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imagewidth (px) 170
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|---|---|---|---|---|---|---|---|---|---|---|
State Prediction
| 6 |
Given the Player name, find in which Nine-grid to place the piece.
|
Medium
|
Hard
|
Now I'll give you a picture, which shows a screenshot of Ultra TicTacToe. The introduction of Ultra TicTacToe is as follows:
1. Board and coordinate representation: In this game, the board is divided into 9 3*3 squares(called Nine-grids). At the same time, we use $(i, j, row, col)$ to represent the coordinates of a cell: $(i, j)$ represents the coordinates of the Nine-grid; $(row, col)$ represents the coordinate of the cell within the Nine-grid; $i, j, row, col$ all range from 1 to 3. Two players take turns placing pieces on the board to mark the cells on the board, with the first player using "X" and the second player using "O" (this is the same as traditional TicTacToe).
2. Rules for placing chess pieces: After the game starts, the first player places a chess piece in any cell in the Nine-grid in the middle (i.e., the Nine-grid (2, 2)). After that, the coordinates of each chess piece placed in the Nine-grid are the same as the coordinates of the Nine-grid in which the opponent's last chess piece was placed; for example, if the first player places a chess piece at the coordinates (2, 2, 3, 1) in the first step, then the second player needs to choose a chess piece in the Nine-grid (3, 1) in the second step.
3. Scoring rules: For each player, each "Straight" (i.e., three identical chess pieces connected in a line, such as in the same row, the same column, or a diagonal line) in each Nine-grid is counted as 1 point. More than 1 point can be counted in each Nine-grid.
Now I will give you a question about the game. Please extract information from the picture I give you, think carefully, reason, and answer: If you are Second Player, from the image, we can see now it's your turn to place a piece. According to the rules of the game, in which Nine-grid should you place the next piece? Options: 1. Nine-grid (1, 1) 2. Nine-grid (1, 2) 3. Nine-grid (1, 3) 4. Nine-grid (2, 1) 5. Nine-grid (2, 2) 6. Nine-grid (2, 3) 7. Nine-grid (3, 1) 8. Nine-grid (3, 2) 9. Nine-grid (3, 3)
|
6
|
[
"Nine-grid (1, 1)",
"Nine-grid (1, 2)",
"Nine-grid (1, 3)",
"Nine-grid (2, 1)",
"Nine-grid (2, 2)",
"Nine-grid (2, 3)",
"Nine-grid (3, 1)",
"Nine-grid (3, 2)",
"Nine-grid (3, 3)"
] |
ultra_tictactoe
|
Strategy Planning
|
|
State Prediction
| 4 |
Predict Pacman's movement result
|
Easy
|
Hard
|
# Game Overview
Pac-Man is a maze arcade game where the player controls Pac-Man to eat as many beans as possible while avoiding ghosts. If a ghost catches Pac-Man, the game ends.
# Basic Elements
- **Pac-Man**: The yellow circular character that the player controls
- **Beans**: Yellow dots that Pac-Man can eat to score points
- **Walls**: Blue barriers that restrict movement
- **Ghosts**: Two ghosts (Pinky and Blinky) that chase Pac-Man
# Game Rules
- Pac-Man must eat beans while avoiding ghosts
- Each bean eaten adds 1 point to the score
- The game ends if a ghost catches Pac-Man
- Movement is restricted by walls
# Movement and Direction
- Pac-Man's mouth opening indicates its current direction
- The direction can be UP, DOWN, LEFT, or RIGHT
- Neither Pac-Man nor ghosts can move through walls
# **Ghost Behavior**
- **Pinky** (Pink Ghost): Targets up to 4 spaces ahead of Pac-Man's current position and direction (stops at walls)
- **Blinky** (Red Ghost): Directly targets Pac-Man's current position
- Both ghosts follow a movement priority system based on the direction they are trying to move:
- When moving in more than one direction is optimal, the priority order for both ghosts is **UP > DOWN > LEFT > RIGHT**.
- This means if a ghost has multiple possible directions to move in, it will first attempt to move **UP** if possible, then **DOWN**, followed by **LEFT**, and finally **RIGHT** if all other directions are blocked.
# Board Layout
- The board is surrounded by walls on all four sides
- Position (0,0) is located at the top-left corner wall
- Movement grid uses (row, column) coordinates
# Scoring
The score equals the total number of beans eaten by Pac-Man
**Question:** Assuming Pac-Man and both ghosts move one step at a time, what would happen if Pac-Man moves RIGHT 3 times, then UP 3 times?
**Options:**
A. It will eat 6 beans, and the score will become 26
B. It will eat 6 beans, and the score will become 28
C. It will eat 2 beans, and the score will become 24
D. It will eat 9 beans, and the score will become 31
E. It will eat 7 beans, and the score will become 29
F. It will eat 5 beans, and the score will become 27
G. It will be caught by Pinky (the pink ghost)
H. It will be caught by Blinky (the red ghost)
|
F
|
[
"A. It will eat 6 beans, and the score will become 26",
"B. It will eat 6 beans, and the score will become 28",
"C. It will eat 2 beans, and the score will become 24",
"D. It will eat 9 beans, and the score will become 31",
"E. It will eat 7 beans, and the score will become 29",
"F. It will eat 5 beans, and the score will become 27",
"G. It will be caught by Pinky (the pink ghost)",
"H. It will be caught by Blinky (the red ghost)"
] |
pacman
|
Strategy Planning
|
|
State Prediction
| 4 |
Predict card move result
|
Hard
|
Medium
|
Spider Solitaire
# OBJECTIVE
Spider is played with eight decks of 13 spade cards each, totaling 104 unique cards. The goal is to arrange all cards in a King-to-Ace sequence in the same suit and move them to the foundation piles. Once all sequences are moved to the foundations, the game is won.
# SETUP
The game features waste piles, a stock pile, and foundation piles. Waste piles are where the action happens, and the stock pile provides new cards when necessary.
**Waste Pile Numbering**: Waste piles are numbered from left to right starting with `0`. The cards within each waste pile are also numbered starting from the bottom card.
# GAME BOARD COMPONENTS
## **Stock Pile**
The **Stock Pile** holds all remaining cards and is used to deal new cards into the waste piles.
Stock Pile is in the top left corner of the board.
- **Staggered Card Stacking**: Cards are stacked in layers, and the number of layers indicates how many more times you can deal cards to the waste piles. Each deal moves one card face-up to each waste pile.
## **Waste Piles**
The **Waste Piles** are where cards are played and organized.
Waste Piles are on the bottom of the chessboard
- **Face-Up vs. Face-Down Cards**: Cards are stacked with face-up cards visible and face-down cards hidden. Only face-up cards can be played. When a face-down card becomes the top card of a pile, it is turned face-up and can be played.
- **Staggered Cards**: Cards in each waste pile are arranged so that face-up cards are on top, and face-down cards are beneath. As you move cards, new face-down cards are revealed.
- **Card Numbering and Screen Position**:
- **Waste Pile Numbering**: Piles are numbered from left to right starting with `0` for the leftmost pile.
- The card at the bottom of each waste pile (usually face-down) is numbered **0** and is the **topmost visible card** in the pile.
- As you move upward in the pile, the next cards are numbered **1**, **2**, **3**, and so on.
- Visually, the bottom card (number **0**) is the one closest to the top of the screen, and the cards above it are stacked above in the pile, going downwards.
## **Foundation Pile**
Foundation pile stores all the arranged suit. When a suit is arranged in sequence, it may be removed to a foundation pile. If all suits are moved to the foundations, the game is won.
Foundation Pile is in the top right corner of the board.
# MOVING CARDS
- **Movement Conditions**: Cards can be moved to another pile as long as they form a **descending sequence of the same suit**, i.e., a King-to-Ace sequence. When moving cards, the new sequence must be a **same-suit sequence** and follow the **descending order** from K, Q, J, 10, 9, ..., 2, A.
- **Same-Suit Sequence Requirement**: The card being moved must be placed on a top card that is of the **same suit** and has a **higher rank** (e.g., a Q can be placed on a K). The top card of the target pile must be larger in rank than the card being moved, and both must be of the same suit.
- **Moving a Sequence**: A complete **descending sequence** of cards (such as K, Q, J, 10, etc.) can be moved from one pile to another, as long as the sequence is in **descending order** and all the cards in the sequence are of the **same suit**.
- **Face-Down Cards**: If the sequence you are moving includes face-down cards, they will be flipped face-up once they are moved. After flipping, the newly face-up cards can continue to be moved or interacted with.
- **Example**: If you have a sequence of K-Q-J-10-9-8-7 in the same suit, you can move a card 6 that has the same suit to the top of this pile, resulting in a new sequence K-Q-J-10-9-8-7-6.
- **Empty Pile Rule**: An empty waste pile can accept any card. After placing the card, you can continue adding a descending same-suit sequence to that pile.
- **Reveal Cards**: If a move leaves a face-down card on top, it will be turned face-up.
# DEALING
Click the stock to deal a new row of face-up cards to the waste piles. You may not deal if there is an empty waste pile.
# STRATEGY
- Turn face-down cards face-up.
- Form runs of the same suit in descending order.
- Use empty waste piles strategically.
# VARIANTS
In **circular spider solitaire**, a King can be placed on an Ace, allowing for extended sequences.
# **NOTE: Important Numbering Reminder**
- **Waste Pile Numbering**: Waste piles are numbered from **left to right** starting with `0` for the leftmost pile.
- **Card Numbering within Waste Piles**: The **bottom-most card** of each pile (usually face-down) is numbered **0**, and the cards above it are numbered **1**, **2**, **3**, etc., moving upwards in the pile.
- **Please Pay Attention** to both the waste pile and card numbering methods, as they will help you navigate and make strategic decisions effectively.
**Question:** What will happen if I want to move the number 5 card of pile 3 to pile 0?
**Options:**
A. The move will be successful, and the cards will be in descending order, following the rules of movement.
B. The move cannot be made because this card is face-down and its value is unknown.
C. The move cannot be made because there is a card above it, and that card does not form a descending order with the selected card.
D. The move cannot be made because the top card of the target pile does not have a rank equal to this card's rank plus one.
E. The move cannot be made because the pile has too few cards, and this card does not exist.
|
C
|
[
"A. The move will be successful, and the cards will be in descending order, following the rules of movement.",
"B. The move cannot be made because this card is face-down and its value is unknown.",
"C. The move cannot be made because there is a card above it, and that card does not form a descending order with the selected card.",
"D. The move cannot be made because the top card of the target pile does not have a rank equal to this card's rank plus one.",
"E. The move cannot be made because the pile has too few cards, and this card does not exist."
] |
spider_solitaire
|
Pattern Recognition & Matching
|
|
State Prediction
| 1 |
Select a coordinate and determine whether a ball can be placed at this coordinate. If so, what would happen after the place of the ball.
|
Easy
|
Medium
|
Pyramid Chess Rules:
0.Game Board:
The game board is square and comes in various sizes: 3x3, 4x4, or 5x5. On an nxn board, there are n levels (0 to n-1). At each level k, the x and y coordinates range from 0 to n-1-k, resulting in (n-k)**2 slots per level. The slots in the lower levels act as the base for the slots in the upper levels. Slots at level 0 have no base, while slots at level j (j!=0) with coordinates (m,n) are supported by four base slots (m,n),(m+1,n),(m,n+1),(m+1,n+1) from level j-1.
1.Players and Initial Setup:
The game is played between two players, designated as PLAYER_0 and PLAYER_1, each using balls of a distinct color from their color pool, blue balls for PLAYER_0 and red balls for PLAYER_1. Players take turns placing their balls on a square game board. The number of balls available to each player depends on the size of the board: on a 3x3 board, each player has 7 balls; on a 4x4 board, each has 15 balls; and on a 5x5 board, PLAYER_0 (the first player to place a ball) has 28 balls, while PLAYER_1 has 27 balls.
2.Placing Balls and Creating New Slots:
At the start of the game, the lowest level of the board (Level 0) is completely open and balls can be placed in any available slot on this level(since there is no base for slots in level 0, slots in level 0 have full base). After a ball is placed in a slot, that slot is no longer available for placing another ball. A ball can only be placed on the upper level if it is supported by a fully completed 2x2 block of balls on the level directly beneath, which means all the base of the slot is full(there is a ball in each of these slots).
3.Take-back mechnism:
If a player places a ball that completes a 2x2 block of the same color (all four balls belonging to that player), they may return up to two balls from the block to their color pool. A ball can only be removed if it does not have another ball directly above it, as removing a "base" ball would collapse the pyramid. Returning a ball reopens the slot it occupied, allowing it to be used for future placements, but the rule requiring a full 2x2 block as a base for placing balls on upper levels still applies.
4.Winning the Game:
The game ends when one player successfully places the last ball on top of the pyramid. The player who place the ball on the top of the pyramid wins.
Question: Can a ball be placed at coordinate [2, 2] on Level 0? If a blue ball is placed there, what would be the outcome?
Options:
1. Can place and no balls taken
2. Can place and then balls can be taken
3. Cannot place, position already occupied
4. Cannot place, ball not ready below
|
3
|
[
"Can place and no balls taken",
"Can place and then balls can be taken",
"Cannot place, position already occupied",
"Cannot place, ball not ready below"
] |
pyramidchess
|
3D Spatial Perception & Reasoning
|
|
Target Perception
| 2 |
Ask the position of goal within the maze.
|
Easy
|
Easy
|
**Rules:**
1. This is a maze mini-game.The player needs to navigate around obstacles to reach the destination and achieve victory.
2. The red circle represents the player, the green block is the goal and the blue blocks are obstacles.
3. The player can only move within the white blocks.
**Question:** Which of the following are the coordinates of the goal?"
**Optoins:**
A. (0, 7)
B. (2, 7)
C. (1, 8)
D. (1, 7)
E. (1, 6)
|
D
|
[
"A. (0, 7)",
"B. (2, 7)",
"C. (1, 8)",
"D. (1, 7)",
"E. (1, 6)"
] |
maze
|
Strategy Planning
|
|
State Prediction
| 0 |
path_finding
|
Medium
|
Hard
|
Rules:
1. Player can only walk on top of cubes
2. Player can climb ladders if they can reach the cube under the ladder
3. From a ladder, player can reach the top of the last cube with the ladder
4. Blue cube is start position, red cube is goal position
5. Numbered cubes are branch points where player must choose a path
Which combination of path choices leads to the goal?
Options:
1: 1-right-forward, 2-right-forward, 3-left-forward, 4-up
2: 1-right-forward, 2-left-forward, 3-left-forward, 4-left-forward
3: 1-right-forward, 2-right-forward, 3-left-forward, 4-left-forward
4: 1-right-forward, 2-right-forward, 3-up, 4-left-forward
5: 1-right-forward, 2-left-forward, 3-up, 4-left-forward
6: 1-up, 2-left-forward, 3-left-forward, 4-left-forward
7: 1-up, 2-right-forward, 3-up, 4-left-forward
8: 1-up, 2-right-forward, 3-left-forward, 4-left-forward
|
1
|
[
"1-right-forward, 2-right-forward, 3-left-forward, 4-up",
"1-right-forward, 2-left-forward, 3-left-forward, 4-left-forward",
"1-right-forward, 2-right-forward, 3-left-forward, 4-left-forward",
"1-right-forward, 2-right-forward, 3-up, 4-left-forward",
"1-right-forward, 2-left-forward, 3-up, 4-left-forward",
"1-up, 2-left-forward, 3-left-forward, 4-left-forward",
"1-up, 2-right-forward, 3-up, 4-left-forward",
"1-up, 2-right-forward, 3-left-forward, 4-left-forward"
] |
3d_maze
|
3D Spatial Perception & Reasoning
|
|
State Prediction
| 3 |
Find the length of Snake block headed by a given coordinate after given sconds.
|
Medium
|
Medium
|
Now I'll give you a picture, which shows a screenshot of a rhythm game, in which there are operation blocks of various colors. In this game, the operation blocks will fall at a speed of 1 cell/second. At the same time, you can select a column to place your finger (you cannot move your finger after selecting it), and click the operation blocks in the column that fall to the first row to score points (of course, you can also choose not to click any column, which will not affect the falling of the operation blocks).
For the operation blocks, we divide them into 3 categories, including Click blocks, Reverse blocks, and Snake blocks, as follows:
1. Click blocks are yellow, occupy 1 cell, and you can get 10 points by clicking them.
2. Reverse blocks are green, occupy 1 cell, and you can get 15 points by clicking them. It should be noted that after you click the Reverse block, the entire game situation will **reverse left and right**, but your finger position **will not** change accordingly.
3. A Snake block occupies 2 or more consecutive cells in a column, and its first cell (called Snake Head block) is pink, its last cell (called Snake Tail block) is grey, and the middle cells (called Snake Body blocks, if any) are blue. Only when you click on **all cells** occupied by the snake block can you score points. The score is related to the length $l$ (including the head and tail) of the snake block. The specific score is $l \cdot (2l + 7)$.
Now I will give you a question about the game. Please extract information from the picture I give you, think carefully, reason and answer: Without selecting any column to click, what is the length of the snake block headed (which means being the lower end) by (3, 5) after 1 second(s)? Options: 1. 2 2. 3 3. 4 4. 5
|
1
|
[
"2",
"3",
"4",
"5"
] |
rhythm_game
|
Strategy Planning
|
|
State Prediction
| 3 |
Find the sequence of moves between two cube states
|
Medium
|
Hard
|
Rules: As shown in the figure, the Rubik's cube consists of both 3D views and an unfolded view. The 3D views show the cube from two angles: left-tilted 30 degrees looking down, and right-tilted ,30 degrees looking up. The cube has six faces: Upper (U), Down (D), Left (L), Right (R), Front (F), and Back (B). Each face can be rotated clockwise or counterclockwise.And for each face, the coordinates are determined based on the unfolded view: column number increases from left to right (0,1,2) and row number increases from bottom to top (0,1,2). Legend shown in the bottom left corner.Handedness issues in the 3D views can be ignored.An uppercase letter indicates which face to rotate ('F' for Front, 'B' for Back, 'L' for Left, 'R' for Right, 'U' for Upper, 'D' for Down), with a prime symbol (') denoting counterclockwise rotation and no prime symbol denoting clockwise rotation.How many moves are needed to solve the Front face face?Options: [1] 3, [2] 12, [3] 7, [4] 10, [5] 2, [6] 11, [7] 5, [8] 1
|
5
|
[
"3",
"12",
"7",
"10",
"2",
"11",
"5",
"1"
] |
rubiks_cube
|
3D Spatial Perception & Reasoning
|
|
Target Perception
| 1 |
letter_count
|
Easy
|
Medium
|
Rules:
1. The grid contains uppercase letters.
2. Count all occurrences of the specified letter.
Question:
How many times does the letter 'G' appear in the grid?
Options:
1: 4
2: 0
3: 5
4: 2
5: 6
6: 7
7: 3
8: 1
|
8
|
[
"4",
"0",
"5",
"2",
"6",
"7",
"3",
"1"
] |
word_search
|
Multi-step Reasoning
|
|
Target Perception
| 2 |
Given the coordinate of last step, find the number of possible coordinates of next step.
|
Hard
|
Easy
|
Now I'll give you a picture, which shows a screenshot of Ultra TicTacToe. The introduction of Ultra TicTacToe is as follows:
1. Board and coordinate representation: In this game, the board is divided into 9 3*3 squares(called Nine-grids). At the same time, we use $(i, j, row, col)$ to represent the coordinates of a cell: $(i, j)$ represents the coordinates of the Nine-grid; $(row, col)$ represents the coordinate of the cell within the Nine-grid; $i, j, row, col$ all range from 1 to 3. Two players take turns placing pieces on the board to mark the cells on the board, with the first player using "X" and the second player using "O" (this is the same as traditional TicTacToe).
2. Rules for placing chess pieces: After the game starts, the first player places a chess piece in any cell in the Nine-grid in the middle (i.e., the Nine-grid (2, 2)). After that, the coordinates of each chess piece placed in the Nine-grid are the same as the coordinates of the Nine-grid in which the opponent's last chess piece was placed; for example, if the first player places a chess piece at the coordinates (2, 2, 3, 1) in the first step, then the second player needs to choose a chess piece in the Nine-grid (3, 1) in the second step.
3. Scoring rules: For each player, each "Straight" (i.e., three identical chess pieces connected in a line, such as in the same row, the same column, or a diagonal line) in each Nine-grid is counted as 1 point. More than 1 point can be counted in each Nine-grid.
Now I will give you a question about the game. Please extract information from the picture I give you, think carefully, reason, and answer: Now your opponent place a piece at (2, 3, 2, 3). What is the number of possible coordinates of your next step? Options: 1. 0 2. 1 3. 2 4. 3 5. 4 6. 5 7. 6 8. 7 9. 8 10. 9
|
4
|
[
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9"
] |
ultra_tictactoe
|
Strategy Planning
|
|
State Prediction
| 5 |
Multi-step deductive reasoning with constraints analysis
|
Easy
|
Hard
|
This is a sudoku game in which the board is filled with a total number of colours equal to the length of the board's sides, and no rows, columns or squares are allowed to have duplicate colours.You should fill the empty cells on the board with following 4 colors:red, green, blue, magenta.In this Sudoku board, the row coordinates are 1-4 from top to bottom, and the column coordinates are 1-4 from left to right.After determining colors at positions (1,1), (1,4), what color should be at position (1,3)?Choose from following options:A.red, B.green, C.blue, D.magenta
|
C
|
[
"A.red",
"B.green",
"C.blue",
"D.magenta"
] |
sudoku
|
Multi-step Reasoning
|
|
State Prediction
| 2 |
Predict the cube state after performing specific moves
|
Hard
|
Medium
|
Rules: As shown in the figure, the Rubik's cube consists of both 3D views and an unfolded view. The 3D views show the cube from two angles: left-tilted 30 degrees looking down, and right-tilted ,30 degrees looking up. The cube has six faces: Upper (U), Down (D), Left (L), Right (R), Front (F), and Back (B). Each face can be rotated clockwise or counterclockwise.And for each face, the coordinates are determined based on the unfolded view: column number increases from left to right (0,1,2) and row number increases from bottom to top (0,1,2). Legend shown in the bottom left corner.Handedness issues in the 3D views can be ignored.An uppercase letter indicates which face to rotate ('F' for Front, 'B' for Back, 'L' for Left, 'R' for Right, 'U' for Upper, 'D' for Down), with a prime symbol (') denoting counterclockwise rotation and no prime symbol denoting clockwise rotation.After the sequence D' U L D' L', what color will be at position (0, 0) on the Upper face face?Options: [1] magenta, [2] purple, [3] yellow, [4] cyan, [5] white, [6] blue, [7] orange, [8] gray
|
6
|
[
"magenta",
"purple",
"yellow",
"cyan",
"white",
"blue",
"orange",
"gray"
] |
rubiks_cube
|
3D Spatial Perception & Reasoning
|
|
Target Perception
| 3 |
Find the number of marked middle cells in the image.
|
Hard
|
Easy
|
Now I'll give you a picture, which shows a screenshot of Ultra TicTacToe. The introduction of Ultra TicTacToe is as follows:
1. Board and coordinate representation: In this game, the board is divided into 9 3*3 squares(called Nine-grids). At the same time, we use $(i, j, row, col)$ to represent the coordinates of a cell: $(i, j)$ represents the coordinates of the Nine-grid; $(row, col)$ represents the coordinate of the cell within the Nine-grid; $i, j, row, col$ all range from 1 to 3. Two players take turns placing pieces on the board to mark the cells on the board, with the first player using "X" and the second player using "O" (this is the same as traditional TicTacToe).
2. Rules for placing chess pieces: After the game starts, the first player places a chess piece in any cell in the Nine-grid in the middle (i.e., the Nine-grid (2, 2)). After that, the coordinates of each chess piece placed in the Nine-grid are the same as the coordinates of the Nine-grid in which the opponent's last chess piece was placed; for example, if the first player places a chess piece at the coordinates (2, 2, 3, 1) in the first step, then the second player needs to choose a chess piece in the Nine-grid (3, 1) in the second step.
3. Scoring rules: For each player, each "Straight" (i.e., three identical chess pieces connected in a line, such as in the same row, the same column, or a diagonal line) in each Nine-grid is counted as 1 point. More than 1 point can be counted in each Nine-grid.
Now I will give you a question about the game. Please extract information from the picture I give you, think carefully, reason, and answer: How many middle cells in the image are marked? Options: 1. 0 2. 1 3. 2 4. 3 5. 4 6. 5 7. 6 8. 7 9. 8 10. 9
|
8
|
[
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9"
] |
ultra_tictactoe
|
Strategy Planning
|
|
Target Perception
| 1 |
Check color state at position
|
Easy
|
Easy
|
This is a sudoku game in which the board is filled with a total number of colours equal to the length of the board's sides, and no rows, columns or squares are allowed to have duplicate colours.You should fill the empty cells on the board with following 4 colors: red, green, blue, magenta.In this Sudoku board, the row coordinates are 1-4 from top to bottom, and the column coordinates are 1-4 from left to right.What color is at position (3,4)(note that on the board the position (3,4) has already been filled with a certain color)?Choose from following options:A.red, B.green, C.blue, D.magenta
|
C
|
[
"A.red",
"B.green",
"C.blue",
"D.magenta"
] |
sudoku
|
Multi-step Reasoning
|
|
Target Perception
| 1 |
Choose the position that contains a voxel from the given options.
|
Easy
|
Easy
|
This is a state in a 3D reconstruction game.
Given:
- A 3x3x3 grid structure containing voxels
- A image containing the voxel structure and its target projections (possibly not the projections of the given structure)
(Note: The projections shown in the image are not relevant for this question)
Game Rules:
1. Grid Space: The game is played on a 3x3x3 cube grid.
2. Coordinates: Position (x,y,z) ranges from 1 to 3, with (1,1,1) at front-left-bottom.
3. Position Rule: Each position can contain at most one voxel.
4. Connectivity: All voxels must be connected face-to-face.
Question:
Which of the following positions contains a voxel?
Choose the correct position from the options below.
Options:
1: (3,1,3)
2: (3,1,2)
3: (1,2,1)
4: (1,1,1)
5: (2,1,2)
6: (1,2,2)
|
3
|
[
"(3,1,3)",
"(3,1,2)",
"(1,2,1)",
"(1,1,1)",
"(2,1,2)",
"(1,2,2)"
] |
3d_reconstruction
|
3D Spatial Perception & Reasoning
|
|
State Prediction
| 0 |
path_finding
|
Medium
|
Hard
|
Rules:
1. Player can only walk on top of cubes
2. Player can climb ladders if they can reach the cube under the ladder
3. From a ladder, player can reach the top of the last cube with the ladder
4. Blue cube is start position, red cube is goal position
5. Numbered cubes are branch points where player must choose a path
Which combination of path choices leads to the goal?
Options:
1: 1-left-forward, 2-right-forward, 3-up, 4-up
2: 1-up, 2-right-forward, 3-left-forward, 4-up
3: 1-up, 2-up, 3-left-forward, 4-up
4: 1-left-forward, 2-up, 3-up, 4-up
5: 1-left-forward, 2-up, 3-left-forward, 4-up
6: 1-up, 2-up, 3-up, 4-up
7: 1-left-forward, 2-up, 3-left-forward, 4-right-forward
8: 1-left-forward, 2-right-forward, 3-left-forward, 4-up
|
7
|
[
"1-left-forward, 2-right-forward, 3-up, 4-up",
"1-up, 2-right-forward, 3-left-forward, 4-up",
"1-up, 2-up, 3-left-forward, 4-up",
"1-left-forward, 2-up, 3-up, 4-up",
"1-left-forward, 2-up, 3-left-forward, 4-up",
"1-up, 2-up, 3-up, 4-up",
"1-left-forward, 2-up, 3-left-forward, 4-right-forward",
"1-left-forward, 2-right-forward, 3-left-forward, 4-up"
] |
3d_maze
|
3D Spatial Perception & Reasoning
|
|
Strategy Optimization
| 6 |
Find choosing which column to click can get the highest score.
|
Hard
|
Hard
|
Now I'll give you a picture, which shows a screenshot of a rhythm game, in which there are operation blocks of various colors. In this game, the operation blocks will fall at a speed of 1 cell/second. At the same time, you can select a column to place your finger (you cannot move your finger after selecting it), and click the operation blocks in the column that fall to the first row to score points (of course, you can also choose not to click any column, which will not affect the falling of the operation blocks).
For the operation blocks, we divide them into 3 categories, including Click blocks, Reverse blocks, and Snake blocks, as follows:
1. Click blocks are yellow, occupy 1 cell, and you can get 10 points by clicking them.
2. Reverse blocks are green, occupy 1 cell, and you can get 15 points by clicking them. It should be noted that after you click the Reverse block, the entire game situation will **reverse left and right**, but your finger position **will not** change accordingly.
3. A Snake block occupies 2 or more consecutive cells in a column, and its first cell (called Snake Head block) is pink, its last cell (called Snake Tail block) is grey, and the middle cells (called Snake Body blocks, if any) are blue. Only when you click on **all cells** occupied by the snake block can you score points. The score is related to the length $l$ (including the head and tail) of the snake block. The specific score is $l \cdot (2l + 7)$.
Now I will give you a question about the game. Please extract information from the picture I give you, think carefully, reason and answer: Which column(s) should I choose to click to get the highest final score? Options: 1. 1 2. 2 3. 3 4. 4 5. 5 6. 6
|
5
|
[
"1",
"2",
"3",
"4",
"5",
"6"
] |
rhythm_game
|
Strategy Planning
|
|
Target Perception
| 3 |
Ask the total number of enemies
|
Hard
|
Medium
|
The given image represents a simplified interface of the game Space Invaders. The enemy area is implicitly divided into a grid of cells, with the row and column numbers shown on the left and top sides of the grid respectively which you should strictly follow. Each cell is either empty or occupied by an incoming enemy which can be purple, blue or green. The ship is at the bottom row, aligned with one of the columns, which shoots the enemies using laser while dodging possible lasers from the enemies.
How many enemies are there in total? Give the number of the correct option.
Options:
1: 28
2: 29
3: 30
4: 31
5: 32
6: 33
7: 34
8: 35
|
6
|
[
"28",
"29",
"30",
"31",
"32",
"33",
"34",
"35"
] |
space_invaders
|
Strategy Planning
|
|
State Prediction
| 4 |
Predict card move result
|
Hard
|
Medium
|
Spider Solitaire
# OBJECTIVE
Spider is played with eight decks of 13 spade cards each, totaling 104 unique cards. The goal is to arrange all cards in a King-to-Ace sequence in the same suit and move them to the foundation piles. Once all sequences are moved to the foundations, the game is won.
# SETUP
The game features waste piles, a stock pile, and foundation piles. Waste piles are where the action happens, and the stock pile provides new cards when necessary.
**Waste Pile Numbering**: Waste piles are numbered from left to right starting with `0`. The cards within each waste pile are also numbered starting from the bottom card.
# GAME BOARD COMPONENTS
## **Stock Pile**
The **Stock Pile** holds all remaining cards and is used to deal new cards into the waste piles.
Stock Pile is in the top left corner of the board.
- **Staggered Card Stacking**: Cards are stacked in layers, and the number of layers indicates how many more times you can deal cards to the waste piles. Each deal moves one card face-up to each waste pile.
## **Waste Piles**
The **Waste Piles** are where cards are played and organized.
Waste Piles are on the bottom of the chessboard
- **Face-Up vs. Face-Down Cards**: Cards are stacked with face-up cards visible and face-down cards hidden. Only face-up cards can be played. When a face-down card becomes the top card of a pile, it is turned face-up and can be played.
- **Staggered Cards**: Cards in each waste pile are arranged so that face-up cards are on top, and face-down cards are beneath. As you move cards, new face-down cards are revealed.
- **Card Numbering and Screen Position**:
- **Waste Pile Numbering**: Piles are numbered from left to right starting with `0` for the leftmost pile.
- The card at the bottom of each waste pile (usually face-down) is numbered **0** and is the **topmost visible card** in the pile.
- As you move upward in the pile, the next cards are numbered **1**, **2**, **3**, and so on.
- Visually, the bottom card (number **0**) is the one closest to the top of the screen, and the cards above it are stacked above in the pile, going downwards.
## **Foundation Pile**
Foundation pile stores all the arranged suit. When a suit is arranged in sequence, it may be removed to a foundation pile. If all suits are moved to the foundations, the game is won.
Foundation Pile is in the top right corner of the board.
# MOVING CARDS
- **Movement Conditions**: Cards can be moved to another pile as long as they form a **descending sequence of the same suit**, i.e., a King-to-Ace sequence. When moving cards, the new sequence must be a **same-suit sequence** and follow the **descending order** from K, Q, J, 10, 9, ..., 2, A.
- **Same-Suit Sequence Requirement**: The card being moved must be placed on a top card that is of the **same suit** and has a **higher rank** (e.g., a Q can be placed on a K). The top card of the target pile must be larger in rank than the card being moved, and both must be of the same suit.
- **Moving a Sequence**: A complete **descending sequence** of cards (such as K, Q, J, 10, etc.) can be moved from one pile to another, as long as the sequence is in **descending order** and all the cards in the sequence are of the **same suit**.
- **Face-Down Cards**: If the sequence you are moving includes face-down cards, they will be flipped face-up once they are moved. After flipping, the newly face-up cards can continue to be moved or interacted with.
- **Example**: If you have a sequence of K-Q-J-10-9-8-7 in the same suit, you can move a card 6 that has the same suit to the top of this pile, resulting in a new sequence K-Q-J-10-9-8-7-6.
- **Empty Pile Rule**: An empty waste pile can accept any card. After placing the card, you can continue adding a descending same-suit sequence to that pile.
- **Reveal Cards**: If a move leaves a face-down card on top, it will be turned face-up.
# DEALING
Click the stock to deal a new row of face-up cards to the waste piles. You may not deal if there is an empty waste pile.
# STRATEGY
- Turn face-down cards face-up.
- Form runs of the same suit in descending order.
- Use empty waste piles strategically.
# VARIANTS
In **circular spider solitaire**, a King can be placed on an Ace, allowing for extended sequences.
# **NOTE: Important Numbering Reminder**
- **Waste Pile Numbering**: Waste piles are numbered from **left to right** starting with `0` for the leftmost pile.
- **Card Numbering within Waste Piles**: The **bottom-most card** of each pile (usually face-down) is numbered **0**, and the cards above it are numbered **1**, **2**, **3**, etc., moving upwards in the pile.
- **Please Pay Attention** to both the waste pile and card numbering methods, as they will help you navigate and make strategic decisions effectively.
**Question:** What will happen if I want to move the number 6 card of pile 1 to pile 9?
**Options:**
A. The move will be successful, and the cards will be in descending order, following the rules of movement.
B. The move cannot be made because this card is face-down and its value is unknown.
C. The move cannot be made because there is a card above it, and that card does not form a descending order with the selected card.
D. The move cannot be made because the top card of the target pile does not have a rank equal to this card's rank plus one.
E. The move cannot be made because the pile has too few cards, and this card does not exist.
|
A
|
[
"A. The move will be successful, and the cards will be in descending order, following the rules of movement.",
"B. The move cannot be made because this card is face-down and its value is unknown.",
"C. The move cannot be made because there is a card above it, and that card does not form a descending order with the selected card.",
"D. The move cannot be made because the top card of the target pile does not have a rank equal to this card's rank plus one.",
"E. The move cannot be made because the pile has too few cards, and this card does not exist."
] |
spider_solitaire
|
Pattern Recognition & Matching
|
|
Target Perception
| 2 |
gradient_pattern
|
Easy
|
Medium
|
Rules:
1. Colors change gradually along rows or columns.
2. A gradient transitions between two colors.
3. Each row or column can have its own independent gradient pattern.
4. Row and column indexes begin from 1 at the top-left corner.
Question:
What is the gradient pattern in column 3?
Options:
1: transitioning from vivid bright cyan to pale dark indigo
2: transitioning from vivid bright red to pale dark indigo
3: transitioning from orange to vivid orange
4: transitioning from pale bright red to vivid cyan
5: transitioning from pale red to vivid bright cyan
6: transitioning from bright indigo to pale yellow
7: transitioning from purple to vivid bright green
8: transitioning from vivid blue to black
|
3
|
[
"transitioning from vivid bright cyan to pale dark indigo",
"transitioning from vivid bright red to pale dark indigo",
"transitioning from orange to vivid orange",
"transitioning from pale bright red to vivid cyan",
"transitioning from pale red to vivid bright cyan",
"transitioning from bright indigo to pale yellow",
"transitioning from purple to vivid bright green",
"transitioning from vivid blue to black"
] |
hue
|
Pattern Recognition & Matching
|
|
Target Perception
| 3 |
Given current state and a region,Your task is to indentify which cell provided by options belongs to this region and has been placed a star.
|
Easy
|
Easy
|
We have a 5*5 grid.The grid is divided into 5 regions.
Cells with the same color belong to the same region.
Region with index 0 has the color of light pink.
Region with index 1 has the color of powder blue.
Region with index 2 has the color of light green.
Region with index 3 has the color of peach.
Region with index 4 has the color of red.
In the image,a star is represented by a black dot. If a cell has been placed a star,a black dot will be shown on this cell.
We should place the star in this Star Battle Puzzle according to the following rules:
Each row must contain exactly 1 star(s).
Each column must contain 1 star(s).
Each region must contain exactly 1 star(s).
Stars cannot be adjacent to each other, including diagonally.
The cells in the grid are labeled with row and column numbers starting from 0. The top-left corner of the grid is (0, 0).
(x,y) means a cell at row x and column y.
Now we have placed some stars in the grid.
In the current puzzle state, region 0 is associated with color light pink.
Please identify which of the following cells in this region that contains a star?
Note that:If no stars have been placed in the target region,please choose the option "null"
Options:
1.(1,0)
2.(4,3)
3.(0,4)
4.(4,4)
5.(4,1)
6.(3,3)
7.(4,2)
8.(3,2)
|
7
|
[
"(1,0)",
"(4,3)",
"(0,4)",
"(4,4)",
"(4,1)",
"(3,3)",
"(4,2)",
"(3,2)"
] |
star_battle
|
Multi-step Reasoning
|
|
State Prediction
| 5 |
piece_placement
|
Easy
|
Hard
|
Rules:
1. Each numbered region represents a piece on the board.
2. Pieces are considered adjacent if they share at least one edge.
3. Pieces that only touch at corners are not considered adjacent.
4. Two adjacent pieces have been removed from the board.
5. A valid placement is one where both pieces fit into the hole without overlapping.
Question:
At which position should Piece 1 be placed? Each option shows (top_row,left_col) to (bottom_row,right_col).
Options:
1: (2,0) to (4,0)
2: (0,0) to (2,0)
3: (0,2) to (2,2)
4: (0,1) to (2,1)
5: (2,3) to (4,3)
6: (0,3) to (2,3)
7: (1,2) to (3,2)
8: (1,1) to (3,1)
|
1
|
[
"(2,0) to (4,0)",
"(0,0) to (2,0)",
"(0,2) to (2,2)",
"(0,1) to (2,1)",
"(2,3) to (4,3)",
"(0,3) to (2,3)",
"(1,2) to (3,2)",
"(1,1) to (3,1)"
] |
tengram
|
Pattern Recognition & Matching
|
|
State Prediction
| 3 |
Given a particular game state,a selected move and a selected cascade pile, the puzzle will present a question about which card is at the top of the cascade pile.
Your task is to indentify the card in the options.
|
Hard
|
Hard
|
In this FreeCell game:
we have 4 cascade piles, and their indexes are [0, 1, 2, 3]We have 4 freecell on the left top, and their indexes are 0,1,2,3.We have 4 foundation piles on the right top, and their indexes are 0,1,2,3.In FreeCell, cards can be moved according to specific rules: A card can be moved to a free cell if available, stacked in descending order alternating colors in cascade piles, or placed in foundation piles starting from Ace. Now, find the top card from cascade pile 1 after moving the card (Club,4) from Cascade 1 to FreeCell 2.the options are as follows:
1.(Heart, Q)
2.(Spade, 1)
3.(Club, J)
4.(Heart, 2)
5.(Diamond, 3)
6.(Club, 7)
7.(Club, 6)
8.(Spade, 3)
|
6
|
[
"(Heart, Q)",
"(Spade, 1)",
"(Club, J)",
"(Heart, 2)",
"(Diamond, 3)",
"(Club, 7)",
"(Club, 6)",
"(Spade, 3)"
] |
freecell
|
Pattern Recognition & Matching
|
|
Target Perception
| 1 |
Identify colors on specific positions
|
Medium
|
Easy
|
Rules: As shown in the figure, the Rubik's cube consists of both 3D views and an unfolded view. The 3D views show the cube from two angles: left-tilted 30 degrees looking down, and right-tilted ,30 degrees looking up. The cube has six faces: Upper (U), Down (D), Left (L), Right (R), Front (F), and Back (B). Each face can be rotated clockwise or counterclockwise.And for each face, the coordinates are determined based on the unfolded view: column number increases from left to right (0,1,2) and row number increases from bottom to top (0,1,2). Legend shown in the bottom left corner.Handedness issues in the 3D views can be ignored.An uppercase letter indicates which face to rotate ('F' for Front, 'B' for Back, 'L' for Left, 'R' for Right, 'U' for Upper, 'D' for Down), with a prime symbol (') denoting counterclockwise rotation and no prime symbol denoting clockwise rotation.What color is at position (1, 2) on the Upper face face?Options: [1] blue, [2] purple, [3] cyan, [4] orange, [5] gray, [6] magenta, [7] black, [8] yellow
|
8
|
[
"blue",
"purple",
"cyan",
"orange",
"gray",
"magenta",
"black",
"yellow"
] |
rubiks_cube
|
3D Spatial Perception & Reasoning
|
|
Target Perception
| 1 |
color_description
|
Medium
|
Easy
|
Rules:
1. Colors change gradually along rows or columns.
2. A gradient transitions between two colors.
3. Each row or column can have its own independent gradient pattern.
4. Row and column indexes begin from 1 at the top-left corner.
Question:
What color is the cell at row 6, column 2?
Options:
1: bright purple
2: cyan
3: dark red
4: vivid red
5: orange
6: bright green
7: blue
8: vivid bright yellow
|
7
|
[
"bright purple",
"cyan",
"dark red",
"vivid red",
"orange",
"bright green",
"blue",
"vivid bright yellow"
] |
hue
|
Pattern Recognition & Matching
|
|
State Prediction
| 1 |
head_state
|
Easy
|
Medium
|
Rules:
State 0, Symbol 0 -> Write 1, Move right, New State 2
State 0, Symbol 1 -> Write 2, Move right, New State 2
State 0, Symbol 2 -> Write 3, Move right, New State 2
State 0, Symbol 3 -> Write 3, Move left, New State 2
State 0, Symbol 4 -> Write 4, Move left, New State 1
State 1, Symbol 0 -> Write 2, Move right, New State 0
State 1, Symbol 1 -> Write 2, Move right, New State 0
State 1, Symbol 2 -> Write 2, Move down, New State 1
State 1, Symbol 3 -> Write 0, Move left, New State 2
State 1, Symbol 4 -> Write 2, Move down, New State 0
State 2, Symbol 0 -> Write 3, Move down, New State 1
State 2, Symbol 1 -> Write 4, Move left, New State 2
State 2, Symbol 2 -> Write 0, Move left, New State 1
State 2, Symbol 3 -> Write 3, Move down, New State 0
State 2, Symbol 4 -> Write 1, Move up, New State 0
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Symbol 4: Color = cyan
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (0, 0) with State 0 on Symbol 0 that is (0).
Question: what will be the head state and symbol under it after 8 steps?
Options:
1: (3)
2: [3]
3: (1)
4: {0}
5: (4)
6: (2)
7: [2]
8: [1]
|
2
|
[
"(3)",
"[3]",
"(1)",
"{0}",
"(4)",
"(2)",
"[2]",
"[1]"
] |
2d_turing_machine
|
Multi-step Reasoning
|
|
Target Perception
| 2 |
Given the coordinate of last step, find the number of possible coordinates of next step.
|
Medium
|
Easy
|
Now I'll give you a picture, which shows a screenshot of Ultra TicTacToe. The introduction of Ultra TicTacToe is as follows:
1. Board and coordinate representation: In this game, the board is divided into 9 3*3 squares(called Nine-grids). At the same time, we use $(i, j, row, col)$ to represent the coordinates of a cell: $(i, j)$ represents the coordinates of the Nine-grid; $(row, col)$ represents the coordinate of the cell within the Nine-grid; $i, j, row, col$ all range from 1 to 3. Two players take turns placing pieces on the board to mark the cells on the board, with the first player using "X" and the second player using "O" (this is the same as traditional TicTacToe).
2. Rules for placing chess pieces: After the game starts, the first player places a chess piece in any cell in the Nine-grid in the middle (i.e., the Nine-grid (2, 2)). After that, the coordinates of each chess piece placed in the Nine-grid are the same as the coordinates of the Nine-grid in which the opponent's last chess piece was placed; for example, if the first player places a chess piece at the coordinates (2, 2, 3, 1) in the first step, then the second player needs to choose a chess piece in the Nine-grid (3, 1) in the second step.
3. Scoring rules: For each player, each "Straight" (i.e., three identical chess pieces connected in a line, such as in the same row, the same column, or a diagonal line) in each Nine-grid is counted as 1 point. More than 1 point can be counted in each Nine-grid.
Now I will give you a question about the game. Please extract information from the picture I give you, think carefully, reason, and answer: Now your opponent place a piece at (2, 3, 2, 3). What is the number of possible coordinates of your next step? Options: 1. 0 2. 1 3. 2 4. 3 5. 4 6. 5 7. 6 8. 7 9. 8 10. 9
|
6
|
[
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9"
] |
ultra_tictactoe
|
Strategy Planning
|
|
Strategy Optimization
| 3 |
Questions about the outcome to take a specific move of the current player of the board, and the optimal strategy to take a move of the opponent player after the specific move.
|
Hard
|
Hard
|
Principles: Tic-Tac-Toe is a classic two-player game played on a 3x3 grid, (row, col) from (0, 0) to (2, 2). Players take turns marking a space in the grid, one using **O** (the red block) and the other using **X** (the blue block). In each game, player **O** starts first. The objective is to be the first to get three of your marks in a row (horizontally, vertically, or diagonally). If all nine squares are filled without either player achieving this, the game ends in a draw. Notice: the current player to make a move should be inferred from the number of pieces for each players on the board. When inferring the optimal move, if optimal move can be inferred by some rules, choose the optimal move. Otherwise, choose the first move. (The order of choices is (0, 0), (0, 1), (0, 2), (1, 0), ..., (2, 2), choose the first move that is not occupied)
Question: If the current player moves to (2, 1), will this move be successful? If not, choose the answer "None". If successful, will the current player win immediately? If yes, choose the answer "None". otherwise, what is the opponent's optimal move following this step?
Options: ['A.None', 'B.(0, 0)', 'C.(0, 1)', 'D.(0, 2)', 'E.(1, 0)', 'F.(1, 1)', 'G.(1, 2)', 'H.(2, 0) or (2, 1) or (2, 2)']
|
A
|
[
"A.None",
"B.(0, 0)",
"C.(0, 1)",
"D.(0, 2)",
"E.(1, 0)",
"F.(1, 1)",
"G.(1, 2)",
"H.(2, 0) or (2, 1) or (2, 2)"
] |
tictactoe
|
Strategy Planning
|
|
State Prediction
| 2 |
Predict the ant's position and direction after several steps
|
Hard
|
Medium
|
In Langton's Ant, we have a grid where each cell is either white or black. A red arrow represents an ant, showing its current position and direction. The ant follows these simple rules:
1. If the ant is on a white cell, it turns right 90 degrees, changes the cell to black, and moves forward one step
2. If the ant is on a black cell, it turns left 90 degrees, changes the cell to white, and moves forward one step
3. If the ant would move off the grid, it wraps around to the opposite side (using modulo with grid size)
The coordinates system: The top-left cell is (0,0), with x increasing downward and y increasing rightward.
After 7 steps, what will be the ant's position and direction?
Answer using one of the following options with its corresponding letter:
A: Position (0, 6), facing left
B: Position (1, 7), facing up
C: Position (4, 2), facing down
D: Position (9, 5), facing up
E: Position (8, 7), facing right
F: Position (11, 1), facing right
G: Position (11, 5), facing left
H: Position (4, 12), facing down
|
G
|
[
"Position (0, 6), facing left",
"Position (1, 7), facing up",
"Position (4, 2), facing down",
"Position (9, 5), facing up",
"Position (8, 7), facing right",
"Position (11, 1), facing right",
"Position (11, 5), facing left",
"Position (4, 12), facing down"
] |
langton_ant
|
Multi-step Reasoning
|
|
Strategy Optimization
| 6 |
Find the optimal sequence of moves to reach a specific position
|
Medium
|
Hard
|
This is a Sokoban puzzle where black figure is player, green X is target, brown box with X is box to push, brown tiles are walls, and light brown areas are movable spaces.The coordinates (x, y) in this puzzle represent the matrix format.Treat the boxes as walls,What is the shortest sequence of moves for human to move himself from position (2, 1) to position (3, 2)?
Options:
[1] Right → Right
[2] Right → Down → Left
[3] Right → Up
[4] Right
[5] Right → Down
[6] Down
[7] Up
[8] Down → Down
|
5
|
[
"Right → Right",
"Right → Down → Left",
"Right → Up",
"Right",
"Right → Down",
"Down",
"Up",
"Down → Down"
] |
sokoban
|
Strategy Planning
|
|
Target Perception
| 1 |
Identify element position
|
Medium
|
Easy
|
# **Game Overview**
Jewel2 is a strategic puzzle game played on a grid. Your primary objective is to eliminate elements by forming horizontal or vertical lines of three or more identical items. Successfully eliminating elements increases your score and clears space on the board for new elements to appear.
# **Elements**
## **Basic Elements**
- **A, B, C, D, E**
- **Description**: These are the standard elements in the game.
- **Shape**: Diamond-shaped gems in various colors (Red, Green, Blue, Yellow, Purple).
- A: Red
- B: Green
- C: Blue
- D: Yellow
- E: Purple
- **Interactions**:
- **Clearing**: When three or more identical basic elements align horizontally or vertically, they are eliminated from the board.
- **Swapping**: Basic elements can be swapped with adjacent basic elements to form eliminations.
## **Special Elements**
- **a, b, c, d, e, +, |**
- **Description**: These elements possess unique abilities that trigger specific elimination patterns when activated.
- **Shape**:
- **a, b, c, d, e**: Round gems in various colors (Red, Green, Blue, Yellow, Purple).
- a: Red
- b: Green
- c: Blue
- d: Yellow
- e: Purple
- **+**: A round black gem with low transparency.
- **|**: A tall, rectangular cyan gem.
- **Effects of Special Elements**:
- **a, b, c, d, e**:
- **Function**: Clearing one of these removes all corresponding uppercase basic elements from the board.
- *Example*: Clearing element 'a' will eliminate all 'A's on the board.
- **| (Vertical Clear)**:
- **Function**: Activating this element clears all elements in its vertical column.
- **+ (Surrounding Clear)**:
- **Function**: Activating this element clears all elements within a distance of 1 from its position, including diagonals.
- **Notes**:
- Special elements do **not** trigger further eliminations if they remove other special elements.
- Swapping involving special elements is **not allowed** and will be rejected by the game.
# **Commands**
## **Available Operations**
1. **Clear Operation**
- **Syntax**: clear x y
- **Description**: Attempts to clear the element located at coordinates (x, y).
- **Conditions**:
- The targeted element must form a valid elimination (i.e., be part of a horizontal or vertical line of three or more identical elements).
- If the element is special, its unique ability is activated upon clearing.
- **State Changes**:
- **Basic Element**: If the clearance is valid, the element(s) are removed, the score (Total Cleared) increases accordingly, and new elements fall into place to fill the gaps.
- **Special Element**: Activating a special element triggers its specific clearance effect as described above.
2. **Swap Operation**
- **Syntax**: swap x y pos
- **Parameters**:
- (x, y): Coordinates of the element to be swapped.
- pos: Direction to swap the element (up, down, left, right).
- **Description**: Swaps the element at (x, y) with the adjacent element in the specified direction.
- **pos** can be one of four directions:
- **up**: Swap with the element directly above (in the same column but one row above).
- **down**: Swap with the element directly below (in the same column but one row below).
- **left**: Swap with the element directly to the left (in the same row but one column left).
- **right**: Swap with the element directly to the right (in the same row but one column right).
- **Conditions**:
- Both elements involved in the swap must be basic elements. Swaps involving special elements are rejected.
- The swap must result in a valid elimination; otherwise, the swap is undone.
- **State Changes**:
- **Successful Swap**: Elements are exchanged, any resulting eliminations are performed, and the score (Total Cleared) is updated accordingly.
- **Unsuccessful Swap**: Elements revert to their original positions, and no changes are made to the score.
# **Coordinate System**
- The board uses **0-based coordinates**.
- **Top-left cell**: (0, 0)
- **Bottom-right cell**: ({size_minus_one}, {size_minus_one})
### **Coordinate Explanation**:
- **x (Row)**: Represents the **row number** of the element. Rows are numbered from **top to bottom**, starting from 0.
- *Example*: In a 5x5 grid, the first row (topmost) would have x = 0, the second row would have x = 1, and so on.
- **y (Column)**: Represents the **column number** of the element. Columns are numbered from **left to right**, starting from 0.
- *Example*: In a 5x5 grid, the first column (leftmost) would have y = 0, the second column would have y = 1, and so on.
### **Coordinate Example**:
- To refer to the element located in the second row and third column, you would use coordinates (1, 2).
- To refer to the element in the fifth row and the first column, you would use coordinates (4, 0).
# **Gameplay Mechanics**
## **Score Tracking**
- **Total Cleared**: Represents the cumulative number of elements that have been eliminated throughout the game.
- **Incremented By**: The number of elements cleared in each successful operation (clear or swap).
# **Objective**
Maximize your **Total Cleared** count by strategically performing clear and swap operations to eliminate as many elements as possible. Effective use of special elements can significantly enhance your score by triggering large-scale eliminations.
# **How to Play**
## **Starting the Game**
1. **Initialization**:
- Upon launching Jewel2, a grid is presented, populated with a mix of basic and special elements based on predefined probabilities.
2. **Understanding the Interface**:
- **Grid Display**: Each cell in the grid represents an element. Basic elements are denoted by uppercase letters (A-E), while special elements use lowercase letters or symbols (a, b, c, d, e, +, |).
- **Score Display**: The current **Total Cleared** count is visible, updating as you eliminate elements.
- **Command Input**: A text input area is provided where you can enter commands (clear or swap) to interact with the game.
## **Performing Operations**
1. **Clear Operation**:
- **Objective**: Remove specific elements to form or extend lines of three or more identical elements.
- **How to Execute**:
- Identify the coordinates (x, y) of the element you wish to clear.
- Enter the command in the format: clear x y.
- Example: To clear the element at row 2, column 3, input clear 2 3.
- **Outcomes**:
- **Successful Clear**: If the targeted element is part of a valid elimination, it and any adjacent identical elements are removed, the **Total Cleared** score increases by the number of elements cleared, and new elements fall into place.
- **Special Element Activation**: If a special element is cleared, its unique ability is triggered, resulting in additional eliminations as defined in the **Special Elements** section.
- **Unsuccessful Clear**: If the targeted element does not form a valid elimination, no changes occur, and the command is rejected.
2. **Swap Operation**:
- **Objective**: Rearrange elements to create new elimination opportunities.
- **How to Execute**:
- Identify the coordinates (x, y) of the element you wish to swap.
- Determine the direction pos (up, down, left, right) to which you want to swap the element.
- Enter the command in the format: swap x y pos.
- Example: To swap the element at row 1, column 1 with the element above it, input swap 1 1 up.
- **Outcomes**:
- **Successful Swap**: If the swap results in a valid elimination, the elements are exchanged, the resulting eliminations are performed, and the **Total Cleared** score is updated accordingly.
- **Unsuccessful Swap**: If the swap does not create any valid elimination or involves special elements, the swap is undone, and no changes are made to the score.
# **Additional Notes**
- **Special Element Chain Reactions**: Activating a special element's ability will **not** trigger further eliminations, even if other special elements are removed as a result.
- **Element Replenishment**: After each elimination, new elements are generated randomly to maintain a fully populated board, ensuring continuous gameplay.
- **Row and Column Elimination**: When checking whether an ordinary element can be eliminated, we check whether its rows and columns have three or more identical elements. If both rows and columns meet the elimination rule, both rows and columns are eliminated.
- **Chain Elimination**: After the elimination operation is performed and new elements are generated, no chain elimination will occur.
**Question:**Which of the following positions does element 'A' reside in?
**Options:**
A. Position (3, 4)
B. Position (1, 0)
C. Position (0, 2)
D. Position (0, 4)
E. Position (3, 1)
F. Position (2, 1)
G. Position (1, 4)
H. Position (3, 2)
|
C
|
[
"A. Position (3, 4)",
"B. Position (1, 0)",
"C. Position (0, 2)",
"D. Position (0, 4)",
"E. Position (3, 1)",
"F. Position (2, 1)",
"G. Position (1, 4)",
"H. Position (3, 2)"
] |
jewel2
|
Pattern Recognition & Matching
|
|
State Prediction
| 4 |
Predict cell reveal outcome
|
Medium
|
Hard
|
This is a Minesweeper game. The size of the chessboard is 5x5, and there are a total of 5 mines hidden on the board.
The numbers on the board indicate how many mines are adjacent to that cell, including diagonals. Cells marked with "F" (flagged) are identified as potential locations of mines based on logical deduction or prior knowledge. These flagged cells play a critical role in guiding your reasoning for answering the questions. Cells with no numbers and no flags are safe and contain no adjacent mines.
The board uses a coordinate system where the top-left cell corresponds to (0,0), and the rows and columns are numbered starting from 0.
Please use the provided board configuration and logical reasoning to deduce the correct answers to the following questions:
**Question:** What will happen if the player reveals the cell at (1,3)?
**Options:**
A: The game will end because the cell contains a mine.
B: The cell will reveal an empty area, and adjacent cells will also be revealed.
C: The cell will reveal the number 2.
D: The cell will reveal the number 0.
|
C
|
[
"A: The game will end because the cell contains a mine. ",
"B: The cell will reveal an empty area, and adjacent cells will also be revealed. ",
"C: The cell will reveal the number 2. ",
"D: The cell will reveal the number 0."
] |
minesweeper
|
Multi-step Reasoning
|
|
State Prediction
| 4 |
Based on the current puzzle state, your task is to identify which of the following cells provided by the options can a star be placed in?
|
Medium
|
Medium
|
We have a 6*6 grid.The grid is divided into 6 regions.
Cells with the same color belong to the same region.
Region with index 0 has the color of light pink.
Region with index 1 has the color of powder blue.
Region with index 2 has the color of light green.
Region with index 3 has the color of peach.
Region with index 4 has the color of red.
Region with index 5 has the color of yellow.
In the image,a star is represented by a black dot. If a cell has been placed a star,a black dot will be shown on this cell.
We should place the star in this Star Battle Puzzle according to the following rules:
Each row must contain exactly 1 star(s).
Each column must contain 1 star(s).
Each region must contain exactly 1 star(s).
Stars cannot be adjacent to each other, including diagonally.
The cells in the grid are labeled with row and column numbers starting from 0. The top-left corner of the grid is (0, 0).
(x,y) means a cell at row x and column y.
Now we have placed some stars in the grid.
Based on the current puzzle state, which of the following cells can a star be placed in?
Options:
1.(1,4)
2.null
3.(1,1)
4.(4,1)
5.(4,3)
6.(0,5)
7.(2,2)
8.(3,3)
|
2
|
[
"(1,4)",
"null",
"(1,1)",
"(4,1)",
"(4,3)",
"(0,5)",
"(2,2)",
"(3,3)"
] |
star_battle
|
Multi-step Reasoning
|
|
State Prediction
| 5 |
Reveal face-down card strategy
|
Hard
|
Hard
|
Spider Solitaire
# OBJECTIVE
Spider is played with eight decks of 13 spade cards each, totaling 104 unique cards. The goal is to arrange all cards in a King-to-Ace sequence in the same suit and move them to the foundation piles. Once all sequences are moved to the foundations, the game is won.
# SETUP
The game features waste piles, a stock pile, and foundation piles. Waste piles are where the action happens, and the stock pile provides new cards when necessary.
**Waste Pile Numbering**: Waste piles are numbered from left to right starting with `0`. The cards within each waste pile are also numbered starting from the bottom card.
# GAME BOARD COMPONENTS
## **Stock Pile**
The **Stock Pile** holds all remaining cards and is used to deal new cards into the waste piles.
Stock Pile is in the top left corner of the board.
- **Staggered Card Stacking**: Cards are stacked in layers, and the number of layers indicates how many more times you can deal cards to the waste piles. Each deal moves one card face-up to each waste pile.
## **Waste Piles**
The **Waste Piles** are where cards are played and organized.
Waste Piles are on the bottom of the chessboard
- **Face-Up vs. Face-Down Cards**: Cards are stacked with face-up cards visible and face-down cards hidden. Only face-up cards can be played. When a face-down card becomes the top card of a pile, it is turned face-up and can be played.
- **Staggered Cards**: Cards in each waste pile are arranged so that face-up cards are on top, and face-down cards are beneath. As you move cards, new face-down cards are revealed.
- **Card Numbering and Screen Position**:
- **Waste Pile Numbering**: Piles are numbered from left to right starting with `0` for the leftmost pile.
- The card at the bottom of each waste pile (usually face-down) is numbered **0** and is the **topmost visible card** in the pile.
- As you move upward in the pile, the next cards are numbered **1**, **2**, **3**, and so on.
- Visually, the bottom card (number **0**) is the one closest to the top of the screen, and the cards above it are stacked above in the pile, going downwards.
## **Foundation Pile**
Foundation pile stores all the arranged suit. When a suit is arranged in sequence, it may be removed to a foundation pile. If all suits are moved to the foundations, the game is won.
Foundation Pile is in the top right corner of the board.
# MOVING CARDS
- **Movement Conditions**: Cards can be moved to another pile as long as they form a **descending sequence of the same suit**, i.e., a King-to-Ace sequence. When moving cards, the new sequence must be a **same-suit sequence** and follow the **descending order** from K, Q, J, 10, 9, ..., 2, A.
- **Same-Suit Sequence Requirement**: The card being moved must be placed on a top card that is of the **same suit** and has a **higher rank** (e.g., a Q can be placed on a K). The top card of the target pile must be larger in rank than the card being moved, and both must be of the same suit.
- **Moving a Sequence**: A complete **descending sequence** of cards (such as K, Q, J, 10, etc.) can be moved from one pile to another, as long as the sequence is in **descending order** and all the cards in the sequence are of the **same suit**.
- **Face-Down Cards**: If the sequence you are moving includes face-down cards, they will be flipped face-up once they are moved. After flipping, the newly face-up cards can continue to be moved or interacted with.
- **Example**: If you have a sequence of K-Q-J-10-9-8-7 in the same suit, you can move a card 6 that has the same suit to the top of this pile, resulting in a new sequence K-Q-J-10-9-8-7-6.
- **Empty Pile Rule**: An empty waste pile can accept any card. After placing the card, you can continue adding a descending same-suit sequence to that pile.
- **Reveal Cards**: If a move leaves a face-down card on top, it will be turned face-up.
# DEALING
Click the stock to deal a new row of face-up cards to the waste piles. You may not deal if there is an empty waste pile.
# STRATEGY
- Turn face-down cards face-up.
- Form runs of the same suit in descending order.
- Use empty waste piles strategically.
# VARIANTS
In **circular spider solitaire**, a King can be placed on an Ace, allowing for extended sequences.
# **NOTE: Important Numbering Reminder**
- **Waste Pile Numbering**: Waste piles are numbered from **left to right** starting with `0` for the leftmost pile.
- **Card Numbering within Waste Piles**: The **bottom-most card** of each pile (usually face-down) is numbered **0**, and the cards above it are numbered **1**, **2**, **3**, etc., moving upwards in the pile.
- **Please Pay Attention** to both the waste pile and card numbering methods, as they will help you navigate and make strategic decisions effectively.
**Question:** What should I do if I want to reveal the first face-down card in waste pile 0?
**Options:**
A. No action is needed; there are no face-down cards in this pile.
B. There is no immediate way to reveal it; we should move cards from other piles first and wait for more information.
C. We should move the 4-th card of pile 6 to pile 0.
D. We should move the top card of pile 0 to pile 7.
E. We should move the 7-th card of pile 6 to pile 8.
F. We should move the 9-th card of pile 4 to pile 3.
G. We should move the 7-th card of pile 0 to pile 0.
H. We should move the 1-th card of pile 8 to pile 4.
|
D
|
[
"A. No action is needed; there are no face-down cards in this pile.",
"B. There is no immediate way to reveal it; we should move cards from other piles first and wait for more information.",
"C. We should move the 4-th card of pile 6 to pile 0.",
"D. We should move the top card of pile 0 to pile 7.",
"E. We should move the 7-th card of pile 6 to pile 8.",
"F. We should move the 9-th card of pile 4 to pile 3.",
"G. We should move the 7-th card of pile 0 to pile 0.",
"H. We should move the 1-th card of pile 8 to pile 4."
] |
spider_solitaire
|
Pattern Recognition & Matching
|
|
State Prediction
| 2 |
symbol_at_position
|
Hard
|
Medium
|
Rules:
State 0, Symbol 0 -> Write 1, Move down, New State 0
State 0, Symbol 1 -> Write 1, Move right, New State 2
State 0, Symbol 2 -> Write 2, Move down, New State 1
State 1, Symbol 0 -> Write 2, Move down, New State 2
State 1, Symbol 1 -> Write 1, Move up, New State 2
State 1, Symbol 2 -> Write 2, Move right, New State 1
State 2, Symbol 0 -> Write 0, Move up, New State 3
State 2, Symbol 1 -> Write 2, Move up, New State 0
State 2, Symbol 2 -> Write 0, Move right, New State 2
State 3, Symbol 0 -> Write 1, Move left, New State 0
State 3, Symbol 1 -> Write 2, Move right, New State 3
State 3, Symbol 2 -> Write 2, Move right, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (0, 1) with State 3 on Symbol 0 that is <0>.
Question: how does the symbol at position (1, 1) change after 7 steps? Writing the same symbol needs to be tracked.
Options:
1: 0->2(at step 4)->2(at step 6)
2: 0->1(at step 2)->2(at step 3)
3: 0->2(at step 2)->1(at step 5)->0(at step 6)
4: 0->2(at step 2)->2(at step 4)->1(at step 5)
5: 0->1(at step 4)
6: 0->1(at step 5)
7: 0->0(at step 1)->2(at step 5)->2(at step 6)
8: 0->0(at step 5)
|
1
|
[
"0->2(at step 4)->2(at step 6)",
"0->1(at step 2)->2(at step 3)",
"0->2(at step 2)->1(at step 5)->0(at step 6)",
"0->2(at step 2)->2(at step 4)->1(at step 5)",
"0->1(at step 4)",
"0->1(at step 5)",
"0->0(at step 1)->2(at step 5)->2(at step 6)",
"0->0(at step 5)"
] |
2d_turing_machine
|
Multi-step Reasoning
|
|
State Prediction
| 5 |
Reveal face-down card strategy
|
Easy
|
Hard
|
Spider Solitaire
# OBJECTIVE
Spider is played with eight decks of 13 spade cards each, totaling 104 unique cards. The goal is to arrange all cards in a King-to-Ace sequence in the same suit and move them to the foundation piles. Once all sequences are moved to the foundations, the game is won.
# SETUP
The game features waste piles, a stock pile, and foundation piles. Waste piles are where the action happens, and the stock pile provides new cards when necessary.
**Waste Pile Numbering**: Waste piles are numbered from left to right starting with `0`. The cards within each waste pile are also numbered starting from the bottom card.
# GAME BOARD COMPONENTS
## **Stock Pile**
The **Stock Pile** holds all remaining cards and is used to deal new cards into the waste piles.
Stock Pile is in the top left corner of the board.
- **Staggered Card Stacking**: Cards are stacked in layers, and the number of layers indicates how many more times you can deal cards to the waste piles. Each deal moves one card face-up to each waste pile.
## **Waste Piles**
The **Waste Piles** are where cards are played and organized.
Waste Piles are on the bottom of the chessboard
- **Face-Up vs. Face-Down Cards**: Cards are stacked with face-up cards visible and face-down cards hidden. Only face-up cards can be played. When a face-down card becomes the top card of a pile, it is turned face-up and can be played.
- **Staggered Cards**: Cards in each waste pile are arranged so that face-up cards are on top, and face-down cards are beneath. As you move cards, new face-down cards are revealed.
- **Card Numbering and Screen Position**:
- **Waste Pile Numbering**: Piles are numbered from left to right starting with `0` for the leftmost pile.
- The card at the bottom of each waste pile (usually face-down) is numbered **0** and is the **topmost visible card** in the pile.
- As you move upward in the pile, the next cards are numbered **1**, **2**, **3**, and so on.
- Visually, the bottom card (number **0**) is the one closest to the top of the screen, and the cards above it are stacked above in the pile, going downwards.
## **Foundation Pile**
Foundation pile stores all the arranged suit. When a suit is arranged in sequence, it may be removed to a foundation pile. If all suits are moved to the foundations, the game is won.
Foundation Pile is in the top right corner of the board.
# MOVING CARDS
- **Movement Conditions**: Cards can be moved to another pile as long as they form a **descending sequence of the same suit**, i.e., a King-to-Ace sequence. When moving cards, the new sequence must be a **same-suit sequence** and follow the **descending order** from K, Q, J, 10, 9, ..., 2, A.
- **Same-Suit Sequence Requirement**: The card being moved must be placed on a top card that is of the **same suit** and has a **higher rank** (e.g., a Q can be placed on a K). The top card of the target pile must be larger in rank than the card being moved, and both must be of the same suit.
- **Moving a Sequence**: A complete **descending sequence** of cards (such as K, Q, J, 10, etc.) can be moved from one pile to another, as long as the sequence is in **descending order** and all the cards in the sequence are of the **same suit**.
- **Face-Down Cards**: If the sequence you are moving includes face-down cards, they will be flipped face-up once they are moved. After flipping, the newly face-up cards can continue to be moved or interacted with.
- **Example**: If you have a sequence of K-Q-J-10-9-8-7 in the same suit, you can move a card 6 that has the same suit to the top of this pile, resulting in a new sequence K-Q-J-10-9-8-7-6.
- **Empty Pile Rule**: An empty waste pile can accept any card. After placing the card, you can continue adding a descending same-suit sequence to that pile.
- **Reveal Cards**: If a move leaves a face-down card on top, it will be turned face-up.
# DEALING
Click the stock to deal a new row of face-up cards to the waste piles. You may not deal if there is an empty waste pile.
# STRATEGY
- Turn face-down cards face-up.
- Form runs of the same suit in descending order.
- Use empty waste piles strategically.
# VARIANTS
In **circular spider solitaire**, a King can be placed on an Ace, allowing for extended sequences.
# **NOTE: Important Numbering Reminder**
- **Waste Pile Numbering**: Waste piles are numbered from **left to right** starting with `0` for the leftmost pile.
- **Card Numbering within Waste Piles**: The **bottom-most card** of each pile (usually face-down) is numbered **0**, and the cards above it are numbered **1**, **2**, **3**, etc., moving upwards in the pile.
- **Please Pay Attention** to both the waste pile and card numbering methods, as they will help you navigate and make strategic decisions effectively.
**Question:** What should I do if I want to reveal the first face-down card in waste pile 7?
**Options:**
A. No action is needed; there are no face-down cards in this pile.
B. There is no immediate way to reveal it; we should move cards from other piles first and wait for more information.
C. We should move the 5-th card of pile 0 to pile 3.
D. We should move the 1-th card of pile 2 to pile 4.
E. We should move the 5-th card of pile 1 to pile 3.
F. We should move the 5-th card of pile 3 to pile 2.
G. We should move the top card of pile 7 to pile 6.
H. We should move the 4-th card of pile 4 to pile 3.
|
G
|
[
"A. No action is needed; there are no face-down cards in this pile.",
"B. There is no immediate way to reveal it; we should move cards from other piles first and wait for more information.",
"C. We should move the 5-th card of pile 0 to pile 3.",
"D. We should move the 1-th card of pile 2 to pile 4.",
"E. We should move the 5-th card of pile 1 to pile 3.",
"F. We should move the 5-th card of pile 3 to pile 2.",
"G. We should move the top card of pile 7 to pile 6.",
"H. We should move the 4-th card of pile 4 to pile 3."
] |
spider_solitaire
|
Pattern Recognition & Matching
|
|
Target Perception
| 1 |
Ask the position of player.
|
Easy
|
Easy
|
**Rules:**
1. This is a maze mini-game.The player needs to navigate around obstacles to reach the destination and achieve victory.
2. The red circle represents the player, the green block is the goal and the blue blocks are obstacles.
3. The player can only move within the white blocks.
**Question:** Which of the following are the coordinates of the player?
**Options:**
A. (0, 6)
B. (2, 6)
C. (1, 7)
D. (1, 6)
E. (1, 5)
|
D
|
[
"A. (0, 6)",
"B. (2, 6)",
"C. (1, 7)",
"D. (1, 6)",
"E. (1, 5)"
] |
maze
|
Strategy Planning
|
|
Target Perception
| 2 |
height_comparison
|
Easy
|
Easy
|
Rules:
1. Player can only walk on top of cubes
2. Player can climb ladders if they can reach the cube under the ladder
3. From a ladder, player can reach the top of the last cube with the ladder
4. Blue cube is start position, red cube is goal position
5. Green cubes are numbered points (1, 2, and 3)
What is the correct height relationship between the three numbered points? Use '<' for 'lower than' and '=' for 'same height as'.
Options:
1: 3 < 1 = 2
2: 1 < 2 < 3
3: 1 = 2 < 3
4: 1 = 3 < 2
5: 1 < 2 = 3
6: 3 < 2 < 1
7: 2 < 1 = 3
8: 3 < 1 < 2
|
1
|
[
"3 < 1 = 2",
"1 < 2 < 3",
"1 = 2 < 3",
"1 = 3 < 2",
"1 < 2 = 3",
"3 < 2 < 1",
"2 < 1 = 3",
"3 < 1 < 2"
] |
3d_maze
|
3D Spatial Perception & Reasoning
|
|
State Prediction
| 1 |
Given a sequence of player moves, predict the final position of the player
|
Easy
|
Medium
|
This is a Sokoban puzzle where black figure is player, green X is target, brown box with X is box to push, brown tiles are walls, and light brown areas are movable spaces.The coordinates (x, y) in this puzzle represent the matrix format.If the player makes these moves: Up → Left → Left → Left → Up, where will player end up?
Options:
[1] (2, 1)
[2] (3, 1)
[3] (2, 2)
[4] (3, 2)
[5] (1, 1)
[6] (3, 3)
[7] (2, 3)
[8] (1, 3)
|
5
|
[
"(2, 1)",
"(3, 1)",
"(2, 2)",
"(3, 2)",
"(1, 1)",
"(3, 3)",
"(2, 3)",
"(1, 3)"
] |
sokoban
|
Strategy Planning
|
|
State Prediction
| 2 |
Questions about predicting the number of live cells after 1 iteration
|
Easy
|
Medium
|
Conway's Game of Life is a cellular automaton where each cell in the grid can be either alive (black) or dead (white).
Each cell interacts with its eight neighbors, which are the cells that are horizontally, vertically, or diagonally adjacent. For a cell at position (r,c), its neighbors are:
- (r-1,c-1) (r-1,c) (r-1,c+1) [above row]
- (r,c-1) (r,c) (r,c+1) [same row]
- (r+1,c-1) (r+1,c) (r+1,c+1) [below row]
Region boundaries wrap around to the opposite side:
- A cell at the top edge connects to cells at the bottom edge
- A cell at the left edge connects to cells at the right edge
- Corner cells connect to the diagonally opposite corner
For example, in a 3x3 region:
- Cell (0,0)'s top neighbor is (2,0)
- Cell (0,0)'s left neighbor is (0,2)
- Cell (0,0)'s top-left neighbor is (2,2)
The game evolves in discrete steps according to these rules:
1. Any live cell with fewer than two live neighbors dies (underpopulation)
2. Any live cell with two or three live neighbors lives on to the next generation
3. Any live cell with more than three live neighbors dies (overpopulation)
4. Any dead cell with exactly three live neighbors becomes alive (reproduction)
In the image, black squares represent live cells, white squares represent dead cells, and the grid lines help visualize the cell boundaries.
In this grid, we use (row, col) coordinates where:
- row increases from top to bottom (0 at top)
- col increases from left to right (0 at left)
For example, the top-left cell is at (0, 0), and the cell below it is at (1, 0).
After 1 iterations, how many live cells will remain in the grid?
Options:
A: 7
B: 1
C: 4
D: 2
E: 9
F: 6
G: 5
H: 3
|
E
|
[
"A: 7",
"B: 1",
"C: 4",
"D: 2",
"E: 9",
"F: 6",
"G: 5",
"H: 3"
] |
lifegame
|
Multi-step Reasoning
|
|
Target Perception
| 1 |
color_description
|
Medium
|
Easy
|
Rules:
1. Colors change gradually along rows or columns.
2. A gradient transitions between two colors.
3. Each row or column can have its own independent gradient pattern.
4. Row and column indexes begin from 1 at the top-left corner.
Question:
What color is the cell at row 6, column 5?
Options:
1: purple
2: vivid red
3: bright blue
4: vivid dark green
5: bright red
6: light gray
7: red
8: vivid blue
|
1
|
[
"purple",
"vivid red",
"bright blue",
"vivid dark green",
"bright red",
"light gray",
"red",
"vivid blue"
] |
hue
|
Pattern Recognition & Matching
|
|
State Prediction
| 1 |
Select a coordinate and determine whether a ball can be placed at this coordinate. If so, what would happen after the place of the ball.
|
Hard
|
Medium
|
Pyramid Chess Rules:
0.Game Board:
The game board is square and comes in various sizes: 3x3, 4x4, or 5x5. On an nxn board, there are n levels (0 to n-1). At each level k, the x and y coordinates range from 0 to n-1-k, resulting in (n-k)**2 slots per level. The slots in the lower levels act as the base for the slots in the upper levels. Slots at level 0 have no base, while slots at level j (j!=0) with coordinates (m,n) are supported by four base slots (m,n),(m+1,n),(m,n+1),(m+1,n+1) from level j-1.
1.Players and Initial Setup:
The game is played between two players, designated as PLAYER_0 and PLAYER_1, each using balls of a distinct color from their color pool, blue balls for PLAYER_0 and red balls for PLAYER_1. Players take turns placing their balls on a square game board. The number of balls available to each player depends on the size of the board: on a 3x3 board, each player has 7 balls; on a 4x4 board, each has 15 balls; and on a 5x5 board, PLAYER_0 (the first player to place a ball) has 28 balls, while PLAYER_1 has 27 balls.
2.Placing Balls and Creating New Slots:
At the start of the game, the lowest level of the board (Level 0) is completely open and balls can be placed in any available slot on this level(since there is no base for slots in level 0, slots in level 0 have full base). After a ball is placed in a slot, that slot is no longer available for placing another ball. A ball can only be placed on the upper level if it is supported by a fully completed 2x2 block of balls on the level directly beneath, which means all the base of the slot is full(there is a ball in each of these slots).
3.Take-back mechnism:
If a player places a ball that completes a 2x2 block of the same color (all four balls belonging to that player), they may return up to two balls from the block to their color pool. A ball can only be removed if it does not have another ball directly above it, as removing a "base" ball would collapse the pyramid. Returning a ball reopens the slot it occupied, allowing it to be used for future placements, but the rule requiring a full 2x2 block as a base for placing balls on upper levels still applies.
4.Winning the Game:
The game ends when one player successfully places the last ball on top of the pyramid. The player who place the ball on the top of the pyramid wins.
Question: Can a ball be placed at coordinate [2, 1] on Level 1? If a red ball is placed there, what would be the outcome?
Options:
1. Can place and no balls taken
2. Can place and then balls can be taken
3. Cannot place, position already occupied
4. Cannot place, ball not ready below
|
4
|
[
"Can place and no balls taken",
"Can place and then balls can be taken",
"Cannot place, position already occupied",
"Cannot place, ball not ready below"
] |
pyramidchess
|
3D Spatial Perception & Reasoning
|
|
Target Perception
| 1 |
color_description
|
Easy
|
Easy
|
Rules:
1. Colors change gradually along rows or columns.
2. A gradient transitions between two colors.
3. Each row or column can have its own independent gradient pattern.
4. Row and column indexes begin from 1 at the top-left corner.
Question:
What color is the cell at row 2, column 2?
Options:
1: green
2: yellow
3: black
4: bright purple
5: purple
6: dark orange
7: bright red
8: vivid bright red
|
4
|
[
"green",
"yellow",
"black",
"bright purple",
"purple",
"dark orange",
"bright red",
"vivid bright red"
] |
hue
|
Pattern Recognition & Matching
|
|
Target Perception
| 5 |
Find the points the given player has got within the given Nine-grid.
|
Medium
|
Medium
|
Now I'll give you a picture, which shows a screenshot of Ultra TicTacToe. The introduction of Ultra TicTacToe is as follows:
1. Board and coordinate representation: In this game, the board is divided into 9 3*3 squares(called Nine-grids). At the same time, we use $(i, j, row, col)$ to represent the coordinates of a cell: $(i, j)$ represents the coordinates of the Nine-grid; $(row, col)$ represents the coordinate of the cell within the Nine-grid; $i, j, row, col$ all range from 1 to 3. Two players take turns placing pieces on the board to mark the cells on the board, with the first player using "X" and the second player using "O" (this is the same as traditional TicTacToe).
2. Rules for placing chess pieces: After the game starts, the first player places a chess piece in any cell in the Nine-grid in the middle (i.e., the Nine-grid (2, 2)). After that, the coordinates of each chess piece placed in the Nine-grid are the same as the coordinates of the Nine-grid in which the opponent's last chess piece was placed; for example, if the first player places a chess piece at the coordinates (2, 2, 3, 1) in the first step, then the second player needs to choose a chess piece in the Nine-grid (3, 1) in the second step.
3. Scoring rules: For each player, each "Straight" (i.e., three identical chess pieces connected in a line, such as in the same row, the same column, or a diagonal line) in each Nine-grid is counted as 1 point. More than 1 point can be counted in each Nine-grid.
Now I will give you a question about the game. Please extract information from the picture I give you, think carefully, reason, and answer: How many points has the First Player got within the Nine-grid (2, 1)? Options: 1. 13 2. 10 3. 4 4. 2 5. 14 6. 6 7. 1 8. 0
|
8
|
[
"13",
"10",
"4",
"2",
"14",
"6",
"1",
"0"
] |
ultra_tictactoe
|
Strategy Planning
|
|
State Prediction
| 3 |
Questions about counting state changes of specific cells over iterations
|
Medium
|
Medium
|
Conway's Game of Life is a cellular automaton where each cell in the grid can be either alive (black) or dead (white).
Each cell interacts with its eight neighbors, which are the cells that are horizontally, vertically, or diagonally adjacent. For a cell at position (r,c), its neighbors are:
- (r-1,c-1) (r-1,c) (r-1,c+1) [above row]
- (r,c-1) (r,c) (r,c+1) [same row]
- (r+1,c-1) (r+1,c) (r+1,c+1) [below row]
Region boundaries wrap around to the opposite side:
- A cell at the top edge connects to cells at the bottom edge
- A cell at the left edge connects to cells at the right edge
- Corner cells connect to the diagonally opposite corner
For example, in a 3x3 region:
- Cell (0,0)'s top neighbor is (2,0)
- Cell (0,0)'s left neighbor is (0,2)
- Cell (0,0)'s top-left neighbor is (2,2)
The game evolves in discrete steps according to these rules:
1. Any live cell with fewer than two live neighbors dies (underpopulation)
2. Any live cell with two or three live neighbors lives on to the next generation
3. Any live cell with more than three live neighbors dies (overpopulation)
4. Any dead cell with exactly three live neighbors becomes alive (reproduction)
In the image, black squares represent live cells, white squares represent dead cells, and the grid lines help visualize the cell boundaries.
In this grid, we use (row, col) coordinates where:
- row increases from top to bottom (0 at top)
- col increases from left to right (0 at left)
For example, the top-left cell is at (0, 0), and the cell below it is at (1, 0).
Consider the cell at position (0, 2). How will its state change over the next 3 iterations?
Options:
A: Initially: dead → Step 1: alive → Step 2: dead → Step 3: alive
B: Initially: alive → Step 1: dead → Step 2: alive → Step 3: alive
C: Initially: dead → Step 1: alive → Step 2: dead → Step 3: dead
D: Initially: dead → Step 1: alive → Step 2: alive → Step 3: dead
E: Initially: alive → Step 1: dead → Step 2: alive → Step 3: dead
F: Initially: alive → Step 1: alive → Step 2: dead → Step 3: alive
G: Initially: dead → Step 1: dead → Step 2: alive → Step 3: dead
H: Initially: dead → Step 1: dead → Step 2: alive → Step 3: alive
|
G
|
[
"A: Initially: dead → Step 1: alive → Step 2: dead → Step 3: alive",
"B: Initially: alive → Step 1: dead → Step 2: alive → Step 3: alive",
"C: Initially: dead → Step 1: alive → Step 2: dead → Step 3: dead",
"D: Initially: dead → Step 1: alive → Step 2: alive → Step 3: dead",
"E: Initially: alive → Step 1: dead → Step 2: alive → Step 3: dead",
"F: Initially: alive → Step 1: alive → Step 2: dead → Step 3: alive",
"G: Initially: dead → Step 1: dead → Step 2: alive → Step 3: dead",
"H: Initially: dead → Step 1: dead → Step 2: alive → Step 3: alive"
] |
lifegame
|
Multi-step Reasoning
|
|
State Prediction
| 4 |
Predict cell reveal outcome
|
Easy
|
Hard
|
This is a Minesweeper game. The size of the chessboard is 4x4, and there are a total of 3 mines hidden on the board.
The numbers on the board indicate how many mines are adjacent to that cell, including diagonals. Cells marked with "F" (flagged) are identified as potential locations of mines based on logical deduction or prior knowledge. These flagged cells play a critical role in guiding your reasoning for answering the questions. Cells with no numbers and no flags are safe and contain no adjacent mines.
The board uses a coordinate system where the top-left cell corresponds to (0,0), and the rows and columns are numbered starting from 0.
Please use the provided board configuration and logical reasoning to deduce the correct answers to the following questions:
**Question:** What will happen if the player reveals the cell at (1,2)?
**Options:**
A: The game will end because the cell contains a mine.
B: The cell will reveal an empty area, and adjacent cells will also be revealed.
C: The cell will reveal the number 0.
D: The cell will reveal the number 2.
|
D
|
[
"A: The game will end because the cell contains a mine. ",
"B: The cell will reveal an empty area, and adjacent cells will also be revealed. ",
"C: The cell will reveal the number 0. ",
"D: The cell will reveal the number 2."
] |
minesweeper
|
Multi-step Reasoning
|
|
State Prediction
| 7 |
Infer Pinky's next move
|
Medium
|
Medium
|
# Game Overview
Pac-Man is a maze arcade game where the player controls Pac-Man to eat as many beans as possible while avoiding ghosts. If a ghost catches Pac-Man, the game ends.
# Basic Elements
- **Pac-Man**: The yellow circular character that the player controls
- **Beans**: Yellow dots that Pac-Man can eat to score points
- **Walls**: Blue barriers that restrict movement
- **Ghosts**: Two ghosts (Pinky and Blinky) that chase Pac-Man
# Game Rules
- Pac-Man must eat beans while avoiding ghosts
- Each bean eaten adds 1 point to the score
- The game ends if a ghost catches Pac-Man
- Movement is restricted by walls
# Movement and Direction
- Pac-Man's mouth opening indicates its current direction
- The direction can be UP, DOWN, LEFT, or RIGHT
- Neither Pac-Man nor ghosts can move through walls
# **Ghost Behavior**
- **Pinky** (Pink Ghost): Targets up to 4 spaces ahead of Pac-Man's current position and direction (stops at walls)
- **Blinky** (Red Ghost): Directly targets Pac-Man's current position
- Both ghosts follow a movement priority system based on the direction they are trying to move:
- When moving in more than one direction is optimal, the priority order for both ghosts is **UP > DOWN > LEFT > RIGHT**.
- This means if a ghost has multiple possible directions to move in, it will first attempt to move **UP** if possible, then **DOWN**, followed by **LEFT**, and finally **RIGHT** if all other directions are blocked.
# Board Layout
- The board is surrounded by walls on all four sides
- Position (0,0) is located at the top-left corner wall
- Movement grid uses (row, column) coordinates
# Scoring
The score equals the total number of beans eaten by Pac-Man
**Question:** If Pac-Man stays still, where will Pinky move in the next turn?
**Options:**
A. Pinky will move one step UP
B. Pinky will move one step DOWN
C. Pinky will move one step RIGHT
D. Pinky will move one step LEFT
|
A
|
[
"A. Pinky will move one step UP",
"B. Pinky will move one step DOWN",
"C. Pinky will move one step RIGHT",
"D. Pinky will move one step LEFT"
] |
pacman
|
Strategy Planning
|
|
State Prediction
| 3 |
Simulate clear operation
|
Easy
|
Medium
|
# **Game Overview**
Jewel2 is a strategic puzzle game played on a grid. Your primary objective is to eliminate elements by forming horizontal or vertical lines of three or more identical items. Successfully eliminating elements increases your score and clears space on the board for new elements to appear.
# **Elements**
## **Basic Elements**
- **A, B, C, D, E**
- **Description**: These are the standard elements in the game.
- **Shape**: Diamond-shaped gems in various colors (Red, Green, Blue, Yellow, Purple).
- A: Red
- B: Green
- C: Blue
- D: Yellow
- E: Purple
- **Interactions**:
- **Clearing**: When three or more identical basic elements align horizontally or vertically, they are eliminated from the board.
- **Swapping**: Basic elements can be swapped with adjacent basic elements to form eliminations.
## **Special Elements**
- **a, b, c, d, e, +, |**
- **Description**: These elements possess unique abilities that trigger specific elimination patterns when activated.
- **Shape**:
- **a, b, c, d, e**: Round gems in various colors (Red, Green, Blue, Yellow, Purple).
- a: Red
- b: Green
- c: Blue
- d: Yellow
- e: Purple
- **+**: A round black gem with low transparency.
- **|**: A tall, rectangular cyan gem.
- **Effects of Special Elements**:
- **a, b, c, d, e**:
- **Function**: Clearing one of these removes all corresponding uppercase basic elements from the board.
- *Example*: Clearing element 'a' will eliminate all 'A's on the board.
- **| (Vertical Clear)**:
- **Function**: Activating this element clears all elements in its vertical column.
- **+ (Surrounding Clear)**:
- **Function**: Activating this element clears all elements within a distance of 1 from its position, including diagonals.
- **Notes**:
- Special elements do **not** trigger further eliminations if they remove other special elements.
- Swapping involving special elements is **not allowed** and will be rejected by the game.
# **Commands**
## **Available Operations**
1. **Clear Operation**
- **Syntax**: clear x y
- **Description**: Attempts to clear the element located at coordinates (x, y).
- **Conditions**:
- The targeted element must form a valid elimination (i.e., be part of a horizontal or vertical line of three or more identical elements).
- If the element is special, its unique ability is activated upon clearing.
- **State Changes**:
- **Basic Element**: If the clearance is valid, the element(s) are removed, the score (Total Cleared) increases accordingly, and new elements fall into place to fill the gaps.
- **Special Element**: Activating a special element triggers its specific clearance effect as described above.
2. **Swap Operation**
- **Syntax**: swap x y pos
- **Parameters**:
- (x, y): Coordinates of the element to be swapped.
- pos: Direction to swap the element (up, down, left, right).
- **Description**: Swaps the element at (x, y) with the adjacent element in the specified direction.
- **pos** can be one of four directions:
- **up**: Swap with the element directly above (in the same column but one row above).
- **down**: Swap with the element directly below (in the same column but one row below).
- **left**: Swap with the element directly to the left (in the same row but one column left).
- **right**: Swap with the element directly to the right (in the same row but one column right).
- **Conditions**:
- Both elements involved in the swap must be basic elements. Swaps involving special elements are rejected.
- The swap must result in a valid elimination; otherwise, the swap is undone.
- **State Changes**:
- **Successful Swap**: Elements are exchanged, any resulting eliminations are performed, and the score (Total Cleared) is updated accordingly.
- **Unsuccessful Swap**: Elements revert to their original positions, and no changes are made to the score.
# **Coordinate System**
- The board uses **0-based coordinates**.
- **Top-left cell**: (0, 0)
- **Bottom-right cell**: ({size_minus_one}, {size_minus_one})
### **Coordinate Explanation**:
- **x (Row)**: Represents the **row number** of the element. Rows are numbered from **top to bottom**, starting from 0.
- *Example*: In a 5x5 grid, the first row (topmost) would have x = 0, the second row would have x = 1, and so on.
- **y (Column)**: Represents the **column number** of the element. Columns are numbered from **left to right**, starting from 0.
- *Example*: In a 5x5 grid, the first column (leftmost) would have y = 0, the second column would have y = 1, and so on.
### **Coordinate Example**:
- To refer to the element located in the second row and third column, you would use coordinates (1, 2).
- To refer to the element in the fifth row and the first column, you would use coordinates (4, 0).
# **Gameplay Mechanics**
## **Score Tracking**
- **Total Cleared**: Represents the cumulative number of elements that have been eliminated throughout the game.
- **Incremented By**: The number of elements cleared in each successful operation (clear or swap).
# **Objective**
Maximize your **Total Cleared** count by strategically performing clear and swap operations to eliminate as many elements as possible. Effective use of special elements can significantly enhance your score by triggering large-scale eliminations.
# **How to Play**
## **Starting the Game**
1. **Initialization**:
- Upon launching Jewel2, a grid is presented, populated with a mix of basic and special elements based on predefined probabilities.
2. **Understanding the Interface**:
- **Grid Display**: Each cell in the grid represents an element. Basic elements are denoted by uppercase letters (A-E), while special elements use lowercase letters or symbols (a, b, c, d, e, +, |).
- **Score Display**: The current **Total Cleared** count is visible, updating as you eliminate elements.
- **Command Input**: A text input area is provided where you can enter commands (clear or swap) to interact with the game.
## **Performing Operations**
1. **Clear Operation**:
- **Objective**: Remove specific elements to form or extend lines of three or more identical elements.
- **How to Execute**:
- Identify the coordinates (x, y) of the element you wish to clear.
- Enter the command in the format: clear x y.
- Example: To clear the element at row 2, column 3, input clear 2 3.
- **Outcomes**:
- **Successful Clear**: If the targeted element is part of a valid elimination, it and any adjacent identical elements are removed, the **Total Cleared** score increases by the number of elements cleared, and new elements fall into place.
- **Special Element Activation**: If a special element is cleared, its unique ability is triggered, resulting in additional eliminations as defined in the **Special Elements** section.
- **Unsuccessful Clear**: If the targeted element does not form a valid elimination, no changes occur, and the command is rejected.
2. **Swap Operation**:
- **Objective**: Rearrange elements to create new elimination opportunities.
- **How to Execute**:
- Identify the coordinates (x, y) of the element you wish to swap.
- Determine the direction pos (up, down, left, right) to which you want to swap the element.
- Enter the command in the format: swap x y pos.
- Example: To swap the element at row 1, column 1 with the element above it, input swap 1 1 up.
- **Outcomes**:
- **Successful Swap**: If the swap results in a valid elimination, the elements are exchanged, the resulting eliminations are performed, and the **Total Cleared** score is updated accordingly.
- **Unsuccessful Swap**: If the swap does not create any valid elimination or involves special elements, the swap is undone, and no changes are made to the score.
# **Additional Notes**
- **Special Element Chain Reactions**: Activating a special element's ability will **not** trigger further eliminations, even if other special elements are removed as a result.
- **Element Replenishment**: After each elimination, new elements are generated randomly to maintain a fully populated board, ensuring continuous gameplay.
- **Row and Column Elimination**: When checking whether an ordinary element can be eliminated, we check whether its rows and columns have three or more identical elements. If both rows and columns meet the elimination rule, both rows and columns are eliminated.
- **Chain Elimination**: After the elimination operation is performed and new elements are generated, no chain elimination will occur.
**Question:** What will happen if you execute clear 2 2?
**Options:**
A. Nothing will happen because the clear does not meet elimination conditions.
B. Trigger a special element, total cleared becomes 20.
C. Perform elimination, eliminate 5 elements, total cleared becomes 12.
D. Perform elimination, eliminate 4 elements, total cleared becomes 14.E. Perform elimination, eliminate 4 elements, total cleared becomes 14.
F. Perform elimination, eliminate 3 elements, total cleared becomes 12.
G. Perform elimination, eliminate 4 elements, total cleared becomes 15.
H. Perform elimination, eliminate 3 elements, total cleared becomes 16.
|
B
|
[
"A. Nothing will happen because the clear does not meet elimination conditions.",
"B. Trigger a special element, total cleared becomes 20.",
"C. Perform elimination, eliminate 5 elements, total cleared becomes 12.",
"D. Perform elimination, eliminate 4 elements, total cleared becomes 14.E. Perform elimination, eliminate 4 elements, total cleared becomes 14.",
"F. Perform elimination, eliminate 3 elements, total cleared becomes 12.",
"G. Perform elimination, eliminate 4 elements, total cleared becomes 15.",
"H. Perform elimination, eliminate 3 elements, total cleared becomes 16."
] |
jewel2
|
Pattern Recognition & Matching
|
|
Target Perception
| 3 |
Given current state and a region,Your task is to indentify which cell provided by options belongs to this region and has been placed a star.
|
Hard
|
Easy
|
We have a 8*8 grid.The grid is divided into 8 regions.
Cells with the same color belong to the same region.
Region with index 0 has the color of light pink.
Region with index 1 has the color of powder blue.
Region with index 2 has the color of light green.
Region with index 3 has the color of peach.
Region with index 4 has the color of red.
Region with index 5 has the color of yellow.
Region with index 6 has the color of cyan.
Region with index 7 has the color of orange.
In the image,a star is represented by a black dot. If a cell has been placed a star,a black dot will be shown on this cell.
We should place the star in this Star Battle Puzzle according to the following rules:
Each row must contain exactly 1 star(s).
Each column must contain 1 star(s).
Each region must contain exactly 1 star(s).
Stars cannot be adjacent to each other, including diagonally.
The cells in the grid are labeled with row and column numbers starting from 0. The top-left corner of the grid is (0, 0).
(x,y) means a cell at row x and column y.
Now we have placed some stars in the grid.
In the current puzzle state, region 4 is associated with color red.
Please identify which of the following cells in this region that contains a star?
Note that:If no stars have been placed in the target region,please choose the option "null"
Options:
1.(0,7)
2.(1,6)
3.(2,5)
4.(0,4)
5.(1,5)
6.(0,6)
7.(0,5)
8.(1,7)
|
5
|
[
"(0,7)",
"(1,6)",
"(2,5)",
"(0,4)",
"(1,5)",
"(0,6)",
"(0,5)",
"(1,7)"
] |
star_battle
|
Multi-step Reasoning
|
|
Strategy Optimization
| 4 |
Determine optimal move sequence to solve the cube
|
Medium
|
Hard
|
Rules: As shown in the figure, the Rubik's cube consists of both 3D views and an unfolded view. The 3D views show the cube from two angles: left-tilted 30 degrees looking down, and right-tilted ,30 degrees looking up. The cube has six faces: Upper (U), Down (D), Left (L), Right (R), Front (F), and Back (B). Each face can be rotated clockwise or counterclockwise.And for each face, the coordinates are determined based on the unfolded view: column number increases from left to right (0,1,2) and row number increases from bottom to top (0,1,2). Legend shown in the bottom left corner.Handedness issues in the 3D views can be ignored.An uppercase letter indicates which face to rotate ('F' for Front, 'B' for Back, 'L' for Left, 'R' for Right, 'U' for Upper, 'D' for Down), with a prime symbol (') denoting counterclockwise rotation and no prime symbol denoting clockwise rotation.How many moves are needed to solve the entire cube?Options: [1] 12, [2] 3, [3] 1, [4] 4, [5] 2, [6] 6, [7] 7, [8] 5
|
5
|
[
"12",
"3",
"1",
"4",
"2",
"6",
"7",
"5"
] |
rubiks_cube
|
3D Spatial Perception & Reasoning
|
|
State Prediction
| 3 |
Given a particular game state,a selected move and a selected cascade pile, the puzzle will present a question about which card is at the top of the cascade pile.
Your task is to indentify the card in the options.
|
Medium
|
Hard
|
In this FreeCell game:
we have 6 cascade piles, and their indexes are [0, 1, 2, 3, 4, 5]We have 4 freecell on the left top, and their indexes are 0,1,2,3.We have 4 foundation piles on the right top, and their indexes are 0,1,2,3.In FreeCell, cards can be moved according to specific rules: A card can be moved to a free cell if available, stacked in descending order alternating colors in cascade piles, or placed in foundation piles starting from Ace. Now, find the top card from cascade pile 1 after moving the card (Diamond,12) from Cascade 1 to FreeCell 2.the options are as follows:
1.(Heart, 3)
2.(Club, 2)
3.(Diamond, 7)
4.(Spade, A)
5.(Club, 1)
6.(Heart, A)
7.(Diamond, 2)
8.(Heart, J)
|
7
|
[
"(Heart, 3)",
"(Club, 2)",
"(Diamond, 7)",
"(Spade, A)",
"(Club, 1)",
"(Heart, A)",
"(Diamond, 2)",
"(Heart, J)"
] |
freecell
|
Pattern Recognition & Matching
|
|
State Prediction
| 5 |
Ask the points gained by shooting once where the ship is
|
Medium
|
Easy
|
The given image represents a simplified interface of the game Space Invaders. The enemy area is implicitly divided into a grid of cells, with the row and column numbers shown on the left and top sides of the grid respectively which you should strictly follow. Each cell is either empty or occupied by an incoming enemy which can be purple, blue or green. The ship is at the bottom row, aligned with one of the columns, which shoots the enemies using laser while dodging possible lasers from the enemies.
If the ship shoots, the enemy closest to the ship (i.e. the lowermost one) on the same column as the ship, if any, will be destroyed and disappear, adding points to the player's score and exposing the enemy behind (if any). Purple enemies are worth 30 points, blue enemies are worth 20 points, and green enemies are worth 10 points.
If the ship shoots at the current position, how many points will the player get? Give the number of the correct option.
Options:
1: 10
2: 20
3: 30
4: 0
|
1
|
[
"10",
"20",
"30",
"0"
] |
space_invaders
|
Strategy Planning
|
|
Target Perception
| 1 |
Ask the position of player.
|
Medium
|
Easy
|
**Rules:**
1. This is a maze mini-game.The player needs to navigate around obstacles to reach the destination and achieve victory.
2. The red circle represents the player, the green block is the goal and the blue blocks are obstacles.
3. The player can only move within the white blocks.
**Question:** Which of the following are the coordinates of the player?
**Options:**
A. (3, 3)
B. (3, 1)
C. (3, 2)
D. (2, 2)
E. (4, 2)
|
C
|
[
"A. (3, 3)",
"B. (3, 1)",
"C. (3, 2)",
"D. (2, 2)",
"E. (4, 2)"
] |
maze
|
Strategy Planning
|
|
Target Perception
| 5 |
Count specific colors on a face
|
Easy
|
Easy
|
Rules: As shown in the figure, the Rubik's cube consists of both 3D views and an unfolded view. The 3D views show the cube from two angles: left-tilted 30 degrees looking down, and right-tilted ,30 degrees looking up. The cube has six faces: Upper (U), Down (D), Left (L), Right (R), Front (F), and Back (B). Each face can be rotated clockwise or counterclockwise.And for each face, the coordinates are determined based on the unfolded view: column number increases from left to right (0,1,2) and row number increases from bottom to top (0,1,2). Legend shown in the bottom left corner.Handedness issues in the 3D views can be ignored.An uppercase letter indicates which face to rotate ('F' for Front, 'B' for Back, 'L' for Left, 'R' for Right, 'U' for Upper, 'D' for Down), with a prime symbol (') denoting counterclockwise rotation and no prime symbol denoting clockwise rotation. How many yellow squares are there on the Front face?
Options: [1] 6, [2] 5, [3] 2, [4] 1, [5] 7, [6] 0, [7] 4, [8] 3
|
8
|
[
"6",
"5",
"2",
"1",
"7",
"0",
"4",
"3"
] |
rubiks_cube
|
3D Spatial Perception & Reasoning
|
|
Target Perception
| 5 |
Provide the higher level status of a coordinate: Is the coordinate legal? Does it contain a ball? Can the ball be taken? Can a ball be placed?
|
Medium
|
Medium
|
Pyramid Chess Rules:
0.Game Board:
The game board is square and comes in various sizes: 3x3, 4x4, or 5x5. On an nxn board, there are n levels (0 to n-1). At each level k, the x and y coordinates range from 0 to n-1-k, resulting in (n-k)**2 slots per level. The slots in the lower levels act as the base for the slots in the upper levels. Slots at level 0 have no base, while slots at level j (j!=0) with coordinates (m,n) are supported by four base slots (m,n),(m+1,n),(m,n+1),(m+1,n+1) from level j-1.
1.Players and Initial Setup:
The game is played between two players, designated as PLAYER_0 and PLAYER_1, each using balls of a distinct color from their color pool, blue balls for PLAYER_0 and red balls for PLAYER_1. Players take turns placing their balls on a square game board. The number of balls available to each player depends on the size of the board: on a 3x3 board, each player has 7 balls; on a 4x4 board, each has 15 balls; and on a 5x5 board, PLAYER_0 (the first player to place a ball) has 28 balls, while PLAYER_1 has 27 balls.
2.Placing Balls and Creating New Slots:
At the start of the game, the lowest level of the board (Level 0) is completely open and balls can be placed in any available slot on this level(since there is no base for slots in level 0, slots in level 0 have full base). After a ball is placed in a slot, that slot is no longer available for placing another ball. A ball can only be placed on the upper level if it is supported by a fully completed 2x2 block of balls on the level directly beneath, which means all the base of the slot is full(there is a ball in each of these slots).
3.Take-back mechnism:
If a player places a ball that completes a 2x2 block of the same color (all four balls belonging to that player), they may return up to two balls from the block to their color pool. A ball can only be removed if it does not have another ball directly above it, as removing a "base" ball would collapse the pyramid. Returning a ball reopens the slot it occupied, allowing it to be used for future placements, but the rule requiring a full 2x2 block as a base for placing balls on upper levels still applies.
4.Winning the Game:
The game ends when one player successfully places the last ball on top of the pyramid. The player who place the ball on the top of the pyramid wins.
Question: What is the status of the ball on Level 0, which has coordinate ([10, 5])?
Is the coordinate legal? Does it contain a ball? Can the ball be taken(has no ball directly above it)? Can a ball be placed?Options:
1. The coordinate is out of bound
2. It contain a ball and the ball can't be taken
3. It contain a ball and can be taken
4. It doesn't contain a ball and a ball can't be put here
5.It doesn't contain a ball and a ball can be put here
|
1
|
[
"The coordinate is out of bound",
"It contain a ball and the ball can't be taken",
"It contain a ball and can be taken",
"It doesn't contain a ball and the player can put a ball here this turn",
"It doesn't contain a ball and the player can't put a ball here this turn"
] |
pyramidchess
|
3D Spatial Perception & Reasoning
|
|
Strategy Optimization
| 6 |
Find the optimal sequence of moves to reach a specific position
|
Hard
|
Hard
|
This is a Sokoban puzzle where black figure is player, green X is target, brown box with X is box to push, brown tiles are walls, and light brown areas are movable spaces.The coordinates (x, y) in this puzzle represent the matrix format.Treat the boxes as walls,What is the shortest sequence of moves for human to move himself from position (5, 1) to position (1, 3)?
Options:
[1] Up → Down → Right → Right → Left → Up
[2] Right → Up → Down → Right → Left
[3] Up → Up → Right → Right → Down → Up
[4] Up → Down → Right → Right → Right → Up
[5] Up → Right → Left → Right → Left → Up
[6] Up → Up → Up → Right → Right → Up
[7] Right → Down → Down → Down → Down → Left → Up → Down
[8] Down → Right → Right → Left → Left
|
6
|
[
"Up → Down → Right → Right → Left → Up",
"Right → Up → Down → Right → Left",
"Up → Up → Right → Right → Down → Up",
"Up → Down → Right → Right → Right → Up",
"Up → Right → Left → Right → Left → Up",
"Up → Up → Up → Right → Right → Up",
"Right → Down → Down → Down → Down → Left → Up → Down",
"Down → Right → Right → Left → Left"
] |
sokoban
|
Strategy Planning
|
|
Target Perception
| 0 |
Choose a random coordinate and ask what status is the cooradinate
|
Medium
|
Easy
|
Pyramid Chess Rules:
0.Game Board:
The game board is square and comes in various sizes: 3x3, 4x4, or 5x5. On an nxn board, there are n levels (0 to n-1). At each level k, the x and y coordinates range from 0 to n-1-k, resulting in (n-k)**2 slots per level. The slots in the lower levels act as the base for the slots in the upper levels. Slots at level 0 have no base, while slots at level j (j!=0) with coordinates (m,n) are supported by four base slots (m,n),(m+1,n),(m,n+1),(m+1,n+1) from level j-1.
1.Players and Initial Setup:
The game is played between two players, designated as PLAYER_0 and PLAYER_1, each using balls of a distinct color from their color pool, blue balls for PLAYER_0 and red balls for PLAYER_1. Players take turns placing their balls on a square game board. The number of balls available to each player depends on the size of the board: on a 3x3 board, each player has 7 balls; on a 4x4 board, each has 15 balls; and on a 5x5 board, PLAYER_0 (the first player to place a ball) has 28 balls, while PLAYER_1 has 27 balls.
2.Placing Balls and Creating New Slots:
At the start of the game, the lowest level of the board (Level 0) is completely open and balls can be placed in any available slot on this level(since there is no base for slots in level 0, slots in level 0 have full base). After a ball is placed in a slot, that slot is no longer available for placing another ball. A ball can only be placed on the upper level if it is supported by a fully completed 2x2 block of balls on the level directly beneath, which means all the base of the slot is full(there is a ball in each of these slots).
3.Take-back mechnism:
If a player places a ball that completes a 2x2 block of the same color (all four balls belonging to that player), they may return up to two balls from the block to their color pool. A ball can only be removed if it does not have another ball directly above it, as removing a "base" ball would collapse the pyramid. Returning a ball reopens the slot it occupied, allowing it to be used for future placements, but the rule requiring a full 2x2 block as a base for placing balls on upper levels still applies.
4.Winning the Game:
The game ends when one player successfully places the last ball on top of the pyramid. The player who place the ball on the top of the pyramid wins.
Question: What is the status of the ball on Level 0, which has coordinate ([0, 3])?
Options:
1. PLAYER_0
2. PLAYER_1
3. Empty
4. Index out of bound
|
2
|
[
"PLAYER_0",
"PLAYER_1",
"Empty",
"Index out of bound"
] |
pyramidchess
|
3D Spatial Perception & Reasoning
|
|
Target Perception
| 1 |
Questions about counting the current number of live cells in the grid
|
Hard
|
Easy
|
Conway's Game of Life is a cellular automaton where each cell in the grid can be either alive (black) or dead (white).
Each cell interacts with its eight neighbors, which are the cells that are horizontally, vertically, or diagonally adjacent. For a cell at position (r,c), its neighbors are:
- (r-1,c-1) (r-1,c) (r-1,c+1) [above row]
- (r,c-1) (r,c) (r,c+1) [same row]
- (r+1,c-1) (r+1,c) (r+1,c+1) [below row]
Region boundaries wrap around to the opposite side:
- A cell at the top edge connects to cells at the bottom edge
- A cell at the left edge connects to cells at the right edge
- Corner cells connect to the diagonally opposite corner
For example, in a 3x3 region:
- Cell (0,0)'s top neighbor is (2,0)
- Cell (0,0)'s left neighbor is (0,2)
- Cell (0,0)'s top-left neighbor is (2,2)
The game evolves in discrete steps according to these rules:
1. Any live cell with fewer than two live neighbors dies (underpopulation)
2. Any live cell with two or three live neighbors lives on to the next generation
3. Any live cell with more than three live neighbors dies (overpopulation)
4. Any dead cell with exactly three live neighbors becomes alive (reproduction)
In the image, black squares represent live cells, white squares represent dead cells, and the grid lines help visualize the cell boundaries.
In this grid, we use (row, col) coordinates where:
- row increases from top to bottom (0 at top)
- col increases from left to right (0 at left)
For example, the top-left cell is at (0, 0), and the cell below it is at (1, 0).
How many live cells are currently in the grid?
Options:
A: 4
B: 12
C: 20
D: 10
E: 5
F: 6
G: 8
H: 25
|
E
|
[
"A: 4",
"B: 12",
"C: 20",
"D: 10",
"E: 5",
"F: 6",
"G: 8",
"H: 25"
] |
lifegame
|
Multi-step Reasoning
|
|
Target Perception
| 3 |
Check cell state
|
Medium
|
Easy
|
This is a Minesweeper game. The size of the chessboard is 5x5, and there are a total of 5 mines hidden on the board.
The numbers on the board indicate how many mines are adjacent to that cell, including diagonals. Cells marked with "F" (flagged) are identified as potential locations of mines based on logical deduction or prior knowledge. These flagged cells play a critical role in guiding your reasoning for answering the questions. Cells with no numbers and no flags are safe and contain no adjacent mines.
The board uses a coordinate system where the top-left cell corresponds to (0,0), and the rows and columns are numbered starting from 0.
Please use the provided board configuration and logical reasoning to deduce the correct answers to the following questions:
**Question**: What is the state of the cell at (2,4)?
**Options:**
A. It is revealed and shows a number.
B. It is flagged as mine.
C. It is still hidden.
D. It is revealed and shows no more information.
|
C
|
[
"A. It is revealed and shows a number. ",
"B. It is flagged as mine. ",
"C. It is still hidden. ",
"D. It is revealed and shows no more information."
] |
minesweeper
|
Multi-step Reasoning
|
|
Target Perception
| 4 |
Asking a piece located at a specific square
|
Medium
|
Easy
|
What piece is at e4?Choose from the following options:A.Pawn,B.Rook,C.Knight,D.Bishop,E.Queen,F.King,G.No Piece
|
E
|
[
"A.Pawn",
"B.Rook",
"C.Knight",
"D.Bishop",
"E.Queen",
"F.King",
"G.No Piece"
] |
chess_ranger
|
Strategy Planning
|
|
State Prediction
| 4 |
Find the final point of choosing a given column to click.
|
Hard
|
Medium
|
Now I'll give you a picture, which shows a screenshot of a rhythm game, in which there are operation blocks of various colors. In this game, the operation blocks will fall at a speed of 1 cell/second. At the same time, you can select a column to place your finger (you cannot move your finger after selecting it), and click the operation blocks in the column that fall to the first row to score points (of course, you can also choose not to click any column, which will not affect the falling of the operation blocks).
For the operation blocks, we divide them into 3 categories, including Click blocks, Reverse blocks, and Snake blocks, as follows:
1. Click blocks are yellow, occupy 1 cell, and you can get 10 points by clicking them.
2. Reverse blocks are green, occupy 1 cell, and you can get 15 points by clicking them. It should be noted that after you click the Reverse block, the entire game situation will **reverse left and right**, but your finger position **will not** change accordingly.
3. A Snake block occupies 2 or more consecutive cells in a column, and its first cell (called Snake Head block) is pink, its last cell (called Snake Tail block) is grey, and the middle cells (called Snake Body blocks, if any) are blue. Only when you click on **all cells** occupied by the snake block can you score points. The score is related to the length $l$ (including the head and tail) of the snake block. The specific score is $l \cdot (2l + 7)$.
Now I will give you a question about the game. Please extract information from the picture I give you, think carefully, reason and answer: While selecting column 4 to click, how many points will you get? Options: 1. 225 2. 207 3. 221 4. 210 5. 205 6. 215 7. 208 8. 230
|
6
|
[
"225",
"207",
"221",
"210",
"205",
"215",
"208",
"230"
] |
rhythm_game
|
Strategy Planning
|
|
Strategy Optimization
| 2 |
Questions about the optimal strategy to take a move of the current player of the board.
|
Hard
|
Medium
|
Principles: Tic-Tac-Toe is a classic two-player game played on a 3x3 grid, (row, col) from (0, 0) to (2, 2). Players take turns marking a space in the grid, one using **O** (the red block) and the other using **X** (the blue block). In each game, player **O** starts first. The objective is to be the first to get three of your marks in a row (horizontally, vertically, or diagonally). If all nine squares are filled without either player achieving this, the game ends in a draw. Notice: the current player to make a move should be inferred from the number of pieces for each players on the board. When inferring the optimal move, if optimal move can be inferred by some rules, choose the optimal move. Otherwise, choose the first move. (The order of choices is (0, 0), (0, 1), (0, 2), (1, 0), ..., (2, 2), choose the first move that is not occupied)
Question: What is the optimal move for the current player? If no move exists, choose the answer "None".
Options: ['A.None', 'B.(0, 0)', 'C.(0, 1)', 'D.(0, 2)', 'E.(1, 0)', 'F.(1, 1)', 'G.(1, 2)', 'H.(2, 0) or (2, 1) or (2, 2)']
|
A
|
[
"A.None",
"B.(0, 0)",
"C.(0, 1)",
"D.(0, 2)",
"E.(1, 0)",
"F.(1, 1)",
"G.(1, 2)",
"H.(2, 0) or (2, 1) or (2, 2)"
] |
tictactoe
|
Strategy Planning
|
|
State Prediction
| 2 |
Predict the cube state after performing specific moves
|
Medium
|
Medium
|
Rules: As shown in the figure, the Rubik's cube consists of both 3D views and an unfolded view. The 3D views show the cube from two angles: left-tilted 30 degrees looking down, and right-tilted ,30 degrees looking up. The cube has six faces: Upper (U), Down (D), Left (L), Right (R), Front (F), and Back (B). Each face can be rotated clockwise or counterclockwise.And for each face, the coordinates are determined based on the unfolded view: column number increases from left to right (0,1,2) and row number increases from bottom to top (0,1,2). Legend shown in the bottom left corner.Handedness issues in the 3D views can be ignored.An uppercase letter indicates which face to rotate ('F' for Front, 'B' for Back, 'L' for Left, 'R' for Right, 'U' for Upper, 'D' for Down), with a prime symbol (') denoting counterclockwise rotation and no prime symbol denoting clockwise rotation.After the sequence U' U' B' L' D, what color will be at position (2, 1) on the Down face face?Options: [1] blue, [2] purple, [3] gray, [4] pink, [5] magenta, [6] green, [7] red, [8] white
|
1
|
[
"blue",
"purple",
"gray",
"pink",
"magenta",
"green",
"red",
"white"
] |
rubiks_cube
|
3D Spatial Perception & Reasoning
|
|
Target Perception
| 1 |
A board_state question about the current state of Klondike Solitaire
|
Easy
|
Easy
|
The given image represents the interface of the game Klondike Solitaire. The user interface consists of a board with 52 playing cards divided into four distinct areas:
1. **Stock Pile (Draw Pile):** Initially composed of 24 face-down cards. The player can draw one card at a time to reveal its face.
2. **Waste Pile (Dump Pile):** This pile holds the cards drawn from the Stock Pile that have not been moved to other areas. Only the topmost card in the Waste Pile is available for play.
3. **Foundation Piles:** These four piles are designated for each suit (hearts, diamonds, clubs, and spades, but not necessarily following this order). From left to right, they are referred to as foundation 1 through foundation 4. Players must build up the foundation starting with the Ace and then place cards in ascending order (2 through King) of the same suit.
4. **Tableau Piles:** There are seven tableau piles. From left to right, these piles are referred to as Tab 1 through Tab 7, and initially contain an increasing number of cards from 1 to 7. Only the topmost cards in each pile are face-up and built in descending order, alternating colors (red and black suits). Only when the topmost cards are removed to some other place (e.g. another tableau pile or the foundation pile) will the hidden card beneath be revealed. Only a King can be placed on an empty tableau pile unless it starts there at the beginning of the game.
**Objective:**
The goal of Klondike Solitaire is to move all cards to the Foundation Piles, organized by suit in ascending order from Ace to King.
Analyze the current state of the board and possible moves.
Choose the correct move or choose option 8 if there are no possible moves from the options
Options:
1. Move from Waste Pile to Foundation 4
2. Move from Tab7 to Tab3
3. Move from Tab2 to Foundation 3
4. Move from Waste Pile to Foundation 2
5. Move from Waste Pile to Foundation 3
6. Move from Tab7 to Foundation 4
7. Move from Tab5 to Foundation 1
8. No possible moves from the options
|
2
|
[
"Move from Waste Pile to Foundation 4",
"Move from Tab7 to Tab3",
"Move from Tab2 to Foundation 3",
"Move from Waste Pile to Foundation 2",
"Move from Waste Pile to Foundation 3",
"Move from Tab7 to Foundation 4",
"Move from Tab5 to Foundation 1",
"No possible moves from the options"
] |
klondike
|
Pattern Recognition & Matching
|
|
Target Perception
| 2 |
gradient_pattern
|
Hard
|
Medium
|
Rules:
1. Colors change gradually along rows or columns.
2. A gradient transitions between two colors.
3. Each row or column can have its own independent gradient pattern.
4. Row and column indexes begin from 1 at the top-left corner.
Question:
What is the gradient pattern in row 6?
Options:
1: transitioning from bright orange to dark blue
2: transitioning from vivid bright indigo to black
3: transitioning from cyan to light gray
4: transitioning from light gray to vivid bright green
5: transitioning from vivid bright red to dark cyan
6: transitioning from pale bright red to vivid cyan
7: transitioning from vivid dark purple to pale bright purple
8: transitioning from indigo to vivid dark yellow
|
7
|
[
"transitioning from bright orange to dark blue",
"transitioning from vivid bright indigo to black",
"transitioning from cyan to light gray",
"transitioning from light gray to vivid bright green",
"transitioning from vivid bright red to dark cyan",
"transitioning from pale bright red to vivid cyan",
"transitioning from vivid dark purple to pale bright purple",
"transitioning from indigo to vivid dark yellow"
] |
hue
|
Pattern Recognition & Matching
|
|
State Prediction
| 1 |
sequence_finding
|
Easy
|
Medium
|
Rules:
1. Player can only walk on top of cubes
2. Player can climb ladders if they can reach the cube under the ladder
3. From a ladder, player can reach the top of the last cube with the ladder
4. Blue cube is start position, red cube is goal position
5. Green cubes are numbered checkpoints
What is the correct sequence of numbered checkpoints when following the path from start to goal?
Options:
1: Start -> 2 -> 1 -> 3 -> Goal
2: Start -> 3 -> 2 -> 1 -> Goal
3: Start -> 2 -> 3 -> 1 -> Goal
4: Start -> 3 -> 1 -> 2 -> Goal
5: Start -> 1 -> 2 -> 3 -> Goal
6: Start -> 1 -> 3 -> 2 -> Goal
|
4
|
[
"Start -> 2 -> 1 -> 3 -> Goal",
"Start -> 3 -> 2 -> 1 -> Goal",
"Start -> 2 -> 3 -> 1 -> Goal",
"Start -> 3 -> 1 -> 2 -> Goal",
"Start -> 1 -> 2 -> 3 -> Goal",
"Start -> 1 -> 3 -> 2 -> Goal"
] |
3d_maze
|
3D Spatial Perception & Reasoning
|
|
State Prediction
| 6 |
Ask the points gained by moving to a given column and shooting once
|
Medium
|
Easy
|
The given image represents a simplified interface of the game Space Invaders. The enemy area is implicitly divided into a grid of cells, with the row and column numbers shown on the left and top sides of the grid respectively which you should strictly follow. Each cell is either empty or occupied by an incoming enemy which can be purple, blue or green. The ship is at the bottom row, aligned with one of the columns, which shoots the enemies using laser while dodging possible lasers from the enemies.
If the ship shoots, the enemy closest to the ship (i.e. the lowermost one) on the same column as the ship, if any, will be destroyed and disappear, adding points to the player's score and exposing the enemy behind (if any). Purple enemies are worth 30 points, blue enemies are worth 20 points, and green enemies are worth 10 points.
Suppose that all the enemies keep still. If the ship moves to column 4 and shoots, how many points will the player get? Give the number of the correct option.
Options:
1: 0
2: 10
3: 20
4: 30
|
2
|
[
"0",
"10",
"20",
"30"
] |
space_invaders
|
Strategy Planning
|
|
Strategy Optimization
| 9 |
Judge Pacman's optimal movement
|
Easy
|
Hard
|
# Game Overview
Pac-Man is a maze arcade game where the player controls Pac-Man to eat as many beans as possible while avoiding ghosts. If a ghost catches Pac-Man, the game ends.
# Basic Elements
- **Pac-Man**: The yellow circular character that the player controls
- **Beans**: Yellow dots that Pac-Man can eat to score points
- **Walls**: Blue barriers that restrict movement
- **Ghosts**: Two ghosts (Pinky and Blinky) that chase Pac-Man
# Game Rules
- Pac-Man must eat beans while avoiding ghosts
- Each bean eaten adds 1 point to the score
- The game ends if a ghost catches Pac-Man
- Movement is restricted by walls
# Movement and Direction
- Pac-Man's mouth opening indicates its current direction
- The direction can be UP, DOWN, LEFT, or RIGHT
- Neither Pac-Man nor ghosts can move through walls
# **Ghost Behavior**
- **Pinky** (Pink Ghost): Targets up to 4 spaces ahead of Pac-Man's current position and direction (stops at walls)
- **Blinky** (Red Ghost): Directly targets Pac-Man's current position
- Both ghosts follow a movement priority system based on the direction they are trying to move:
- When moving in more than one direction is optimal, the priority order for both ghosts is **UP > DOWN > LEFT > RIGHT**.
- This means if a ghost has multiple possible directions to move in, it will first attempt to move **UP** if possible, then **DOWN**, followed by **LEFT**, and finally **RIGHT** if all other directions are blocked.
# Board Layout
- The board is surrounded by walls on all four sides
- Position (0,0) is located at the top-left corner wall
- Movement grid uses (row, column) coordinates
# Scoring
The score equals the total number of beans eaten by Pac-Man
**Question:** If Pac-Man and both ghosts move one step at a time, in which direction should Pac-Man move continuously until hitting a wall to eat the most beans without being caught by a ghost?
**Options:**
A. Pac-Man should move UP
B. Pac-Man should move DOWN
C. Pac-Man should move RIGHT
D. Pac-Man should move LEFT
E. Pac-Man will be caught by a ghost regardless of direction
|
A
|
[
"A. Pac-Man should move UP",
"B. Pac-Man should move DOWN",
"C. Pac-Man should move RIGHT",
"D. Pac-Man should move LEFT",
"E. Pac-Man will be caught by a ghost regardless of direction"
] |
pacman
|
Strategy Planning
|
|
Target Perception
| 1 |
Identify the current position and direction of the ant
|
Hard
|
Easy
|
In Langton's Ant, we have a grid where each cell is either white or black. A red arrow represents an ant, showing its current position and direction. The ant follows these simple rules:
1. If the ant is on a white cell, it turns right 90 degrees, changes the cell to black, and moves forward one step
2. If the ant is on a black cell, it turns left 90 degrees, changes the cell to white, and moves forward one step
3. If the ant would move off the grid, it wraps around to the opposite side (using modulo with grid size)
The coordinates system: The top-left cell is (0,0), with x increasing downward and y increasing rightward.
What is the current position and direction of the ant in the image?
Answer using one of the following options with its corresponding letter:
A: Position (0, 12), facing up
B: Position (8, 11), facing right
C: Position (2, 11), facing down
D: Position (6, 6), facing up
E: Position (6, 12), facing up
F: Position (10, 12), facing down
G: Position (6, 6), facing down
H: Position (3, 0), facing left
|
G
|
[
"Position (0, 12), facing up",
"Position (8, 11), facing right",
"Position (2, 11), facing down",
"Position (6, 6), facing up",
"Position (6, 12), facing up",
"Position (10, 12), facing down",
"Position (6, 6), facing down",
"Position (3, 0), facing left"
] |
langton_ant
|
Multi-step Reasoning
|
|
Target Perception
| 2 |
Ask the position of goal within the maze.
|
Hard
|
Easy
|
**Rules:**
1. This is a maze mini-game.The player needs to navigate around obstacles to reach the destination and achieve victory.
2. The red circle represents the player, the green block is the goal and the blue blocks are obstacles.
3. The player can only move within the white blocks.
**Question:** Which of the following are the coordinates of the goal?"
**Optoins:**
A. (8, 11)
B. (10, 11)
C. (9, 12)
D. (9, 11)
E. (9, 10)
|
D
|
[
"A. (8, 11)",
"B. (10, 11)",
"C. (9, 12)",
"D. (9, 11)",
"E. (9, 10)"
] |
maze
|
Strategy Planning
|
|
TransitionPath
| 3 |
find_word_location
|
Medium
|
Hard
|
Rules:
1. This is a word search game. Words can be placed in different directions: right, down, diagonal-right-down, diagonal-right-up, diagonal-left-down, diagonal-left-up, up, or left.
2. Words read from start to end in the specified direction.
Question:
Find the word 'BIELID' in the grid. Where does it start and in which direction does it go?
Options:
1: Row 6, Column 2, Direction: diagonal-left-down
2: Row 6, Column 2, Direction: down
3: Row 6, Column 2, Direction: diagonal-right-down
4: Row 6, Column 2, Direction: diagonal-left-up
5: Row 6, Column 2, Direction: diagonal-right-up
6: Row 6, Column 2, Direction: left
7: Row 6, Column 2, Direction: up
8: Row 6, Column 2, Direction: right
|
7
|
[
"Row 6, Column 2, Direction: diagonal-left-down",
"Row 6, Column 2, Direction: down",
"Row 6, Column 2, Direction: diagonal-right-down",
"Row 6, Column 2, Direction: diagonal-left-up",
"Row 6, Column 2, Direction: diagonal-right-up",
"Row 6, Column 2, Direction: left",
"Row 6, Column 2, Direction: up",
"Row 6, Column 2, Direction: right"
] |
word_search
|
Multi-step Reasoning
|
|
Target Perception
| 1 |
Identify the current position and direction of the ant
|
Hard
|
Easy
|
In Langton's Ant, we have a grid where each cell is either white or black. A red arrow represents an ant, showing its current position and direction. The ant follows these simple rules:
1. If the ant is on a white cell, it turns right 90 degrees, changes the cell to black, and moves forward one step
2. If the ant is on a black cell, it turns left 90 degrees, changes the cell to white, and moves forward one step
3. If the ant would move off the grid, it wraps around to the opposite side (using modulo with grid size)
The coordinates system: The top-left cell is (0,0), with x increasing downward and y increasing rightward.
What is the current position and direction of the ant in the image?
Answer using one of the following options with its corresponding letter:
A: Position (12, 9), facing right
B: Position (7, 5), facing right
C: Position (1, 5), facing left
D: Position (8, 9), facing up
E: Position (6, 10), facing right
F: Position (8, 3), facing left
G: Position (3, 0), facing right
H: Position (7, 2), facing up
|
D
|
[
"Position (12, 9), facing right",
"Position (7, 5), facing right",
"Position (1, 5), facing left",
"Position (8, 9), facing up",
"Position (6, 10), facing right",
"Position (8, 3), facing left",
"Position (3, 0), facing right",
"Position (7, 2), facing up"
] |
langton_ant
|
Multi-step Reasoning
|
|
State Prediction
| 2 |
Predict the cube state after performing specific moves
|
Hard
|
Medium
|
Rules: As shown in the figure, the Rubik's cube consists of both 3D views and an unfolded view. The 3D views show the cube from two angles: left-tilted 30 degrees looking down, and right-tilted ,30 degrees looking up. The cube has six faces: Upper (U), Down (D), Left (L), Right (R), Front (F), and Back (B). Each face can be rotated clockwise or counterclockwise.And for each face, the coordinates are determined based on the unfolded view: column number increases from left to right (0,1,2) and row number increases from bottom to top (0,1,2). Legend shown in the bottom left corner.Handedness issues in the 3D views can be ignored.An uppercase letter indicates which face to rotate ('F' for Front, 'B' for Back, 'L' for Left, 'R' for Right, 'U' for Upper, 'D' for Down), with a prime symbol (') denoting counterclockwise rotation and no prime symbol denoting clockwise rotation.After the sequence F' B', what color will be at position (1, 0) on the Down face face?Options: [1] pink, [2] red, [3] magenta, [4] orange, [5] white, [6] black, [7] purple, [8] green
|
5
|
[
"pink",
"red",
"magenta",
"orange",
"white",
"black",
"purple",
"green"
] |
rubiks_cube
|
3D Spatial Perception & Reasoning
|
|
State Prediction
| 4 |
Predict Pacman's movement result
|
Hard
|
Hard
|
# Game Overview
Pac-Man is a maze arcade game where the player controls Pac-Man to eat as many beans as possible while avoiding ghosts. If a ghost catches Pac-Man, the game ends.
# Basic Elements
- **Pac-Man**: The yellow circular character that the player controls
- **Beans**: Yellow dots that Pac-Man can eat to score points
- **Walls**: Blue barriers that restrict movement
- **Ghosts**: Two ghosts (Pinky and Blinky) that chase Pac-Man
# Game Rules
- Pac-Man must eat beans while avoiding ghosts
- Each bean eaten adds 1 point to the score
- The game ends if a ghost catches Pac-Man
- Movement is restricted by walls
# Movement and Direction
- Pac-Man's mouth opening indicates its current direction
- The direction can be UP, DOWN, LEFT, or RIGHT
- Neither Pac-Man nor ghosts can move through walls
# **Ghost Behavior**
- **Pinky** (Pink Ghost): Targets up to 4 spaces ahead of Pac-Man's current position and direction (stops at walls)
- **Blinky** (Red Ghost): Directly targets Pac-Man's current position
- Both ghosts follow a movement priority system based on the direction they are trying to move:
- When moving in more than one direction is optimal, the priority order for both ghosts is **UP > DOWN > LEFT > RIGHT**.
- This means if a ghost has multiple possible directions to move in, it will first attempt to move **UP** if possible, then **DOWN**, followed by **LEFT**, and finally **RIGHT** if all other directions are blocked.
# Board Layout
- The board is surrounded by walls on all four sides
- Position (0,0) is located at the top-left corner wall
- Movement grid uses (row, column) coordinates
# Scoring
The score equals the total number of beans eaten by Pac-Man
**Question:** Assuming Pac-Man and both ghosts move one step at a time, what would happen if Pac-Man moves DOWN 2 times, then LEFT 2 times?
**Options:**
A. It will eat 4 beans, and the score will becfme 31
B. It will eat 6 beans, and the score will become 32
C. It will eat 1 beans, and the score will become 27
D. It will eat 7 beans, and the score will become 33
E. It will eat 4 beans, and the score will become 30
F. It will eat 5 beans, and the score will become 31
G. It will be caught by Pinky (the pink ghost)
H. It will be caught by Blinky (the red ghost)
|
E
|
[
"A. It will eat 4 beans, and the score will become 31",
"B. It will eat 6 beans, and the score will become 32",
"C. It will eat 1 beans, and the score will become 27",
"D. It will eat 7 beans, and the score will become 33",
"E. It will eat 4 beans, and the score will become 30",
"F. It will eat 5 beans, and the score will become 31",
"G. It will be caught by Pinky (the pink ghost)",
"H. It will be caught by Blinky (the red ghost)"
] |
pacman
|
Strategy Planning
|
|
State Prediction
| 0 |
position
|
Easy
|
Medium
|
Rules:
State 0, Symbol 0 -> Write 0, Move right, New State 1
State 0, Symbol 1 -> Write 4, Move right, New State 1
State 0, Symbol 2 -> Write 1, Move right, New State 0
State 0, Symbol 3 -> Write 3, Move right, New State 1
State 0, Symbol 4 -> Write 4, Move left, New State 1
State 1, Symbol 0 -> Write 2, Move up, New State 1
State 1, Symbol 1 -> Write 3, Move down, New State 2
State 1, Symbol 2 -> Write 1, Move left, New State 0
State 1, Symbol 3 -> Write 3, Move up, New State 1
State 1, Symbol 4 -> Write 4, Move down, New State 1
State 2, Symbol 0 -> Write 0, Move left, New State 0
State 2, Symbol 1 -> Write 4, Move right, New State 2
State 2, Symbol 2 -> Write 4, Move right, New State 2
State 2, Symbol 3 -> Write 3, Move down, New State 2
State 2, Symbol 4 -> Write 2, Move left, New State 1
Color Legend for Symbols:
Symbol 0: Color = red
Symbol 1: Color = green
Symbol 2: Color = blue
Symbol 3: Color = magenta
Symbol 4: Color = cyan
Bracket Legend for States:
State 0: Bracket = ( )
State 1: Bracket = [ ]
State 2: Bracket = { }
State 3: Bracket = < >
Current head position is (1, 0) with State 0 on Symbol 1 that is (1).
Question: where will the head be after 4 steps?
Options:
1: (0, 2)
2: (1, 0)
3: (2, 2)
4: (2, 1)
5: (0, 1)
6: (2, 0)
7: (3, 2)
8: (1, 2)
|
4
|
[
"(0, 2)",
"(1, 0)",
"(2, 2)",
"(2, 1)",
"(0, 1)",
"(2, 0)",
"(3, 2)",
"(1, 2)"
] |
2d_turing_machine
|
Multi-step Reasoning
|
|
Strategy Optimization
| 9 |
Ask the maximum points gained by shooting twice
|
Hard
|
Hard
|
The given image represents a simplified interface of the game Space Invaders. The enemy area is implicitly divided into a grid of cells, with the row and column numbers shown on the left and top sides of the grid respectively which you should strictly follow. Each cell is either empty or occupied by an incoming enemy which can be purple, blue or green. The ship is at the bottom row, aligned with one of the columns, which shoots the enemies using laser while dodging possible lasers from the enemies.
If the ship shoots, the enemy closest to the ship (i.e. the lowermost one) on the same column as the ship, if any, will be destroyed and disappear, adding points to the player's score and exposing the enemy behind (if any). Purple enemies are worth 30 points, blue enemies are worth 20 points, and green enemies are worth 10 points.
The enemies keep on uniformly moving in a certain direction (left or right). Carefully understand the time sequence rules below.
- Consider the consecutive time intervals, denoted by t, t+1, t+2, ...
- During each time interval t:
- The ship can shoot at most once.
- The ship can move to another column before shooting.
- The enemies keep still.
- At the very end of this time interval t, the enemies move one step in the direction they are moving, thus changing the columns they are on.
Given that the image depicts the scene at the beginning of time interval t, and the enemies keep on moving right.
What is the maximum number of points the player can at the end of time interval t+1?Give the number of the correct option.
Options:
1: 50
2: 55
3: 60
4: 65
5: 70
6: 75
7: 80
8: 85
|
1
|
[
"50",
"55",
"60",
"65",
"70",
"75",
"80",
"85"
] |
space_invaders
|
Strategy Planning
|
|
State Prediction
| 3 |
Simulate clear operation
|
Easy
|
Medium
|
# **Game Overview**
Jewel2 is a strategic puzzle game played on a grid. Your primary objective is to eliminate elements by forming horizontal or vertical lines of three or more identical items. Successfully eliminating elements increases your score and clears space on the board for new elements to appear.
# **Elements**
## **Basic Elements**
- **A, B, C, D, E**
- **Description**: These are the standard elements in the game.
- **Shape**: Diamond-shaped gems in various colors (Red, Green, Blue, Yellow, Purple).
- A: Red
- B: Green
- C: Blue
- D: Yellow
- E: Purple
- **Interactions**:
- **Clearing**: When three or more identical basic elements align horizontally or vertically, they are eliminated from the board.
- **Swapping**: Basic elements can be swapped with adjacent basic elements to form eliminations.
## **Special Elements**
- **a, b, c, d, e, +, |**
- **Description**: These elements possess unique abilities that trigger specific elimination patterns when activated.
- **Shape**:
- **a, b, c, d, e**: Round gems in various colors (Red, Green, Blue, Yellow, Purple).
- a: Red
- b: Green
- c: Blue
- d: Yellow
- e: Purple
- **+**: A round black gem with low transparency.
- **|**: A tall, rectangular cyan gem.
- **Effects of Special Elements**:
- **a, b, c, d, e**:
- **Function**: Clearing one of these removes all corresponding uppercase basic elements from the board.
- *Example*: Clearing element 'a' will eliminate all 'A's on the board.
- **| (Vertical Clear)**:
- **Function**: Activating this element clears all elements in its vertical column.
- **+ (Surrounding Clear)**:
- **Function**: Activating this element clears all elements within a distance of 1 from its position, including diagonals.
- **Notes**:
- Special elements do **not** trigger further eliminations if they remove other special elements.
- Swapping involving special elements is **not allowed** and will be rejected by the game.
# **Commands**
## **Available Operations**
1. **Clear Operation**
- **Syntax**: clear x y
- **Description**: Attempts to clear the element located at coordinates (x, y).
- **Conditions**:
- The targeted element must form a valid elimination (i.e., be part of a horizontal or vertical line of three or more identical elements).
- If the element is special, its unique ability is activated upon clearing.
- **State Changes**:
- **Basic Element**: If the clearance is valid, the element(s) are removed, the score (Total Cleared) increases accordingly, and new elements fall into place to fill the gaps.
- **Special Element**: Activating a special element triggers its specific clearance effect as described above.
2. **Swap Operation**
- **Syntax**: swap x y pos
- **Parameters**:
- (x, y): Coordinates of the element to be swapped.
- pos: Direction to swap the element (up, down, left, right).
- **Description**: Swaps the element at (x, y) with the adjacent element in the specified direction.
- **pos** can be one of four directions:
- **up**: Swap with the element directly above (in the same column but one row above).
- **down**: Swap with the element directly below (in the same column but one row below).
- **left**: Swap with the element directly to the left (in the same row but one column left).
- **right**: Swap with the element directly to the right (in the same row but one column right).
- **Conditions**:
- Both elements involved in the swap must be basic elements. Swaps involving special elements are rejected.
- The swap must result in a valid elimination; otherwise, the swap is undone.
- **State Changes**:
- **Successful Swap**: Elements are exchanged, any resulting eliminations are performed, and the score (Total Cleared) is updated accordingly.
- **Unsuccessful Swap**: Elements revert to their original positions, and no changes are made to the score.
# **Coordinate System**
- The board uses **0-based coordinates**.
- **Top-left cell**: (0, 0)
- **Bottom-right cell**: ({size_minus_one}, {size_minus_one})
### **Coordinate Explanation**:
- **x (Row)**: Represents the **row number** of the element. Rows are numbered from **top to bottom**, starting from 0.
- *Example*: In a 5x5 grid, the first row (topmost) would have x = 0, the second row would have x = 1, and so on.
- **y (Column)**: Represents the **column number** of the element. Columns are numbered from **left to right**, starting from 0.
- *Example*: In a 5x5 grid, the first column (leftmost) would have y = 0, the second column would have y = 1, and so on.
### **Coordinate Example**:
- To refer to the element located in the second row and third column, you would use coordinates (1, 2).
- To refer to the element in the fifth row and the first column, you would use coordinates (4, 0).
# **Gameplay Mechanics**
## **Score Tracking**
- **Total Cleared**: Represents the cumulative number of elements that have been eliminated throughout the game.
- **Incremented By**: The number of elements cleared in each successful operation (clear or swap).
# **Objective**
Maximize your **Total Cleared** count by strategically performing clear and swap operations to eliminate as many elements as possible. Effective use of special elements can significantly enhance your score by triggering large-scale eliminations.
# **How to Play**
## **Starting the Game**
1. **Initialization**:
- Upon launching Jewel2, a grid is presented, populated with a mix of basic and special elements based on predefined probabilities.
2. **Understanding the Interface**:
- **Grid Display**: Each cell in the grid represents an element. Basic elements are denoted by uppercase letters (A-E), while special elements use lowercase letters or symbols (a, b, c, d, e, +, |).
- **Score Display**: The current **Total Cleared** count is visible, updating as you eliminate elements.
- **Command Input**: A text input area is provided where you can enter commands (clear or swap) to interact with the game.
## **Performing Operations**
1. **Clear Operation**:
- **Objective**: Remove specific elements to form or extend lines of three or more identical elements.
- **How to Execute**:
- Identify the coordinates (x, y) of the element you wish to clear.
- Enter the command in the format: clear x y.
- Example: To clear the element at row 2, column 3, input clear 2 3.
- **Outcomes**:
- **Successful Clear**: If the targeted element is part of a valid elimination, it and any adjacent identical elements are removed, the **Total Cleared** score increases by the number of elements cleared, and new elements fall into place.
- **Special Element Activation**: If a special element is cleared, its unique ability is triggered, resulting in additional eliminations as defined in the **Special Elements** section.
- **Unsuccessful Clear**: If the targeted element does not form a valid elimination, no changes occur, and the command is rejected.
2. **Swap Operation**:
- **Objective**: Rearrange elements to create new elimination opportunities.
- **How to Execute**:
- Identify the coordinates (x, y) of the element you wish to swap.
- Determine the direction pos (up, down, left, right) to which you want to swap the element.
- Enter the command in the format: swap x y pos.
- Example: To swap the element at row 1, column 1 with the element above it, input swap 1 1 up.
- **Outcomes**:
- **Successful Swap**: If the swap results in a valid elimination, the elements are exchanged, the resulting eliminations are performed, and the **Total Cleared** score is updated accordingly.
- **Unsuccessful Swap**: If the swap does not create any valid elimination or involves special elements, the swap is undone, and no changes are made to the score.
# **Additional Notes**
- **Special Element Chain Reactions**: Activating a special element's ability will **not** trigger further eliminations, even if other special elements are removed as a result.
- **Element Replenishment**: After each elimination, new elements are generated randomly to maintain a fully populated board, ensuring continuous gameplay.
- **Row and Column Elimination**: When checking whether an ordinary element can be eliminated, we check whether its rows and columns have three or more identical elements. If both rows and columns meet the elimination rule, both rows and columns are eliminated.
- **Chain Elimination**: After the elimination operation is performed and new elements are generated, no chain elimination will occur.
**Question:** What will happen if you execute clear 0 1?
**Options:**
A. Nothing will happen because the clear does not meet elimination conditions.
B. Trigger a special element, total cleared becomes 6.
C. Perform elimination, eliminate 5 elements, total cleared becomes 5.
D. Perform elimination, eliminate 3 elements, total cleared becomes 6.E. Perform elimination, eliminate 3 elements, total cleared becomes 7.
F. Perform elimination, eliminate 1 elements, total cleared becomes 3.
G. Perform elimination, eliminate 3 elements, total cleared becomes 4.
H. Perform elimination, eliminate 5 elements, total cleared becomes 5.
|
A
|
[
"A. Nothing will happen because the clear does not meet elimination conditions.",
"B. Trigger a special element, total cleared becomes 6.",
"C. Perform elimination, eliminate 5 elements, total cleared becomes 5.",
"D. Perform elimination, eliminate 3 elements, total cleared becomes 6.E. Perform elimination, eliminate 3 elements, total cleared becomes 7.",
"F. Perform elimination, eliminate 1 elements, total cleared becomes 3.",
"G. Perform elimination, eliminate 3 elements, total cleared becomes 4.",
"H. Perform elimination, eliminate 5 elements, total cleared becomes 5."
] |
jewel2
|
Pattern Recognition & Matching
|
|
Target Perception
| 2 |
Given current state and an index of a region.You should idectify which cell provided in the options belongs the region.
|
Medium
|
Easy
|
We have a 6*6 grid.The grid is divided into 6 regions.
Cells with the same color belong to the same region.
Region with index 0 has the color of light pink.
Region with index 1 has the color of powder blue.
Region with index 2 has the color of light green.
Region with index 3 has the color of peach.
Region with index 4 has the color of red.
Region with index 5 has the color of yellow.
In the image,a star is represented by a black dot. If a cell has been placed a star,a black dot will be shown on this cell.
We should place the star in this Star Battle Puzzle according to the following rules:
Each row must contain exactly 1 star(s).
Each column must contain 1 star(s).
Each region must contain exactly 1 star(s).
Stars cannot be adjacent to each other, including diagonally.
The cells in the grid are labeled with row and column numbers starting from 0. The top-left corner of the grid is (0, 0).
(x,y) means a cell at row x and column y.
Now we have placed some stars in the grid.
The region with index 3 is represented by the color peach in the grid.Given the current state, which cell in the following options belong to region 3?
Options:
1.(2,2)
2.(2,5)
3.(1,2)
4.(1,1)
5.(0,3)
6.(0,5)
7.(5,5)
8.(2,4)
|
7
|
[
"(2,2)",
"(2,5)",
"(1,2)",
"(1,1)",
"(0,3)",
"(0,5)",
"(5,5)",
"(2,4)"
] |
star_battle
|
Multi-step Reasoning
|
|
Target Perception
| 4 |
piece_adjacency
|
Medium
|
Medium
|
Rules:
1. Each numbered region represents a piece on the board.
2. Pieces are considered adjacent if they share at least one edge.
3. Pieces that only touch at corners are not considered adjacent.
Question:
How many different pieces are adjacent to Piece 5?
Options:
1: 3
2: 0
3: 6
4: 5
5: 1
6: 7
7: 4
8: 2
|
5
|
[
"3",
"0",
"6",
"5",
"1",
"7",
"4",
"2"
] |
tengram
|
Pattern Recognition & Matching
|
|
Target Perception
| 1 |
Questions about the current state of a specific block of the board.
|
Easy
|
Easy
|
Principles: Tic-Tac-Toe is a classic two-player game played on a 3x3 grid, (row, col) from (0, 0) to (2, 2). Players take turns marking a space in the grid, one using **O** (the red block) and the other using **X** (the blue block). In each game, player **O** starts first. The objective is to be the first to get three of your marks in a row (horizontally, vertically, or diagonally). If all nine squares are filled without either player achieving this, the game ends in a draw. Notice: the current player to make a move should be inferred from the number of pieces for each players on the board. When inferring the optimal move, if optimal move can be inferred by some rules, choose the optimal move. Otherwise, choose the first move. (The order of choices is (0, 0), (0, 1), (0, 2), (1, 0), ..., (2, 2), choose the first move that is not occupied)
Question: What is the color of the block at (2, 0)?
Options: ['A.red', 'B.blue', 'C.white']
|
A
|
[
"A.red",
"B.blue",
"C.white"
] |
tictactoe
|
Strategy Planning
|
|
State Prediction
| 6 |
Given the Player name, find in which Nine-grid to place the piece.
|
Hard
|
Hard
|
Now I'll give you a picture, which shows a screenshot of Ultra TicTacToe. The introduction of Ultra TicTacToe is as follows:
1. Board and coordinate representation: In this game, the board is divided into 9 3*3 squares(called Nine-grids). At the same time, we use $(i, j, row, col)$ to represent the coordinates of a cell: $(i, j)$ represents the coordinates of the Nine-grid; $(row, col)$ represents the coordinate of the cell within the Nine-grid; $i, j, row, col$ all range from 1 to 3. Two players take turns placing pieces on the board to mark the cells on the board, with the first player using "X" and the second player using "O" (this is the same as traditional TicTacToe).
2. Rules for placing chess pieces: After the game starts, the first player places a chess piece in any cell in the Nine-grid in the middle (i.e., the Nine-grid (2, 2)). After that, the coordinates of each chess piece placed in the Nine-grid are the same as the coordinates of the Nine-grid in which the opponent's last chess piece was placed; for example, if the first player places a chess piece at the coordinates (2, 2, 3, 1) in the first step, then the second player needs to choose a chess piece in the Nine-grid (3, 1) in the second step.
3. Scoring rules: For each player, each "Straight" (i.e., three identical chess pieces connected in a line, such as in the same row, the same column, or a diagonal line) in each Nine-grid is counted as 1 point. More than 1 point can be counted in each Nine-grid.
Now I will give you a question about the game. Please extract information from the picture I give you, think carefully, reason, and answer: If you are First Player, from the image, we can see now it's your turn to place a piece. According to the rules of the game, in which Nine-grid should you place the next piece? Options: 1. Nine-grid (1, 1) 2. Nine-grid (1, 2) 3. Nine-grid (1, 3) 4. Nine-grid (2, 1) 5. Nine-grid (2, 2) 6. Nine-grid (2, 3) 7. Nine-grid (3, 1) 8. Nine-grid (3, 2) 9. Nine-grid (3, 3)
|
1
|
[
"Nine-grid (1, 1)",
"Nine-grid (1, 2)",
"Nine-grid (1, 3)",
"Nine-grid (2, 1)",
"Nine-grid (2, 2)",
"Nine-grid (2, 3)",
"Nine-grid (3, 1)",
"Nine-grid (3, 2)",
"Nine-grid (3, 3)"
] |
ultra_tictactoe
|
Strategy Planning
|
|
Target Perception
| 1 |
Identify colors on specific positions
|
Medium
|
Easy
|
Rules: As shown in the figure, the Rubik's cube consists of both 3D views and an unfolded view. The 3D views show the cube from two angles: left-tilted 30 degrees looking down, and right-tilted ,30 degrees looking up. The cube has six faces: Upper (U), Down (D), Left (L), Right (R), Front (F), and Back (B). Each face can be rotated clockwise or counterclockwise.And for each face, the coordinates are determined based on the unfolded view: column number increases from left to right (0,1,2) and row number increases from bottom to top (0,1,2). Legend shown in the bottom left corner.Handedness issues in the 3D views can be ignored.An uppercase letter indicates which face to rotate ('F' for Front, 'B' for Back, 'L' for Left, 'R' for Right, 'U' for Upper, 'D' for Down), with a prime symbol (') denoting counterclockwise rotation and no prime symbol denoting clockwise rotation.What color is at position (2, 1) on the Left face face?Options: [1] orange, [2] green, [3] yellow, [4] blue, [5] red, [6] black, [7] brown, [8] magenta
|
1
|
[
"orange",
"green",
"yellow",
"blue",
"red",
"black",
"brown",
"magenta"
] |
rubiks_cube
|
3D Spatial Perception & Reasoning
|
|
Target Perception
| 3 |
Check cell state
|
Easy
|
Easy
|
This is a Minesweeper game. The size of the chessboard is 4x4, and there are a total of 3 mines hidden on the board.
The numbers on the board indicate how many mines are adjacent to that cell, including diagonals. Cells marked with "F" (flagged) are identified as potential locations of mines based on logical deduction or prior knowledge. These flagged cells play a critical role in guiding your reasoning for answering the questions. Cells with no numbers and no flags are safe and contain no adjacent mines.
The board uses a coordinate system where the top-left cell corresponds to (0,0), and the rows and columns are numbered starting from 0.
Please use the provided board configuration and logical reasoning to deduce the correct answers to the following questions:
**Question**: What is the state of the cell at (1,1)?
**Options:**
A. It is revealed and shows a number.
B. It is flagged as mine.
C. It is still hidden.
D. It is revealed and shows no more information.
|
A
|
[
"A. It is revealed and shows a number. ",
"B. It is flagged as mine. ",
"C. It is still hidden. ",
"D. It is revealed and shows no more information."
] |
minesweeper
|
Multi-step Reasoning
|
|
Target Perception
| 1 |
Ask to recognize the sceneries in the scene.
|
Medium
|
Easy
|
You are provided with a game interface that mimics "Minecraft", where all objects are composed of equal-sized cubes. Players build and explore in this world. They have numerous blocks and can place them following the basic placement rules of "Minecraft." In simple terms, players can place blocks around their current position, and new blocks must be adjacent to existing ones (i.e., sharing a common face). Placing blocks in fluids (such as river water) is allowed, replacing the fluid at that position directly with the block. Players can also sometimes remove blocks.
The scene contains several sceneries. Sceneries can be:
1. Bricks
2. Gold Ore (embedded with gold-colored stone)
3. Diamond Ore (embedded with blue-green stone)
4. TNT (like dynamite, a red block labeled "TNT")
5. Pumpkin (a yellow block resembling a pumpkin)
6. Ladder (not a block, but a wooden ladder attached to blocks, similar to those in "Minecraft")
7. River (beneath ground level, blue, spanning the screen. Specifically, rivers are sometimes presented in clearly bounded grids to allow players to discern the river's width)
8. Lava (beneath ground level, consisting of orange and yellow)
Please select the option that correctly describes the sceneries contained in the image.
Options:
1: Diamond Ore, Ladder, Lava, River
2: Brick, Diamond Ore, Gold Ore, Ladder
3: Diamond Ore, Lava, Pumpkin, TNT
4: Brick, Diamond Ore, Gold Ore, Tree
5: Brick, Diamond Ore, River, Tree
6: Gold Ore, River, TNT, Tree
7: Gold Ore, Lava, River, TNT
8: Diamond Ore, Gold Ore, Ladder, Lava
|
7
|
[
"Diamond Ore, Ladder, Lava, River",
"Brick, Diamond Ore, Gold Ore, Ladder",
"Diamond Ore, Lava, Pumpkin, TNT",
"Brick, Diamond Ore, Gold Ore, Tree",
"Brick, Diamond Ore, River, Tree",
"Gold Ore, River, TNT, Tree",
"Gold Ore, Lava, River, TNT",
"Diamond Ore, Gold Ore, Ladder, Lava"
] |
minecraft
|
3D Spatial Perception & Reasoning
|
|
State Prediction
| 4 |
Predict card move result
|
Hard
|
Medium
|
Spider Solitaire
# OBJECTIVE
Spider is played with eight decks of 13 spade cards each, totaling 104 unique cards. The goal is to arrange all cards in a King-to-Ace sequence in the same suit and move them to the foundation piles. Once all sequences are moved to the foundations, the game is won.
# SETUP
The game features waste piles, a stock pile, and foundation piles. Waste piles are where the action happens, and the stock pile provides new cards when necessary.
**Waste Pile Numbering**: Waste piles are numbered from left to right starting with `0`. The cards within each waste pile are also numbered starting from the bottom card.
# GAME BOARD COMPONENTS
## **Stock Pile**
The **Stock Pile** holds all remaining cards and is used to deal new cards into the waste piles.
Stock Pile is in the top left corner of the board.
- **Staggered Card Stacking**: Cards are stacked in layers, and the number of layers indicates how many more times you can deal cards to the waste piles. Each deal moves one card face-up to each waste pile.
## **Waste Piles**
The **Waste Piles** are where cards are played and organized.
Waste Piles are on the bottom of the chessboard
- **Face-Up vs. Face-Down Cards**: Cards are stacked with face-up cards visible and face-down cards hidden. Only face-up cards can be played. When a face-down card becomes the top card of a pile, it is turned face-up and can be played.
- **Staggered Cards**: Cards in each waste pile are arranged so that face-up cards are on top, and face-down cards are beneath. As you move cards, new face-down cards are revealed.
- **Card Numbering and Screen Position**:
- **Waste Pile Numbering**: Piles are numbered from left to right starting with `0` for the leftmost pile.
- The card at the bottom of each waste pile (usually face-down) is numbered **0** and is the **topmost visible card** in the pile.
- As you move upward in the pile, the next cards are numbered **1**, **2**, **3**, and so on.
- Visually, the bottom card (number **0**) is the one closest to the top of the screen, and the cards above it are stacked above in the pile, going downwards.
## **Foundation Pile**
Foundation pile stores all the arranged suit. When a suit is arranged in sequence, it may be removed to a foundation pile. If all suits are moved to the foundations, the game is won.
Foundation Pile is in the top right corner of the board.
# MOVING CARDS
- **Movement Conditions**: Cards can be moved to another pile as long as they form a **descending sequence of the same suit**, i.e., a King-to-Ace sequence. When moving cards, the new sequence must be a **same-suit sequence** and follow the **descending order** from K, Q, J, 10, 9, ..., 2, A.
- **Same-Suit Sequence Requirement**: The card being moved must be placed on a top card that is of the **same suit** and has a **higher rank** (e.g., a Q can be placed on a K). The top card of the target pile must be larger in rank than the card being moved, and both must be of the same suit.
- **Moving a Sequence**: A complete **descending sequence** of cards (such as K, Q, J, 10, etc.) can be moved from one pile to another, as long as the sequence is in **descending order** and all the cards in the sequence are of the **same suit**.
- **Face-Down Cards**: If the sequence you are moving includes face-down cards, they will be flipped face-up once they are moved. After flipping, the newly face-up cards can continue to be moved or interacted with.
- **Example**: If you have a sequence of K-Q-J-10-9-8-7 in the same suit, you can move a card 6 that has the same suit to the top of this pile, resulting in a new sequence K-Q-J-10-9-8-7-6.
- **Empty Pile Rule**: An empty waste pile can accept any card. After placing the card, you can continue adding a descending same-suit sequence to that pile.
- **Reveal Cards**: If a move leaves a face-down card on top, it will be turned face-up.
# DEALING
Click the stock to deal a new row of face-up cards to the waste piles. You may not deal if there is an empty waste pile.
# STRATEGY
- Turn face-down cards face-up.
- Form runs of the same suit in descending order.
- Use empty waste piles strategically.
# VARIANTS
In **circular spider solitaire**, a King can be placed on an Ace, allowing for extended sequences.
# **NOTE: Important Numbering Reminder**
- **Waste Pile Numbering**: Waste piles are numbered from **left to right** starting with `0` for the leftmost pile.
- **Card Numbering within Waste Piles**: The **bottom-most card** of each pile (usually face-down) is numbered **0**, and the cards above it are numbered **1**, **2**, **3**, etc., moving upwards in the pile.
- **Please Pay Attention** to both the waste pile and card numbering methods, as they will help you navigate and make strategic decisions effectively.
**Question:** What will happen if I want to move the number 5 card of pile 1 to pile 0?
**Options:**
A. The move will be successful, and the cards will be in descending order, following the rules of movement.
B. The move cannot be made because this card is face-down and its value is unknown.
C. The move cannot be made because there is a card above it, and that card does not form a descending order with the selected card.
D. The move cannot be made because the top card of the target pile does not have a rank equal to this card's rank plus one.
E. The move cannot be made because the pile has too few cards, and this card does not exist.
|
C
|
[
"A. The move will be successful, and the cards will be in descending order, following the rules of movement.",
"B. The move cannot be made because this card is face-down and its value is unknown.",
"C. The move cannot be made because there is a card above it, and that card does not form a descending order with the selected card.",
"D. The move cannot be made because the top card of the target pile does not have a rank equal to this card's rank plus one.",
"E. The move cannot be made because the pile has too few cards, and this card does not exist."
] |
spider_solitaire
|
Pattern Recognition & Matching
|
|
Target Perception
| 1 |
Identify colors on specific positions
|
Medium
|
Easy
|
Rules: As shown in the figure, the Rubik's cube consists of both 3D views and an unfolded view. The 3D views show the cube from two angles: left-tilted 30 degrees looking down, and right-tilted ,30 degrees looking up. The cube has six faces: Upper (U), Down (D), Left (L), Right (R), Front (F), and Back (B). Each face can be rotated clockwise or counterclockwise.And for each face, the coordinates are determined based on the unfolded view: column number increases from left to right (0,1,2) and row number increases from bottom to top (0,1,2). Legend shown in the bottom left corner.Handedness issues in the 3D views can be ignored.An uppercase letter indicates which face to rotate ('F' for Front, 'B' for Back, 'L' for Left, 'R' for Right, 'U' for Upper, 'D' for Down), with a prime symbol (') denoting counterclockwise rotation and no prime symbol denoting clockwise rotation.What color is at position (1, 1) on the Front face face?Options: [1] white, [2] brown, [3] cyan, [4] orange, [5] blue, [6] purple, [7] pink, [8] gray
|
5
|
[
"white",
"brown",
"cyan",
"orange",
"blue",
"purple",
"pink",
"gray"
] |
rubiks_cube
|
3D Spatial Perception & Reasoning
|
|
TransitionPath
| 3 |
find_word_location
|
Hard
|
Hard
|
Rules:
1. This is a word search game. Words can be placed in different directions: right, down, diagonal-right-down, diagonal-right-up, diagonal-left-down, diagonal-left-up, up, or left.
2. Words read from start to end in the specified direction.
Question:
Find the word 'THETAS' in the grid. Where does it start and in which direction does it go?
Options:
1: Row 6, Column 5, Direction: diagonal-left-down
2: Row 6, Column 5, Direction: left
3: Row 3, Column 3, Direction: up
4: Row 2, Column 6, Direction: left
5: Row 3, Column 3, Direction: diagonal-left-down
6: Row 3, Column 8, Direction: diagonal-left-down
7: Row 2, Column 8, Direction: right
8: Row 3, Column 3, Direction: diagonal-left-up
|
6
|
[
"Row 6, Column 5, Direction: diagonal-left-down",
"Row 6, Column 5, Direction: left",
"Row 3, Column 3, Direction: up",
"Row 2, Column 6, Direction: left",
"Row 3, Column 3, Direction: diagonal-left-down",
"Row 3, Column 8, Direction: diagonal-left-down",
"Row 2, Column 8, Direction: right",
"Row 3, Column 3, Direction: diagonal-left-up"
] |
word_search
|
Multi-step Reasoning
|
|
Target Perception
| 0 |
cell_letter
|
Medium
|
Easy
|
Rules:
1. The grid contains uppercase letters.
2. Row and column indexes begin from 1 at the top-left corner.
Question:
What letter is at row 1, column 4?
Options:
1: Y
2: D
3: C
4: S
5: L
6: V
7: K
8: E
|
6
|
[
"Y",
"D",
"C",
"S",
"L",
"V",
"K",
"E"
] |
word_search
|
Multi-step Reasoning
|
|
Target Perception
| 1 |
Questions about counting the current number of live cells in the grid
|
Easy
|
Easy
|
Conway's Game of Life is a cellular automaton where each cell in the grid can be either alive (black) or dead (white).
Each cell interacts with its eight neighbors, which are the cells that are horizontally, vertically, or diagonally adjacent. For a cell at position (r,c), its neighbors are:
- (r-1,c-1) (r-1,c) (r-1,c+1) [above row]
- (r,c-1) (r,c) (r,c+1) [same row]
- (r+1,c-1) (r+1,c) (r+1,c+1) [below row]
Region boundaries wrap around to the opposite side:
- A cell at the top edge connects to cells at the bottom edge
- A cell at the left edge connects to cells at the right edge
- Corner cells connect to the diagonally opposite corner
For example, in a 3x3 region:
- Cell (0,0)'s top neighbor is (2,0)
- Cell (0,0)'s left neighbor is (0,2)
- Cell (0,0)'s top-left neighbor is (2,2)
The game evolves in discrete steps according to these rules:
1. Any live cell with fewer than two live neighbors dies (underpopulation)
2. Any live cell with two or three live neighbors lives on to the next generation
3. Any live cell with more than three live neighbors dies (overpopulation)
4. Any dead cell with exactly three live neighbors becomes alive (reproduction)
In the image, black squares represent live cells, white squares represent dead cells, and the grid lines help visualize the cell boundaries.
In this grid, we use (row, col) coordinates where:
- row increases from top to bottom (0 at top)
- col increases from left to right (0 at left)
For example, the top-left cell is at (0, 0), and the cell below it is at (1, 0).
How many live cells are currently in the grid?
Options:
A: 1
B: 0
C: 4
D: 7
E: 5
F: 2
G: 6
H: 3
|
H
|
[
"A: 1",
"B: 0",
"C: 4",
"D: 7",
"E: 5",
"F: 2",
"G: 6",
"H: 3"
] |
lifegame
|
Multi-step Reasoning
|
|
State Prediction
| 5 |
Multi-step deductive reasoning with constraints analysis
|
Easy
|
Hard
|
This is a sudoku game in which the board is filled with a total number of colours equal to the length of the board's sides, and no rows, columns or squares are allowed to have duplicate colours.You should fill the empty cells on the board with following 4 colors:red, green, blue, magenta.In this Sudoku board, the row coordinates are 1-4 from top to bottom, and the column coordinates are 1-4 from left to right.After determining colors at positions (1,2), (2,2), what color should be at position (2,3)?Choose from following options:A.red, B.green, C.blue, D.magenta
|
D
|
[
"A.red",
"B.green",
"C.blue",
"D.magenta"
] |
sudoku
|
Multi-step Reasoning
|
|
State Prediction
| 4 |
Predict card move result
|
Medium
|
Medium
|
Spider Solitaire
# OBJECTIVE
Spider is played with eight decks of 13 spade cards each, totaling 104 unique cards. The goal is to arrange all cards in a King-to-Ace sequence in the same suit and move them to the foundation piles. Once all sequences are moved to the foundations, the game is won.
# SETUP
The game features waste piles, a stock pile, and foundation piles. Waste piles are where the action happens, and the stock pile provides new cards when necessary.
**Waste Pile Numbering**: Waste piles are numbered from left to right starting with `0`. The cards within each waste pile are also numbered starting from the bottom card.
# GAME BOARD COMPONENTS
## **Stock Pile**
The **Stock Pile** holds all remaining cards and is used to deal new cards into the waste piles.
Stock Pile is in the top left corner of the board.
- **Staggered Card Stacking**: Cards are stacked in layers, and the number of layers indicates how many more times you can deal cards to the waste piles. Each deal moves one card face-up to each waste pile.
## **Waste Piles**
The **Waste Piles** are where cards are played and organized.
Waste Piles are on the bottom of the chessboard
- **Face-Up vs. Face-Down Cards**: Cards are stacked with face-up cards visible and face-down cards hidden. Only face-up cards can be played. When a face-down card becomes the top card of a pile, it is turned face-up and can be played.
- **Staggered Cards**: Cards in each waste pile are arranged so that face-up cards are on top, and face-down cards are beneath. As you move cards, new face-down cards are revealed.
- **Card Numbering and Screen Position**:
- **Waste Pile Numbering**: Piles are numbered from left to right starting with `0` for the leftmost pile.
- The card at the bottom of each waste pile (usually face-down) is numbered **0** and is the **topmost visible card** in the pile.
- As you move upward in the pile, the next cards are numbered **1**, **2**, **3**, and so on.
- Visually, the bottom card (number **0**) is the one closest to the top of the screen, and the cards above it are stacked above in the pile, going downwards.
## **Foundation Pile**
Foundation pile stores all the arranged suit. When a suit is arranged in sequence, it may be removed to a foundation pile. If all suits are moved to the foundations, the game is won.
Foundation Pile is in the top right corner of the board.
# MOVING CARDS
- **Movement Conditions**: Cards can be moved to another pile as long as they form a **descending sequence of the same suit**, i.e., a King-to-Ace sequence. When moving cards, the new sequence must be a **same-suit sequence** and follow the **descending order** from K, Q, J, 10, 9, ..., 2, A.
- **Same-Suit Sequence Requirement**: The card being moved must be placed on a top card that is of the **same suit** and has a **higher rank** (e.g., a Q can be placed on a K). The top card of the target pile must be larger in rank than the card being moved, and both must be of the same suit.
- **Moving a Sequence**: A complete **descending sequence** of cards (such as K, Q, J, 10, etc.) can be moved from one pile to another, as long as the sequence is in **descending order** and all the cards in the sequence are of the **same suit**.
- **Face-Down Cards**: If the sequence you are moving includes face-down cards, they will be flipped face-up once they are moved. After flipping, the newly face-up cards can continue to be moved or interacted with.
- **Example**: If you have a sequence of K-Q-J-10-9-8-7 in the same suit, you can move a card 6 that has the same suit to the top of this pile, resulting in a new sequence K-Q-J-10-9-8-7-6.
- **Empty Pile Rule**: An empty waste pile can accept any card. After placing the card, you can continue adding a descending same-suit sequence to that pile.
- **Reveal Cards**: If a move leaves a face-down card on top, it will be turned face-up.
# DEALING
Click the stock to deal a new row of face-up cards to the waste piles. You may not deal if there is an empty waste pile.
# STRATEGY
- Turn face-down cards face-up.
- Form runs of the same suit in descending order.
- Use empty waste piles strategically.
# VARIANTS
In **circular spider solitaire**, a King can be placed on an Ace, allowing for extended sequences.
# **NOTE: Important Numbering Reminder**
- **Waste Pile Numbering**: Waste piles are numbered from **left to right** starting with `0` for the leftmost pile.
- **Card Numbering within Waste Piles**: The **bottom-most card** of each pile (usually face-down) is numbered **0**, and the cards above it are numbered **1**, **2**, **3**, etc., moving upwards in the pile.
- **Please Pay Attention** to both the waste pile and card numbering methods, as they will help you navigate and make strategic decisions effectively.
**Question:** What will happen if I want to move the number 7 card of pile 1 to pile 3?
**Options:**
A. The move will be successful, and the cards will be in descending order, following the rules of movement.
B. The move cannot be made because this card is face-down and its value is unknown.
C. The move cannot be made because there is a card above it, and that card does not form a descending order with the selected card.
D. The move cannot be made because the top card of the target pile does not have a rank equal to this card's rank plus one.
E. The move cannot be made because the pile has too few cards, and this card does not exist.
|
C
|
[
"A. The move will be successful, and the cards will be in descending order, following the rules of movement.",
"B. The move cannot be made because this card is face-down and its value is unknown.",
"C. The move cannot be made because there is a card above it, and that card does not form a descending order with the selected card.",
"D. The move cannot be made because the top card of the target pile does not have a rank equal to this card's rank plus one.",
"E. The move cannot be made because the pile has too few cards, and this card does not exist."
] |
spider_solitaire
|
Pattern Recognition & Matching
|
|
State Prediction
| 1 |
Asking the number of moves to solve the puzzle
|
Easy
|
Hard
|
This game is called Chess Ranger. The rules are as follows:Pieces move like in standard chess.You can only perform capture moves.The king is allowed to be captured.The goal is to end up with a single piece remaining on the board.How many steps are needed to solve the puzzle?Choose from the following options:A.5,B.3,C.7,D.8,E.2,F.4,G.6,H.1
|
B
|
[
"A.5",
"B.3",
"C.7",
"D.8",
"E.2",
"F.4",
"G.6",
"H.1"
] |
chess_ranger
|
Strategy Planning
|
|
Target Perception
| 0 |
Choose a random coordinate and ask what status is the cooradinate
|
Easy
|
Easy
|
Pyramid Chess Rules:
0.Game Board:
The game board is square and comes in various sizes: 3x3, 4x4, or 5x5. On an nxn board, there are n levels (0 to n-1). At each level k, the x and y coordinates range from 0 to n-1-k, resulting in (n-k)**2 slots per level. The slots in the lower levels act as the base for the slots in the upper levels. Slots at level 0 have no base, while slots at level j (j!=0) with coordinates (m,n) are supported by four base slots (m,n),(m+1,n),(m,n+1),(m+1,n+1) from level j-1.
1.Players and Initial Setup:
The game is played between two players, designated as PLAYER_0 and PLAYER_1, each using balls of a distinct color from their color pool, blue balls for PLAYER_0 and red balls for PLAYER_1. Players take turns placing their balls on a square game board. The number of balls available to each player depends on the size of the board: on a 3x3 board, each player has 7 balls; on a 4x4 board, each has 15 balls; and on a 5x5 board, PLAYER_0 (the first player to place a ball) has 28 balls, while PLAYER_1 has 27 balls.
2.Placing Balls and Creating New Slots:
At the start of the game, the lowest level of the board (Level 0) is completely open and balls can be placed in any available slot on this level(since there is no base for slots in level 0, slots in level 0 have full base). After a ball is placed in a slot, that slot is no longer available for placing another ball. A ball can only be placed on the upper level if it is supported by a fully completed 2x2 block of balls on the level directly beneath, which means all the base of the slot is full(there is a ball in each of these slots).
3.Take-back mechnism:
If a player places a ball that completes a 2x2 block of the same color (all four balls belonging to that player), they may return up to two balls from the block to their color pool. A ball can only be removed if it does not have another ball directly above it, as removing a "base" ball would collapse the pyramid. Returning a ball reopens the slot it occupied, allowing it to be used for future placements, but the rule requiring a full 2x2 block as a base for placing balls on upper levels still applies.
4.Winning the Game:
The game ends when one player successfully places the last ball on top of the pyramid. The player who place the ball on the top of the pyramid wins.
Question: What is the status of the ball on Level 0, which has coordinate ([2, 1])?
Options:
1. PLAYER_0
2. PLAYER_1
3. Empty
4. Index out of bound
|
1
|
[
"PLAYER_0",
"PLAYER_1",
"Empty",
"Index out of bound"
] |
pyramidchess
|
3D Spatial Perception & Reasoning
|
|
Target Perception
| 0 |
cell_letter
|
Medium
|
Easy
|
Rules:
1. The grid contains uppercase letters.
2. Row and column indexes begin from 1 at the top-left corner.
Question:
What letter is at row 5, column 3?
Options:
1: Q
2: G
3: W
4: R
5: S
6: J
7: M
8: C
|
3
|
[
"Q",
"G",
"W",
"R",
"S",
"J",
"M",
"C"
] |
word_search
|
Multi-step Reasoning
|
|
State Prediction
| 4 |
Find the final point of choosing a given column to click.
|
Easy
|
Medium
|
Now I'll give you a picture, which shows a screenshot of a rhythm game, in which there are operation blocks of various colors. In this game, the operation blocks will fall at a speed of 1 cell/second. At the same time, you can select a column to place your finger (you cannot move your finger after selecting it), and click the operation blocks in the column that fall to the first row to score points (of course, you can also choose not to click any column, which will not affect the falling of the operation blocks).
For the operation blocks, we divide them into 3 categories, including Click blocks, Reverse blocks, and Snake blocks, as follows:
1. Click blocks are yellow, occupy 1 cell, and you can get 10 points by clicking them.
2. Reverse blocks are green, occupy 1 cell, and you can get 15 points by clicking them. It should be noted that after you click the Reverse block, the entire game situation will **reverse left and right**, but your finger position **will not** change accordingly.
3. A Snake block occupies 2 or more consecutive cells in a column, and its first cell (called Snake Head block) is pink, its last cell (called Snake Tail block) is grey, and the middle cells (called Snake Body blocks, if any) are blue. Only when you click on **all cells** occupied by the snake block can you score points. The score is related to the length $l$ (including the head and tail) of the snake block. The specific score is $l \cdot (2l + 7)$.
Now I will give you a question about the game. Please extract information from the picture I give you, think carefully, reason and answer: While selecting column 1 to click, how many points will you get? Options: 1. 150 2. 159 3. 156 4. 162 5. 163 6. 155 7. 138 8. 160
|
1
|
[
"150",
"159",
"156",
"162",
"163",
"155",
"138",
"160"
] |
rhythm_game
|
Strategy Planning
|
|
State Prediction
| 3 |
Given a particular game state,a selected move and a selected cascade pile, the puzzle will present a question about which card is at the top of the cascade pile.
Your task is to indentify the card in the options.
|
Easy
|
Hard
|
In this FreeCell game:
we have 8 cascade piles, and their indexes are [0, 1, 2, 3, 4, 5, 6, 7]We have 4 freecell on the left top, and their indexes are 0,1,2,3.We have 4 foundation piles on the right top, and their indexes are 0,1,2,3.In FreeCell, cards can be moved according to specific rules: A card can be moved to a free cell if available, stacked in descending order alternating colors in cascade piles, or placed in foundation piles starting from Ace. Now, find the top card from cascade pile 2 after moving the card (Spade,8) from Cascade 2 to FreeCell 0.the options are as follows:
1.(Club, 9)
2.(Spade, A)
3.(Club, 6)
4.(Heart, 5)
5.(Heart, 7)
6.(Club, 2)
7.(Spade, 5)
8.(Diamond, 4)
|
2
|
[
"(Club, 9)",
"(Spade, A)",
"(Club, 6)",
"(Heart, 5)",
"(Heart, 7)",
"(Club, 2)",
"(Spade, 5)",
"(Diamond, 4)"
] |
freecell
|
Pattern Recognition & Matching
|
|
Strategy Optimization
| 3 |
Determine the minimum number of moves needed to solve the puzzle
|
Easy
|
Hard
|
This is a Sokoban puzzle where black figure is player, green X is target, brown box with X is box to push, brown tiles are walls, and light brown areas are movable spaces.The coordinates (x, y) in this puzzle represent the matrix format.What is the minimum number of moves needed to solve this puzzle?
Options:
[1] 3
[2] 5
[3] 8
[4] 2
[5] 4
[6] 7
[7] 12
[8] 6
|
2
|
[
"3",
"5",
"8",
"2",
"4",
"7",
"12",
"6"
] |
sokoban
|
Strategy Planning
|
|
State Prediction
| 9 |
which of the following positions is available to place a new tent?
|
Medium
|
Medium
|
This is a Tents puzzle. In this game, you will start with a grid that only marks the positions of the trees, the number of tents that should be in each row, and the number of tents that should be in each column. Your goal is to place the tents step by step on the grid according to the following rules until there are no more missing tents in the grid:
1. **Valid Cell States**: Each cell in the grid can only be in one of the following three states, which are empty, containing a tree, and containing a tent.
2. **Equal Number of Tents and Trees**: The total number of tents you place must be equal to the number of trees present on the grid.
3. **Tent Placement Restrictions**: Tents can only be placed horizontally or vertically (diagonally does not count) adjacent to at least one tree.
4. **No Adjacent Tents**: No two tents can be adjacent, including diagonally.
5. **Row and Column Constraints**: The number of tents that should be placed in each row or column is given by the numbers on the left and top of the grid.
The positions of the trees and the tents are represented by their icons on the grid respectively. The blue numbers on the left and top of the grid indicate the number of tents that should be placed in each row or column finally. The black numbers on the left and top of the grid are the row numbers and column numbers, respectively. In the coordinates (x, y), x corresponds to the row number, and y corresponds to the column number. The row and column numbering both start from 0, meaning that the first row is actually row 0. The origin (0,0) is in the upper-left corner of the grid.
In the current state, only some of the correct positions of the tents are marked in the grid.Given the current state, which of the following positions is allowed to place a new tent without breaking the game rules immediately (it does not have to be a part of a whole solution to the puzzle)?
Options:
1: (2, 0)
2: (5, 4)
3: (2, 2)
4: (5, 8)
5: (0, 4)
6: (0, 2)
7: (9, 6)
8: (3, 9)
|
7
|
[
"[2, 0]",
"[5, 4]",
"[2, 2]",
"[5, 8]",
"[0, 4]",
"[0, 2]",
"[9, 6]",
"[3, 9]"
] |
tents
|
Multi-step Reasoning
|
|
State Prediction
| 3 |
Questions about counting state changes of specific cells over iterations
|
Medium
|
Medium
|
Conway's Game of Life is a cellular automaton where each cell in the grid can be either alive (black) or dead (white).
Each cell interacts with its eight neighbors, which are the cells that are horizontally, vertically, or diagonally adjacent. For a cell at position (r,c), its neighbors are:
- (r-1,c-1) (r-1,c) (r-1,c+1) [above row]
- (r,c-1) (r,c) (r,c+1) [same row]
- (r+1,c-1) (r+1,c) (r+1,c+1) [below row]
Region boundaries wrap around to the opposite side:
- A cell at the top edge connects to cells at the bottom edge
- A cell at the left edge connects to cells at the right edge
- Corner cells connect to the diagonally opposite corner
For example, in a 3x3 region:
- Cell (0,0)'s top neighbor is (2,0)
- Cell (0,0)'s left neighbor is (0,2)
- Cell (0,0)'s top-left neighbor is (2,2)
The game evolves in discrete steps according to these rules:
1. Any live cell with fewer than two live neighbors dies (underpopulation)
2. Any live cell with two or three live neighbors lives on to the next generation
3. Any live cell with more than three live neighbors dies (overpopulation)
4. Any dead cell with exactly three live neighbors becomes alive (reproduction)
In the image, black squares represent live cells, white squares represent dead cells, and the grid lines help visualize the cell boundaries.
In this grid, we use (row, col) coordinates where:
- row increases from top to bottom (0 at top)
- col increases from left to right (0 at left)
For example, the top-left cell is at (0, 0), and the cell below it is at (1, 0).
Consider the cell at position (1, 2). How will its state change over the next 3 iterations?
Options:
A: Initially: dead → Step 1: dead → Step 2: dead → Step 3: alive
B: Initially: dead → Step 1: dead → Step 2: alive → Step 3: dead
C: Initially: dead → Step 1: alive → Step 2: alive → Step 3: alive
D: Initially: dead → Step 1: alive → Step 2: dead → Step 3: dead
E: Initially: alive → Step 1: alive → Step 2: alive → Step 3: dead
F: Initially: dead → Step 1: dead → Step 2: dead → Step 3: dead
G: Initially: alive → Step 1: dead → Step 2: alive → Step 3: dead
H: Initially: alive → Step 1: dead → Step 2: dead → Step 3: alive
|
A
|
[
"A: Initially: dead → Step 1: dead → Step 2: dead → Step 3: alive",
"B: Initially: dead → Step 1: dead → Step 2: alive → Step 3: dead",
"C: Initially: dead → Step 1: alive → Step 2: alive → Step 3: alive",
"D: Initially: dead → Step 1: alive → Step 2: dead → Step 3: dead",
"E: Initially: alive → Step 1: alive → Step 2: alive → Step 3: dead",
"F: Initially: dead → Step 1: dead → Step 2: dead → Step 3: dead",
"G: Initially: alive → Step 1: dead → Step 2: alive → Step 3: dead",
"H: Initially: alive → Step 1: dead → Step 2: dead → Step 3: alive"
] |
lifegame
|
Multi-step Reasoning
|
|
Strategy Optimization
| 3 |
Determine the minimum number of moves needed to solve the puzzle
|
Hard
|
Hard
|
This is a Sokoban puzzle where black figure is player, green X is target, brown box with X is box to push, brown tiles are walls, and light brown areas are movable spaces.The coordinates (x, y) in this puzzle represent the matrix format.What is the minimum number of moves needed to solve this puzzle?
Options:
[1] 24
[2] 22
[3] 27
[4] 31
[5] 21
[6] 25
[7] 23
[8] 26
|
1
|
[
"24",
"22",
"27",
"31",
"21",
"25",
"23",
"26"
] |
sokoban
|
Strategy Planning
|
Subsets and Splits
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