out of the glass when placed on the table, because the glass was placed opening downward. This would leave it there, on the table. |
A piece of paper is folded in half, then folded in half again the other direction, leaving it a fourth of the original size in the original dimensions. A pen with black ink is used to draw a letter on the paper, then the paper is placed on a surface with the letter facing upward. If the paper were to unfold once, which direction would the letter face: up or down? | The letter would face down. | When the fold is undone, taking the paper from quarter to half size, the side of the paper containing a letter would turn and face down at the surface. |
You are a piano mover. You are moving a piano up a flight of stairs. The flight of stairs has 8 steps. The keys on the piano are the distance of 2 steps above the ground when the piano is placed on the ground. After being moved to the second floor, how many steps will the distance of the keys be from the ground of the second floor it is now resting atop? | The keys will be the distance of 2 steps above the floor. | When the piano is moved, the relative distance is not affected. Therefore, the keys will sill be 2 steps above the new floor the piano is placed atop. |
I place two dice atop a table. One of the dice is on the right side of the table, and the other is on the left side of the table. Which will slide when the table is tilted to the right enough to cause sliding? | Both dice will slide. | Regardless of their position on the table, both dice are affected by the new slant of the surface, so both dice will slide. |
If a person is lying with their back facing the ground, which way is their stomach facing? | Their stomach faces upwards, towards the sky. | The stomach is opposite the back, so their stomach would be facing upwards, towards the sky. |
Smoke always travels upward, regardless of the direction of its source. This is because it travels opposite gravity. A fire which is angled 90 degrees to the right is releasing smoke. If you were angled in the same direction as the fire, relative to your perspective, which way would the smoke appear to travel? | The smoke would appear to travel 90 degrees to the left from your perspective. | You are facing toward the right 90 degrees. The smoke would travel up, so from your perspective, you would see it travel to the left 90 degrees. |
If you place a pebble inside a shot glass, and place the shot glass with the bottom facing upward on a table, then pick up the shot glass, where is the pebble? | The pebble is on the table. | The pebble fell to the table when you placed the shot glass down, as it was upside-down, and remained there when you picked it up. |
Take an empty bowl and set it on a coffee table. Place two pennies inside. Pick up the bowl vertically and hover it above the table, rotate it a full circle slowly so it is facing the same direction at the end of the rotation, then put the bowl back down on the table the same spot. Are the pennies above, inside, or below the bowl at the end? | The pennies are below the bowl. | When you rotated the bowl, the pennies fell out. Upon placing it back down on the table, the pennies are now on the table below the bowl. |
If a woman constantly holding a purse walks into a house, walks all the way up the stairs, goes inside a room, then inside the closet, where is her purse? | Her purse is in the closet. | She takes the purse with her, as she's holding it, so it's inside the closet. |
If a tower is made with red blocks atop yellow blocks atop blue blocks above green blocks, what color of blocks is below the yellow blocks? | The blocks below the yellow blocks are the blue blocks. | The arrangement of the tower is red on top, then yellow, then blue, then green on the bottom. Directly below the yellow blocks are the blue blocks. |
An elevator on the bottom of a tall building travels upward until there are an equal amount of floors above and below the elevator, then travels this distance upward again. How many floors are above the elevator now? | No floors are above the elevator now. | The elevator travels to the middle of the height of the building, then travels this distance again. Since it starts by traveling half the distance, then travels half again, it ends by having traveled the full distance. This leaves no floors above the elevator at the end. |
If you use your head to look up, then turn around without moving your head, which way are you looking? | You would remain looking up. | When you turn your body around, your head would turn; however, the direction of your gaze is determined by the orientation of your head, not your body. This leaves your head facing upward, and you remain looking up. |
A tower is built from bottom to top with bricks colored red, green, purple, yellow, then blue. If the tower is turned upside down, which brick is now directly above the yellow? | The purple brick will be above the yellow brick. | The tower is turned upside down, which inverts the order of the bricks. The purple brick was below the yellow brick in the previous configuration, so the purple brick is now above the yellow brick. |
If a train is traveling north, and its path changes to the right 90 degrees, which way is it traveling? | The train is traveling east. | The train rotated 90 degrees, changing its direction of travel from north to east. |
Two men face one another. One man is facing east. Which way is the other man facing? | The other man is facing west. | The other man is facing the opposite direction of the original man, who is facing east. Therefore, the other man is facing west. |
Two men face eachother. One of the men is facing south. Which way is the other man facing? | The other is facing north. | The other man is facing the opposite direction of the original man, who is facing south; therefore, the other man is facing north. |
If you have one penny directly beneath a cloth and one resting atop it, and the entirety is simply resting on a table, then you take the cloth and lift it up, which penny is closer to the cloth? | The penny initially on top is the closest. | The penny initially on top stays in contact with the cloth as you raise it, maintaining its proximity. The other penny remains far away on the table. This leaves the penny on top the as the closest. |
You see a stack of books on a table. On the bottom is a blue book. Atop the blue book is a red book. Atop the red book, a purple one. On the very top is a yellow book with the purple book right beneath it. Which book is below the purple book? | The red book is below the purple book. | We know that there are four books in total, placed one on top of another from bottom to top. This stack contains blue, then red, then purple, then yellow. In this order, the red book is below the purple book. |
A yellow castle is in the center of a plot of land, viewed from the top. To the left of the yellow castle is a red castle. Above the red castle, from the top view, there is a blue castle. To the right of the blue castle is a green one. If you are standing in the yellow castle and looking at the red castle, which way must you turn to view the green one? | You must turn right to view the green castle. | From the top view, there is a yellow castle in the center. You are in the yellow castle. You are looking at the red castle, and the blue is to your right 45 degrees. The green one is to your right 90 degrees. Therefore, you must turn right to view the green castle. |
If a laptop facing north is opened, which way is the logo on the back of the laptop facing? | The logo would face south. | When the laptop is closed, the screen is facing downward and the logo is opposite it, facing upward. When you open the laptop, the screen faces the same way as the laptop: north. The logo faces the opposite way: south. |
A tower is made of blocks. On the bottom is a red block. On the top is a yellow block. In the middle is a blue block. The tower is turned upside down, as to invert the order. Which block experiences the least change in position? | The blue block experiences the least change in position. | The block with the least change in position is the block which remains is in the middle, since inverting the order does not change it from being in the middle. Therefore, the blue block experiences the least change in position. |
When a bird hears a rock land, it travels in the opposite direction the rock landed. If you're standing next to a bird and throw a rock north, which way will the bird travel once the rock lands? | The bird will travel north. | The bird will travel in the opposite direction from where you threw the rock. When you throw it, it travels north, then lands and makes a noise. Since it's north from you and the bird, the bird will travel south. |
I place a spiral-bound book on a table, and open it a quarter way through to a page 25 percent through the book. Which stack of pages is higher, the one to the left of the spiral, or the one to the right? | The stack of pages to the right will be higher. | When you open the book, a quarter of the pages will rotate around the spine to the left. Three quarters of the pages remain on the right, so the stack of pages on the right is higher. |
A tower of bricks is made. It is five bricks tall. The first brick on the bottom is red, then blue, then green, then purple, then on the top is a yellow brick. If I turn the tower upsidedown, which brick is below the purple brick? | The yellow brick is below the purple brick. | When you turn the tower upsidedown, the order of the bricks reverses. The yellow brick was above the purple brick, so now the yellow brick is below it. |
I place a penny on a table, then a quarter on top of the penny. I place a dime on top of the quarter, then place a nickel on top of the dime. If I pick up the stack and turn it upsidedown, then put it back on the table, which coin is on top of the quarter? | The penny is on top of the quarter. | The coin order inverted when it was turned upsidedown, so the penny is on top of the quarter. |
If I'm facing north, then turn a quarter revolution to the left, which way am I facing now? | You're facing west. | You turned to the left, and west is to the left of north. You are facing west now. |
If I'm facing east, then turn around 180 degrees, which way am I facing now? | You're facing west. | You turned around, and the direction opposite east is west. You're facing west now. |
If I'm facing west, and turn to the right 90 degrees, which way am I facing? | You're facing north. | You turned to the right, and the direction to the right of west is north. You're facing north. |
A train is on a track heading south. If the track makes a 90 degree turn to the left, which way will the train go? | The train will go east. | The train turned 90 degrees to the left. It was facing south, and from that perspective the direction to the left is east. The train is going east now. |
A tower is made with five blocks. Red on the bottom, above that green, above that blue, above that yellow, above that magenta on the top. The tower is turned over to the right, resting on its side. Which block is to the left of the yellow? | The block to the left of the yellow is blue. | You turned the tower over on its right side. Blue was under yellow, so now blue is the block to the left of yellow. |
Which direction is to the right if I face east? | South. | The direction to the right of east is south. |
List the directions I'll see, in order, if I face north then turn to the right until I face north again. | North, east, south, west, north. | If you start facing north and continuously turn to your right (which is equivalent to turning clockwise) until you face north again, you will go through all four cardinal directions. First north, then east, then south, then west, then back around to north. |
Someone starts facing south. If they turn to the left 360 degrees, name all the directions they see, in order of when they see them. | South, east, north, west, then south again at the end. | If someone starts facing south, then turns to the left, they turn counter-clockwise. Turning counterclockwise starting at south for 360 degrees is a full circle with the following directions: South, then east, then north, then west, then finally south again after the completion of the circle. |
Peter has 3 candles that are all the same. He lights them all at the same time. He blows them out at different points in time. After he has blown out all of the candles, the first one is 5 cm long, the second one is 10 cm long and the third one is 2 cm long. Which one of the three candles did he blow out first? | The second candle was blown out first. | If we assume the candles burn at the same rate, the candle with the most wax left remaining was blown out first. 10 cm is the most wax in any candle, therefore, the second candle was blown out first. |
What directions are on a compass? | North, east, south, and west. | The directions on a compass are north, east, south, and west. |
Jeremy faces to the south, and turns 180 degrees to his left. What directions does he see as he begins, turns, and ends? | South, east, then finally north. | He starts looking south, then turns to the left 180 degrees. During the turn he will be facing east, then finally end facing north. |
OpenSpatialLogic
Dataset Card for OpenSpatialLogic
Dataset Summary
OpenSpatialLogic is a handcrafted dataset of 50 riddles which test understanding of spatial relationships in reality.
These include questions about compass directions, ordering of bricks within towers after transformations, and permeability of objects in certain configurations.
The only way for a model to get better at something is to train on data about it. Large Language Models are bad at understanding spatial reality because their knowledge about the universe is based on relationships between words in a text corpus, not understanding of the universe directly. This data has been crafted so models can be trained to understand these physical relationships better.
Dataset Structure
OpenSpatialLogic contains a question under the "Context" field, and then a "briefResponse" and "detailedResponse" field which both answer the question in varying levels of brevity.
Example:
Context: A tower is built from bottom to top with bricks colored red, green, purple, yellow, then blue. If the tower is turned upside down, which brick is now directly above the yellow?
briefResponse: The purple brick will be above the yellow brick.
detailedResponse: The tower is turned upside down, which inverts the order of the bricks. The purple brick was below the yellow brick in the previous configuration, so the purple brick is now above the yellow brick.
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