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<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
0 1 0 0 0 0 0
1 1 0 1 0 1 0
0 1 1 1 0 0 1
0 1 1 1 1 0 1
0 1 1 1 1 0 0
0 1 1 0 0 1 0
1 1 1 1 0 1 0
```
Option B:
```
0 1 0 0 0 0 0
1 1 1 1 0 0 0
0 1 1 1 0 0 1
0 1 1 1 1 0 1
0 1 1 1 1 0 0
0 1 1 0 0 1 1
1 1 1 1 0 1 1
```
Option C:
```
0 1 0 0 0 0 0
1 1 1 1 0 0 0
0 1 1 1 0 0 1
0 1 1 1 1 0 1
0 1 1 1 1 0 0
0 1 1 0 0 1 1
1 1 1 1 0 1 0
```
Option D:
```
0 1 0 0 0 0 0
1 1 1 1 0 0 0
0 1 1 1 0 0 1
0 1 1 1 1 0 1
0 1 1 1 1 0 0
0 1 1 0 0 1 1
1 1 1 0 0 1 0
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>You are a Nonogram player. You need to fill in cells in a grid based on numbers at the side of the grid.
**Nonogram Rules:**
1. For each row or column, the numbers indicate the lengths of consecutive filled cells in that row/column.
2. For example, '2 3' means there are two blocks of filled cells - first 2 cells, then 3 cells, with at least one empty cell between them.
3. '0' means the row/column is completely empty.
**Row hints:** 7, 7, 6, 3 2, 0, 0, 0, 0
**Column hints:** 0, 2 1, 4, 4, 3, 3, 4, 4
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.
Option A:
```
e s s s s s s s
e s s s s s s s
e e s s s s s s
e s s s e e s s
e e e e e e e e
e e s e e e e e
e e s e e e e e
e e e e e e e e
```
Option B:
```
e s s s s s s s
e s s s s s s s
e e s s s s s s
e s s s e e s s
e e e e e e e e
e e e e e e e e
e e e e e e e e
e e e e s e e e
```
Option C:
```
e s s s s s s s
e e s s s s s s
e e s s e s e s
e s s s e e s s
e e e e e e e e
e e e e e e e e
e e e e s e e e
e e e e e e e e
```
Option D:
```
e s s s s s s s
e s s s s s s s
e e s s s s s s
e s s s e e s s
e e e e e e e e
e e e e e e e e
e e e e e e e e
e e e e e e e e
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
D
|
|
<image>You need to solve a Binairo puzzle.
**Binairo Puzzle Rules:**
1. Each cell must contain either a 0 or a 1.
2. There can be no more than two consecutive identical numbers in any row or column (e.g., 000 or 111 are not allowed).
3. Each row and each column must contain an equal number of 0s and 1s.
4. No two rows can be identical, and no two columns can be identical.
The red squares represent 1 and the blue squares represent 0.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle. Each cell is represented by 0 or 1.
Option A:
```
1 1 0 0 1 1 0 0
1 1 0 1 0 0 1 0
0 0 1 1 0 0 1 1
1 0 1 0 1 1 0 0
0 1 0 1 1 0 0 1
1 0 1 0 1 1 1 0
0 0 1 0 1 1 0 1
0 1 0 1 0 0 1 1
```
Option B:
```
1 1 0 0 1 1 0 0
1 1 0 1 0 0 1 0
0 0 1 1 0 0 1 1
1 0 1 0 1 1 0 0
0 1 0 1 1 0 0 1
1 0 1 0 0 1 1 0
0 0 1 0 1 1 0 1
0 1 0 1 0 0 1 1
```
Option C:
```
1 1 1 0 1 1 0 0
1 1 1 1 0 0 1 0
0 0 0 1 0 0 1 1
1 0 0 0 1 1 0 0
0 1 1 1 1 0 0 1
1 0 0 0 0 1 1 0
0 0 0 0 1 1 0 1
0 1 1 1 0 0 1 1
```
Option D:
```
1 1 0 0 1 1 0 0
1 1 0 1 0 0 1 0
0 0 1 1 0 0 1 1
1 0 1 0 1 1 0 0
0 1 1 1 1 0 0 1
1 0 1 0 0 1 1 0
0 0 1 0 1 1 0 1
0 1 0 1 0 0 1 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You need to solve a Sudoku puzzle of size 9x9.
**Sudoku Puzzle Rules (9x9 grid):**
1. **The Grid:** The grid is a 9x9 square, further divided into each 3x3 subgrid (non-overlapping regions).
2. **The Goal:** Fill all empty cells in the grid with digits from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must appear exactly once in:
a. Each row.
b. Each column.
c. Each 3x3 subgrid.
4. **Given Numbers:** The puzzle starts with some cells already filled with digits. These are your clues.
5. **Solving:** Use logic to deduce the correct digit for each empty cell based on the given numbers and the rules.
Option A:
```
3 8 1 2 4 5 6 7 9
6 4 7 1 3 9 2 5 8
5 2 9 6 7 8 1 4 3
7 3 8 4 6 2 5 9 1
1 5 2 7 9 3 4 8 6
4 9 6 5 8 1 7 3 2
8 6 5 3 1 7 9 2 4
9 7 4 8 2 6 3 1 5
2 1 3 9 5 4 8 6 7
```
Option B:
```
3 8 1 2 4 5 6 7 9
6 4 7 1 3 9 2 5 8
5 2 9 6 7 8 1 4 3
7 3 8 4 6 2 5 9 1
1 5 2 7 9 3 4 8 6
4 9 6 5 8 1 7 3 2
8 6 5 3 1 7 9 2 4
9 7 4 8 2 6 3 1 5
2 1 3 9 5 2 8 6 7
```
Option C:
```
3 8 1 2 4 5 6 7 9
6 4 7 1 3 9 2 5 8
5 2 9 6 7 8 1 4 3
7 3 8 4 6 2 5 9 1
1 5 2 7 9 3 4 8 6
4 9 6 5 8 1 7 3 2
8 6 5 3 2 7 9 2 4
9 7 4 8 2 6 3 1 5
2 1 3 9 5 4 8 6 7
```
Option D:
```
3 8 1 2 4 5 6 7 9
6 4 7 1 3 9 2 5 8
5 2 9 6 7 8 1 4 3
7 3 8 4 6 2 5 9 1
1 5 2 7 9 3 4 8 6
4 9 6 5 8 1 7 5 2
8 6 5 3 1 7 9 2 4
9 7 4 8 2 6 3 1 5
2 1 3 9 5 4 8 6 7
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>You need to solve a Sudoku puzzle of size 9x9.
**Sudoku Puzzle Rules (9x9 grid):**
1. **The Grid:** The grid is a 9x9 square, further divided into each 3x3 subgrid (non-overlapping regions).
2. **The Goal:** Fill all empty cells in the grid with digits from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must appear exactly once in:
a. Each row.
b. Each column.
c. Each 3x3 subgrid.
4. **Given Numbers:** The puzzle starts with some cells already filled with digits. These are your clues.
5. **Solving:** Use logic to deduce the correct digit for each empty cell based on the given numbers and the rules.
Option A:
```
7 3 1 2 4 5 6 9 8
8 9 6 1 3 7 4 2 5
4 2 5 8 9 6 3 1 7
3 7 8 6 1 2 9 5 4
1 4 9 5 7 3 8 6 2
5 6 2 4 8 9 7 3 1
9 1 3 7 5 4 2 8 6
2 5 7 3 5 8 1 4 9
6 8 4 9 2 1 5 7 3
```
Option B:
```
7 3 1 2 4 5 6 9 8
8 9 6 1 3 7 4 2 5
4 2 5 8 9 6 3 1 7
3 7 8 6 1 2 9 5 4
1 4 9 5 7 3 8 6 2
5 6 2 4 8 9 7 3 1
9 1 3 7 5 4 2 8 6
2 5 7 3 6 8 1 4 9
6 8 4 9 2 1 5 7 3
```
Option C:
```
7 3 1 2 4 5 6 9 8
8 9 6 1 3 7 4 2 5
4 2 5 8 9 6 3 1 7
8 7 3 6 1 2 9 5 4
1 4 9 5 7 3 8 6 2
5 6 2 4 8 9 7 3 1
9 1 3 7 5 4 2 8 6
2 5 7 3 6 8 1 4 9
6 8 4 9 2 1 5 7 3
```
Option D:
```
7 3 1 2 4 5 6 9 8
8 9 6 1 3 7 4 1 5
4 2 5 8 9 6 3 1 7
3 7 8 6 1 2 9 5 4
1 4 9 5 7 3 8 6 2
5 6 2 4 8 9 7 3 1
9 1 3 7 5 4 2 8 6
2 5 7 3 6 8 1 4 9
6 8 4 9 2 1 5 7 3
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You need to solve a Sudoku puzzle of size 9x9.
**Sudoku Puzzle Rules (9x9 grid):**
1. **The Grid:** The grid is a 9x9 square, further divided into each 3x3 subgrid (non-overlapping regions).
2. **The Goal:** Fill all empty cells in the grid with digits from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must appear exactly once in:
a. Each row.
b. Each column.
c. Each 3x3 subgrid.
4. **Given Numbers:** The puzzle starts with some cells already filled with digits. These are your clues.
5. **Solving:** Use logic to deduce the correct digit for each empty cell based on the given numbers and the rules.
Option A:
```
9 7 5 1 4 2 6 3 8
1 2 8 3 6 9 4 5 7
3 6 4 5 7 8 1 2 9
2 3 7 4 1 6 8 9 5
8 5 1 9 3 7 2 4 6
4 9 6 8 2 5 7 1 3
5 4 9 6 8 1 3 7 2
7 8 3 2 9 4 5 6 1
6 1 2 7 5 3 9 8 4
```
Option B:
```
9 7 5 1 4 2 6 3 8
1 2 8 3 6 9 7 5 7
3 6 4 5 7 8 1 2 9
2 3 7 4 1 6 8 9 5
8 5 1 9 3 7 2 4 6
4 9 6 8 2 5 4 1 3
5 4 9 6 8 1 3 7 2
7 8 3 2 9 4 5 6 1
6 1 2 7 5 3 9 8 4
```
Option C:
```
5 9 1 2 3 4 7 6 8
3 7 6 1 5 8 2 9 4
2 8 4 6 9 7 1 3 5
1 2 7 9 8 3 5 4 6
4 6 3 5 7 2 9 8 1
8 5 9 4 1 6 3 2 7
7 1 2 8 4 9 6 5 3
6 4 5 3 2 1 8 7 9
9 3 8 7 6 5 4 1 2
```
Option D:
```
9 7 5 1 4 2 6 3 8
1 2 8 3 6 9 4 5 7
3 6 4 5 7 8 1 2 9
2 3 7 4 1 6 8 9 5
8 5 1 9 3 7 2 4 6
4 9 6 8 2 5 7 1 3
5 4 3 6 8 1 3 7 2
7 8 3 2 9 4 5 6 1
6 1 2 7 5 3 9 8 4
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
0 0 1 1
1 1 0 0
0 0 0 0
0 0 0 0
```
Option B:
```
1 0 1 1
1 1 0 0
0 0 0 0
0 0 0 1
```
Option C:
```
1 0 1 1
1 1 0 0
1 0 0 0
0 0 0 0
```
Option D:
```
0 0 1 1
1 1 0 1
0 0 0 0
0 0 0 0
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>You need to solve a Sudoku puzzle of size 9x9.
**Sudoku Puzzle Rules (9x9 grid):**
1. **The Grid:** The grid is a 9x9 square, further divided into each 3x3 subgrid (non-overlapping regions).
2. **The Goal:** Fill all empty cells in the grid with digits from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must appear exactly once in:
a. Each row.
b. Each column.
c. Each 3x3 subgrid.
4. **Given Numbers:** The puzzle starts with some cells already filled with digits. These are your clues.
5. **Solving:** Use logic to deduce the correct digit for each empty cell based on the given numbers and the rules.
Option A:
```
3 5 1 6 2 7 9 4 8
4 7 1 5 9 8 2 3 6
2 8 9 4 3 6 1 5 7
7 2 8 3 5 1 6 9 4
1 3 4 6 7 9 5 8 2
9 6 5 2 8 4 3 7 1
6 1 3 8 4 5 7 2 9
5 4 7 9 1 2 8 6 3
8 9 2 7 6 3 4 1 5
```
Option B:
```
3 5 6 1 2 7 9 4 8
4 7 1 5 9 8 2 3 6
2 8 9 4 3 6 1 5 7
7 2 8 3 5 1 6 9 4
1 6 4 3 7 9 5 8 2
9 6 5 2 8 4 3 7 1
6 1 3 8 4 5 7 2 9
5 4 7 9 1 2 8 6 3
8 9 2 7 6 3 4 1 5
```
Option C:
```
3 5 6 1 2 7 9 4 8
4 7 1 5 9 8 2 3 6
2 8 9 4 3 6 1 5 7
7 2 8 3 5 1 6 9 4
1 3 4 6 7 9 5 8 2
9 6 5 2 8 4 3 7 1
6 1 3 8 4 5 7 2 9
5 4 7 9 1 2 8 6 3
8 9 2 7 6 3 4 1 5
```
Option D:
```
3 5 6 1 2 7 9 4 8
4 7 1 5 9 8 2 3 6
2 8 9 4 3 6 1 5 7
7 2 8 3 5 1 7 9 4
1 3 4 6 7 9 5 8 2
9 6 5 2 8 4 3 6 1
6 1 3 8 4 5 7 2 9
5 4 7 9 1 2 8 6 3
8 9 2 7 6 3 4 1 5
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Is cell ((3, 3)) filled with water?
A: Yes
B: No
Please provide your answer as a single letter (A or B) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
1 1 1 1 1 1
1 1 1 0 1 1
1 1 1 0 0 0
1 0 1 1 0 1
0 0 0 1 1 1
1 0 1 1 1 1
```
Option B:
```
1 1 0 1 1 1
1 0 1 0 0 1
1 0 1 0 0 0
1 0 1 1 0 1
0 0 0 1 1 1
1 1 1 1 1 1
```
Option C:
```
1 1 0 1 1 1
1 1 1 0 0 1
1 1 1 0 0 0
1 0 1 1 0 1
0 0 0 1 1 1
1 1 1 1 1 1
```
Option D:
```
1 1 0 1 1 1
1 1 1 0 0 1
1 1 1 0 0 0
1 0 0 1 0 1
0 0 0 1 1 1
1 1 1 0 1 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>You are a Nonogram player. You need to fill in cells in a grid based on numbers at the side of the grid.
**Nonogram Rules:**
1. For each row or column, the numbers indicate the lengths of consecutive filled cells in that row/column.
2. For example, '2 3' means there are two blocks of filled cells - first 2 cells, then 3 cells, with at least one empty cell between them.
3. '0' means the row/column is completely empty.
**Row hints:** 3, 3, 4, 2, 2, 0, 1, 2 1 2, 5 2, 6 5, 6 4, 10
**Column hints:** 6, 5, 4, 4, 5, 3, 1, 3, 1 3, 3 5, 5 4, 5 1
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.
Option A:
```
e e e e e e e e e s s s
e e e e e e e e e s s s
e e e e e e e e s e s s
e e e e e e e e e e s s
e e e e e e e e e e s s
e e e e e e e e e e s e
s e e e e e e e e e e e
s s e e s e e e e s s e
s s s s s e e e e s s e
s e s s s s e s s s s s
s s s s s s e s s s s e
s s s s s s s s s s e e
```
Option B:
```
e e e e e e e e e s s s
e e e e e e e e e s s s
e e e e e e e e s s s s
e e e e e e e e e e s s
e e e e e e e e e e s s
e e e e e e e e e e e e
s e e e e e e e e e e e
s s e e s e e e e e s e
s s s s s e e e e s s e
s s s s s s e s s s s s
s s s s s s e s s s s e
s s s s s s s s s s e e
```
Option C:
```
e e e e e e e e e s s s
e e e e e e e e e s s s
e e e e e e e e s s s s
e e e e e e e e e e s s
e e e e e e e e e e s s
e e e e e e e e e e e e
s e e e e e e e e e e e
s s e e s e e e e s s e
s s s s s e e e e s s e
s s s s s s e s s s s s
s s s s s s e s s s s e
s s s s s s s s s s e e
```
Option D:
```
e e e e e e e e e s s s
e e e e e e e e e s s s
e e e e e e e e s e s s
e e e e e e e e e e s s
e e e e e e e e e e s s
e e e e e e e e e e e e
s e e e e e e e e e e e
s s e e s e e e e s s e
s s s s s e e e e s s e
s s s s s s e s s s s s
s s s s s s e s s s s e
s s s s s s s s s s e e
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>You need to solve a 3x3 Kakuro puzzle.
**Kakuro Puzzle Rules (3x3 Grid):**
1. **Grid:** The grid is a 3x3 square, containing blank cells and clue cells.
2. **Objective:** Fill all blank cells with numbers from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must satisfy the following conditions:
a. The sum of the digits in each horizontal block must equal the clue value for that block.
b. The sum of the digits in each vertical block must equal the clue value for that block.
(Note: No digit can be repeated within the same horizontal or vertical block, although this wasn't explicitly in the original Chinese, it's a standard Kakuro rule and crucial for solving. Adding it for clarity.)
4. **Clues:** Clue cells display the required sum for the adjacent horizontal or vertical block of blank cells.
5. **Solving:** Use logic to deduce the correct digit for each blank cell based on the clue values.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.Option A:
```
7 9 6
1 3 7
8 7 5
```
Option B:
```
7 9 6
9 3 7
8 7 -2
```
Option C:
```
7 9 6
9 3 7
8 7 5
```
Option D:
```
7 9 6
9 3 7
8 1 5
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>You need to solve a Light Up puzzle.
**Puzzle Rules:**
1. A bulb (`s`) illuminates its entire row and column until blocked by a wall.
2. Numbered walls must have exactly that many bulbs adjacent (up/down/left/right).
3. Bulbs cannot illuminate each other.
Below is the puzzle (walls shown in the image). Fill bulbs (`s`) and empty cells (`e`) to satisfy the rules.
Option A:
```
e s w e e e s e e w s w
s e e e e w e e s e e w
e e e s e e e w e w w s
e e s e w e e s e e e w
w w e e e s e w e s e w
e s e w s e e e w e e e
e w e w w w e s e w s e
s e w e e s e w e e e s
w s e e e e e w e s e e
e e w e s w e s e e e w
e e e s e e e e e w w s
s e w e e s e e w s e w
```
Option B:
```
e s w e e e s e e w s w
s e e e e w e e s e e w
e e e s e e e w e w w s
e e s e w e e e e e e w
w w e e e s e e e s e w
e s e w e e e e w e e e
e w e w w w e s e w s e
s e w s e s e w e e e s
w s e e e e s w e e e e
e e w e s w e s e e e w
e s e s e e e e e w w s
s e w e e s e s w e e w
```
Option C:
```
e s w e e e s e e w s e
s e e s e w e e s e e w
e e e s e e e w e w w s
e e s e w e e s e e e w
w w e e e s e w e s e w
e s e w s e e e w e e e
e w e w w w e s e w e e
s e w e e s e w e e e s
w s e e e e e w e s e e
e e w e s w e s e e e w
e e e s e e e e e w w s
s e w e e s e e w s e w
```
Option D:
```
e s w e e e s e e w s w
s e e e e w e e s e e w
e e e s e e e w e w w s
e e s e w e e s e e e w
w w e e e s e e e s e w
e s e w s e e e w e e e
e w e w w w e s e w s e
s e w e e s e w e e e s
w s e e e e e w e s e e
e e w e s w e s e e e w
e e e s e e e e e w w s
s e w e e s e e w s e w
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Which of the following cells has water?
A: (5,9)
B: (1,6)
C: (9,5)
D: (8,5)
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You need to solve a Binairo puzzle.
**Binairo Puzzle Rules:**
1. Each cell must contain either a 0 or a 1.
2. There can be no more than two consecutive identical numbers in any row or column (e.g., 000 or 111 are not allowed).
3. Each row and each column must contain an equal number of 0s and 1s.
4. No two rows can be identical, and no two columns can be identical.
The red squares represent 1 and the blue squares represent 0.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle. Each cell is represented by 0 or 1.
Option A:
```
0 0 1 1
0 1 0 1
1 1 1 0
1 1 0 0
```
Option B:
```
0 0 0 1
0 1 0 1
1 0 1 0
1 1 0 0
```
Option C:
```
0 0 1 1
0 1 0 1
1 0 1 0
1 1 0 0
```
Option D:
```
0 0 1 0
0 1 0 0
1 0 1 1
1 1 0 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Is cell ((0, 0)) filled with water?
A: Yes
B: No
Please provide your answer as a single letter (A or B) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>You need to solve a Light Up puzzle.
**Puzzle Rules:**
1. A bulb (`s`) illuminates its entire row and column until blocked by a wall.
2. Numbered walls must have exactly that many bulbs adjacent (up/down/left/right).
3. Bulbs cannot illuminate each other.
Below is the puzzle (walls shown in the image). Fill bulbs (`s`) and empty cells (`e`) to satisfy the rules.
Option A:
```
s e w s
e e s e
e s e e
w s w w
```
Option B:
```
s e w s
e e s e
e s e e
w e w w
```
Option C:
```
s s w s
e e s e
e s e e
w e w w
```
Option D:
```
s e w s
e e s e
e e e e
w e w w
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You need to solve a Sudoku puzzle of size 9x9.
**Sudoku Puzzle Rules (9x9 grid):**
1. **The Grid:** The grid is a 9x9 square, further divided into each 3x3 subgrid (non-overlapping regions).
2. **The Goal:** Fill all empty cells in the grid with digits from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must appear exactly once in:
a. Each row.
b. Each column.
c. Each 3x3 subgrid.
4. **Given Numbers:** The puzzle starts with some cells already filled with digits. These are your clues.
5. **Solving:** Use logic to deduce the correct digit for each empty cell based on the given numbers and the rules.
Option A:
```
1 6 7 2 3 4 5 8 9
9 2 5 1 8 6 4 3 7
4 3 8 5 7 9 2 6 1
3 4 6 9 1 8 7 2 5
7 8 1 4 5 2 6 9 3
2 5 9 7 6 3 8 1 4
8 2 4 6 9 7 3 5 1
6 9 2 3 4 5 1 7 8
5 7 3 8 2 1 9 4 6
```
Option B:
```
1 8 7 2 3 4 5 8 9
9 2 5 1 8 6 4 3 7
4 3 6 5 7 9 2 6 1
3 4 6 9 1 8 7 2 5
7 8 1 4 5 2 6 9 3
2 5 9 7 6 3 8 1 4
8 1 4 6 9 7 3 5 2
6 9 2 3 4 5 1 7 8
5 7 3 8 2 1 9 4 6
```
Option C:
```
1 6 7 2 3 4 5 8 9
9 2 5 1 8 6 4 3 7
4 3 8 5 7 9 2 6 1
3 4 6 9 1 8 7 2 5
7 8 1 4 5 2 6 9 3
2 5 9 7 6 3 8 1 4
8 1 4 6 9 7 3 5 2
6 9 2 3 4 5 1 7 8
5 7 3 8 2 1 9 4 6
```
Option D:
```
1 6 7 2 3 4 5 8 9
9 2 5 1 8 6 4 3 7
4 3 8 5 7 9 2 6 1
9 4 6 9 1 8 7 2 5
7 8 1 4 5 2 6 9 3
2 5 3 7 6 3 8 1 4
8 1 4 6 9 7 3 5 2
6 9 2 3 4 5 1 7 8
5 7 3 8 2 1 9 4 6
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>You are a Star Battle player. You have to place stars on the grid such that each row, column, and region contains exactly one star. Additional rule is: stars cannot touch each other, not even diagonally.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.
Option A:
```
e s e e e e e e e e e e
e s e e e s e e e e e e
e e s e e e e e e e e e
s e e e e e e e e e e e
e e e e s e e e e e e e
e e e e e e e s e e e e
e e e e e e e e e s e e
e e e s e e e e e e e e
e e e e e e s e e e e e
e e e e e e e e e e e s
e e e e e e e e s e e e
e e e e e e e e e e s e
```
Option B:
```
e s e e e e e e e e e e
e e e e e s e e e e e e
e e s e e e e e e e e e
s e e e e e e e e e e e
e e e e s e e e e e e e
e e e e e e e s e e e e
e e e e e e e e e s e e
e e e s e e e e e e e e
e e e e e e s e e e e e
e e e e e e e e e e e s
e e e e e e e e s e e e
e e e e e e e e e e s e
```
Option C:
```
s s e e e e e e e e e e
e e e e e s e e e e e e
e e s e e e e e e e e e
s e e e e e e e e e e e
e e e e s e e e e e e e
e e e e e e e s e e e e
e e e e e e e e e s e e
e e e s e e e e e e e e
e e e e e e s e e e e e
e e e e e e e e e e e s
e e e e e e e e s e e e
e e e e e e e e e e s e
```
Option D:
```
e s e e e e e e e e e e
s e e e e s e e e e e e
e e s e e e e e e e e e
s e e e e e e e e e e e
e e e e s e e e e e e e
e e e e e e e s e e e e
e e e e e e e e e s e e
e e e s e e e e e e e e
e e e e e e s e e e e e
e e e e e e e e e e e s
e e e e e e e e s e e e
e e e e e e e e e e e e
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You need to solve a Sudoku puzzle of size 9x9.
**Sudoku Puzzle Rules (9x9 grid):**
1. **The Grid:** The grid is a 9x9 square, further divided into each 3x3 subgrid (non-overlapping regions).
2. **The Goal:** Fill all empty cells in the grid with digits from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must appear exactly once in:
a. Each row.
b. Each column.
c. Each 3x3 subgrid.
4. **Given Numbers:** The puzzle starts with some cells already filled with digits. These are your clues.
5. **Solving:** Use logic to deduce the correct digit for each empty cell based on the given numbers and the rules.
Option A:
```
1 8 2 3 5 4 6 7 9
5 3 9 6 2 7 8 1 4
6 4 7 1 8 9 2 5 3
3 6 4 2 1 7 5 9 8
2 9 5 8 6 3 7 4 1
7 1 8 9 4 5 3 6 2
8 5 1 4 3 6 9 2 7
9 7 3 5 2 1 4 8 6
4 2 6 7 9 8 1 3 5
```
Option B:
```
1 8 2 3 5 4 6 7 9
5 3 9 6 7 2 8 1 4
6 4 7 1 8 9 2 5 3
3 6 4 2 1 7 5 9 8
2 9 5 8 6 3 7 5 1
7 1 8 9 4 5 3 6 2
8 5 1 4 3 6 9 2 7
9 7 3 5 2 1 4 8 6
4 2 6 7 9 8 1 3 5
```
Option C:
```
1 8 2 3 5 4 6 7 9
5 3 9 6 7 2 8 1 4
6 4 7 1 8 9 2 5 3
3 6 4 2 1 7 5 9 8
2 9 5 8 6 3 7 4 1
7 1 8 9 4 5 3 6 2
8 5 1 4 3 6 9 2 7
9 7 3 5 2 1 4 8 6
4 2 6 7 9 8 1 3 5
```
Option D:
```
1 8 2 3 5 4 6 7 9
5 3 9 6 7 2 8 1 4
6 4 7 1 8 9 2 5 3
3 6 2 2 1 7 5 9 8
2 9 5 8 6 3 7 4 1
7 1 8 9 4 5 3 6 2
8 5 1 4 3 6 9 2 7
9 7 3 5 2 1 4 8 6
4 2 6 7 9 8 1 3 5
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>You need to solve a Binairo puzzle.
**Binairo Puzzle Rules:**
1. Each cell must contain either a 0 or a 1.
2. There can be no more than two consecutive identical numbers in any row or column (e.g., 000 or 111 are not allowed).
3. Each row and each column must contain an equal number of 0s and 1s.
4. No two rows can be identical, and no two columns can be identical.
The red squares represent 1 and the blue squares represent 0.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle. Each cell is represented by 0 or 1.
Option A:
```
0 0 1 0 1 1
1 0 1 0 1 0
0 0 1 1 0 1
1 0 1 0 1 0
0 1 0 1 0 1
1 1 0 1 0 0
```
Option B:
```
0 0 1 0 1 1
1 1 0 0 1 0
0 0 1 1 0 1
1 0 1 0 1 0
0 1 0 1 0 1
1 1 0 1 0 0
```
Option C:
```
0 0 1 0 1 1
1 1 0 0 0 0
0 0 1 1 0 1
1 0 1 0 1 0
0 1 0 1 0 1
1 1 0 1 0 0
```
Option D:
```
0 0 1 0 1 1
1 1 0 0 1 0
0 0 1 1 0 1
1 0 1 0 1 1
0 1 0 1 0 1
1 1 0 1 0 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You are a Star Battle player. You have to place stars on the grid such that each row, column, and region contains exactly one star. Additional rule is: stars cannot touch each other, not even diagonally.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.
Option A:
```
e e s e e e e e e e e e
s e e e e e e e e e e e
e e e s e e e e e e e e
s s e e e e e e e e e e
e e e e s e e e e e e e
e e e e e e e e s e e e
e e e e e e s e e e e e
e e e e e e e e e s e e
e e e e e e e s e e e e
e e e e e e e e e e e s
e e e e e s e e e e e e
e e e e e e e e e e s e
```
Option B:
```
e e s e e e e e e e e e
s e e e e e e e e e e e
e e e s e e e e e e e e
e s e e e e e e e e e e
e e e e s e e e e e e e
e e e e e e e e s e e e
e e e e e e s e e e e e
e e e e e e e e e s e e
e e e e e e e s e e e e
e e e e e e e e e e e s
e e e e e s e e e e e e
e e e e e e e e e e s e
```
Option C:
```
e e s e e e e e s e e e
s e e e e e e e e e e e
e e e e e e e e e e e e
e s e e e e e e e e e e
e e e e s e e e e e e e
e e e e e e e e s e e e
e e e e e e s e e e e e
e e e e e e e e e s e e
e e e e e e e s e e e e
e e e e e e e e e e e s
e e e e e s e e e e e e
e e e e e e e e e e s e
```
Option D:
```
e s s e e e e e e e e e
s e e e e e e e e e e e
e e e s e e e e e e e e
e s e e e e e e e e e e
e e e e s e e e e e e e
e e e e e e e e s e e e
e e e e e e s e e e e e
e e e e e e e e e s e e
e e e e e e e s e e e e
e e e e e e e e e e e s
e e e e e s e e e e e e
e e e e e e e e e e s e
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You need to solve a Sudoku puzzle of size 9x9.
**Sudoku Puzzle Rules (9x9 grid):**
1. **The Grid:** The grid is a 9x9 square, further divided into each 3x3 subgrid (non-overlapping regions).
2. **The Goal:** Fill all empty cells in the grid with digits from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must appear exactly once in:
a. Each row.
b. Each column.
c. Each 3x3 subgrid.
4. **Given Numbers:** The puzzle starts with some cells already filled with digits. These are your clues.
5. **Solving:** Use logic to deduce the correct digit for each empty cell based on the given numbers and the rules.
Option A:
```
4 5 3 2 1 6 7 8 9
7 2 1 4 9 8 3 5 6
8 6 9 5 3 7 2 1 4
3 7 8 1 6 5 9 4 2
1 4 2 8 7 9 6 3 5
5 9 6 3 4 2 8 7 1
6 8 5 7 2 1 4 9 3
2 1 4 9 8 3 5 6 7
9 3 7 6 5 4 1 2 8
```
Option B:
```
4 5 3 2 1 6 7 8 9
7 2 1 4 9 8 3 5 6
8 6 9 5 3 7 2 1 4
3 7 8 1 6 5 9 4 2
1 4 2 8 7 9 6 3 5
5 9 6 3 4 2 8 7 1
6 8 5 7 2 1 4 9 3
2 1 4 9 5 3 5 6 7
9 3 7 6 5 4 1 2 8
```
Option C:
```
7 4 9 1 2 3 5 6 8
5 2 6 7 4 8 1 9 3
1 3 8 6 5 9 2 4 7
2 5 3 4 9 1 8 7 6
6 8 1 3 7 5 4 2 9
4 9 7 8 6 2 3 1 5
8 6 4 2 3 7 9 5 1
9 1 2 5 8 6 7 3 4
3 7 5 9 1 4 6 8 2
```
Option D:
```
4 5 3 2 1 6 7 8 9
7 2 1 4 9 8 3 5 6
8 6 9 5 3 3 2 1 4
3 7 8 1 6 5 9 4 2
1 4 2 8 7 9 6 3 5
5 9 6 3 4 2 8 7 1
6 8 5 7 2 1 4 9 3
2 1 4 9 8 7 5 6 7
9 3 7 6 5 4 1 2 8
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>You need to solve a 4x4 Kakuro puzzle.
**Kakuro Puzzle Rules (4x4 Grid):**
1. **Grid:** The grid is a 4x4 square, containing blank cells and clue cells.
2. **Objective:** Fill all blank cells with numbers from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must satisfy the following conditions:
a. The sum of the digits in each horizontal block must equal the clue value for that block.
b. The sum of the digits in each vertical block must equal the clue value for that block.
(Note: No digit can be repeated within the same horizontal or vertical block, although this wasn't explicitly in the original Chinese, it's a standard Kakuro rule and crucial for solving. Adding it for clarity.)
4. **Clues:** Clue cells display the required sum for the adjacent horizontal or vertical block of blank cells.
5. **Solving:** Use logic to deduce the correct digit for each blank cell based on the clue values.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.Option A:
```
7 6 5 3
3 3 8 2
1 4 2 6
4 3 1 5
```
Option B:
```
7 6 5 3
3 5 8 2
1 4 2 6
4 3 1 5
```
Option C:
```
7 6 5 1
3 5 8 2
1 4 2 6
4 3 1 5
```
Option D:
```
7 6 5 3
3 0 8 2
1 4 2 6
4 3 1 5
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You need to solve a Binairo puzzle.
**Binairo Puzzle Rules:**
1. Each cell must contain either a 0 or a 1.
2. There can be no more than two consecutive identical numbers in any row or column (e.g., 000 or 111 are not allowed).
3. Each row and each column must contain an equal number of 0s and 1s.
4. No two rows can be identical, and no two columns can be identical.
The red squares represent 1 and the blue squares represent 0.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle. Each cell is represented by 0 or 1.
Option A:
```
1 0 0 1 1 0
0 0 1 1 0 1
0 1 1 0 1 0
1 1 0 1 0 0
1 0 1 0 0 1
1 1 0 1 0 0
```
Option B:
```
1 0 0 1 1 0
0 0 1 1 0 1
0 1 1 0 1 0
1 1 0 1 0 0
1 0 1 0 0 1
0 1 0 0 1 1
```
Option C:
```
0 0 0 1 1 0
0 0 1 1 0 1
0 1 1 0 1 0
1 1 0 1 0 0
1 0 1 0 0 1
0 1 0 0 1 1
```
Option D:
```
1 1 0 1 1 0
0 0 1 1 0 1
0 1 1 0 1 0
1 1 0 1 0 0
1 0 1 0 0 1
0 1 0 0 1 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>Now you are asked to solve a new ARC puzzle. You are given up to three example pairs of ARC grids, each showing an input state and its correct output state. You should learn the transformation rules from these examples. Below these training examples is a new test input grid. Four candidate outputs labeled A, B, C, and D are provided in the lower half of the image. Select the single letter whose output grid correctly completes the test input according to the same transformation rules. After your thinking process, respond only with the chosen letter enclosed in \boxed{}.
|
A
|
|
<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
0 0 1 1 0 0 0
1 0 1 0 1 0 0
1 0 0 0 0 1 0
1 0 1 1 1 1 1
1 0 1 1 1 1 1
1 1 1 1 1 1 0
1 1 1 0 0 1 0
```
Option B:
```
0 0 1 0 0 0 0
0 0 1 0 1 0 0
1 0 0 0 0 1 0
1 0 0 1 1 1 1
1 0 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 0 0 1 0
```
Option C:
```
0 0 1 1 0 0 0
0 0 1 0 1 0 0
1 0 0 0 0 1 0
1 0 0 1 1 1 1
1 0 1 1 1 1 1
1 1 1 1 1 1 0
1 1 1 0 0 1 0
```
Option D:
```
0 0 1 1 0 0 0
0 0 1 0 0 0 0
1 0 0 0 0 1 0
1 0 0 1 1 1 1
1 0 1 1 1 1 1
1 1 1 1 1 1 0
1 1 1 0 0 1 0
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>You are solving a Star Battle puzzle. The rules are:
1. Each row, column, and region must contain exactly one star
2. Stars cannot touch each other, not even diagonally
Look at the puzzle image which shows the current state. Different colors in the image represent different regions, and any stars that have already been placed are shown on the grid.
How many empty positions can you place a star in the next move without violating any constraints?
Option A: 24
Option B: 25
Option C: 26
Option D: 23
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct count.
|
B
|
|
<image>**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Which of the following cells has water?
A: (1,4)
B: (3,5)
C: (5,3)
D: (0,4)
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>Now you are asked to solve a new ARC puzzle. You are given up to three example pairs of ARC grids, each showing an input state and its correct output state. You should learn the transformation rules from these examples. Below these training examples is a new test input grid. Four candidate outputs labeled A, B, C, and D are provided in the lower half of the image. Select the single letter whose output grid correctly completes the test input according to the same transformation rules. After your thinking process, respond only with the chosen letter enclosed in \boxed{}.
|
C
|
|
<image>You are a Star Battle player. You have to place stars on the grid such that each row, column, and region contains exactly one star. Additional rule is: stars cannot touch each other, not even diagonally.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.
Option A:
```
e s e s e e e e
e e e s e e e e
s e e e e e e e
e e e e s e e e
e e e e e e e s
e e e e e s e e
e e s e e e e e
e e e e e e s e
```
Option B:
```
e s e e e e e e
s e e s e e e e
s e e e e e e e
e e e e s e e e
e e e e e e e s
e e e e e e e e
e e s e e e e e
e e e e e e s e
```
Option C:
```
s s e e e e e e
e e e s e e e e
s e e e e e e e
e e e e s e e e
e e e e e e e s
e e e e e s e e
e e s e e e e e
e e e e e e s e
```
Option D:
```
e s e e e e e e
e e e s e e e e
s e e e e e e e
e e e e s e e e
e e e e e e e s
e e e e e s e e
e e s e e e e e
e e e e e e s e
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
D
|
|
<image>You need to solve a 9x9 Kakuro puzzle.
**Kakuro Puzzle Rules (9x9 Grid):**
1. **Grid:** The grid is a 9x9 square, containing blank cells and clue cells.
2. **Objective:** Fill all blank cells with numbers from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must satisfy the following conditions:
a. The sum of the digits in each horizontal block must equal the clue value for that block.
b. The sum of the digits in each vertical block must equal the clue value for that block.
(Note: No digit can be repeated within the same horizontal or vertical block, although this wasn't explicitly in the original Chinese, it's a standard Kakuro rule and crucial for solving. Adding it for clarity.)
4. **Clues:** Clue cells display the required sum for the adjacent horizontal or vertical block of blank cells.
5. **Solving:** Use logic to deduce the correct digit for each blank cell based on the clue values.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.Option A:
```
8 3 5 4 6 2 7 9 1
3 9 8 2 9 4 5 1 7
2 5 6 7 3 8 1 4 9
7 8 3 1 4 9 2 5 6
4 2 1 3 8 6 9 7 5
1 7 4 9 5 3 6 2 8
9 4 7 8 1 5 3 6 2
6 1 9 5 2 7 4 8 3
5 9 2 6 7 1 8 3 4
```
Option B:
```
8 3 5 4 6 2 7 9 1
3 6 8 2 9 4 8 1 7
2 5 6 7 3 8 1 4 9
7 8 3 1 4 9 2 5 6
4 2 1 3 8 6 9 7 5
1 7 4 9 5 3 6 2 8
9 4 7 8 1 5 3 6 2
6 1 9 5 2 7 4 8 3
5 9 2 6 7 1 8 3 4
```
Option C:
```
8 3 5 4 6 2 7 9 1
3 6 8 2 9 4 5 1 7
2 5 6 7 3 8 1 4 9
7 8 3 1 4 9 2 5 6
4 2 1 3 8 6 9 7 5
1 7 4 9 5 3 6 2 8
9 4 7 8 1 5 3 6 2
6 1 9 5 2 7 4 8 4
5 9 2 6 7 1 8 3 4
```
Option D:
```
8 3 5 4 6 2 7 9 1
3 6 8 2 9 4 5 1 7
2 5 6 7 3 8 1 4 9
7 8 3 1 4 9 2 5 6
4 2 1 3 8 6 9 7 5
1 7 4 9 5 3 6 2 8
9 4 7 8 1 5 3 6 2
6 1 9 5 2 7 4 8 3
5 9 2 6 7 1 8 3 4
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
D
|
|
<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
1 1 1 1 1
0 1 0 1 1
0 0 0 0 1
0 0 0 1 1
1 1 1 1 1
```
Option B:
```
1 1 1 1 1
0 1 1 1 1
0 0 0 0 1
0 0 0 1 1
1 1 1 1 1
```
Option C:
```
1 1 1 1 1
0 1 1 1 1
0 0 0 0 1
0 0 0 0 1
1 1 1 1 1
```
Option D:
```
1 1 0 1 1
0 1 1 1 1
0 1 0 0 1
0 0 0 0 1
1 1 1 1 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>You are a Star Battle player. You have to place stars on the grid such that each row, column, and region contains exactly one star. Additional rule is: stars cannot touch each other, not even diagonally.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.
Option A:
```
e e e s e
e s e s e
e e e e s
e e e e e
s e e e e
```
Option B:
```
e e e s e
e s e e e
e e e e s
e e s e e
s e e e e
```
Option C:
```
e e e s e
e e e e e
s e e e s
e e s e e
s e e e e
```
Option D:
```
s e e s e
e s e e e
e e e e s
e e s e e
s e e e e
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You need to solve a 3x3 Kakuro puzzle.
**Kakuro Puzzle Rules (3x3 Grid):**
1. **Grid:** The grid is a 3x3 square, containing blank cells and clue cells.
2. **Objective:** Fill all blank cells with numbers from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must satisfy the following conditions:
a. The sum of the digits in each horizontal block must equal the clue value for that block.
b. The sum of the digits in each vertical block must equal the clue value for that block.
(Note: No digit can be repeated within the same horizontal or vertical block, although this wasn't explicitly in the original Chinese, it's a standard Kakuro rule and crucial for solving. Adding it for clarity.)
4. **Clues:** Clue cells display the required sum for the adjacent horizontal or vertical block of blank cells.
5. **Solving:** Use logic to deduce the correct digit for each blank cell based on the clue values.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.Option A:
```
2 4 8
3 1 4
4 2 1
```
Option B:
```
2 3 8
3 1 4
4 3 1
```
Option C:
```
2 4 8
3 1 4
4 3 1
```
Option D:
```
2 4 1
3 1 4
4 3 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
0 0 0 0 0 0 1 0
0 0 0 0 0 1 1 1
0 0 0 1 1 1 1 1
0 0 0 0 1 1 1 1
0 1 0 0 1 1 1 0
1 0 0 0 0 0 0 1
0 0 0 0 0 0 0 1
1 0 0 1 1 1 1 1
```
Option B:
```
1 0 0 0 0 0 1 0
0 0 0 0 0 1 1 1
0 0 0 1 1 1 1 1
0 0 0 0 0 1 1 1
0 1 0 0 1 1 1 0
1 0 0 0 0 0 0 0
0 0 0 0 1 0 0 1
1 0 0 1 1 1 1 1
```
Option C:
```
1 0 0 0 0 0 1 0
0 0 0 0 0 1 1 1
0 0 0 1 1 1 1 1
0 0 0 0 1 1 1 1
0 1 0 0 1 1 1 0
1 0 0 0 0 0 1 0
0 0 0 0 0 0 0 1
1 0 0 1 1 1 1 1
```
Option D:
```
1 0 0 0 0 0 1 0
0 0 0 0 0 1 1 1
0 0 0 1 1 1 1 1
0 0 0 0 1 1 1 1
0 1 0 0 1 1 1 0
1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1
1 0 0 1 1 1 1 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
D
|
|
<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
0 0 0 1
1 1 1 0
1 1 1 1
1 1 1 1
```
Option B:
```
0 0 0 1
1 1 1 1
1 1 1 1
1 1 1 1
```
Option C:
```
1 0 0 1
1 1 1 1
1 1 1 1
1 1 1 1
```
Option D:
```
0 1 0 1
1 1 1 1
1 1 1 1
1 1 1 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>Now you are asked to solve a new ARC puzzle. You are given up to three example pairs of ARC grids, each showing an input state and its correct output state. You should learn the transformation rules from these examples. Below these training examples is a new test input grid. Four candidate outputs labeled A, B, C, and D are provided in the lower half of the image. Select the single letter whose output grid correctly completes the test input according to the same transformation rules. After your thinking process, respond only with the chosen letter enclosed in \boxed{}.
|
C
|
|
<image>You need to solve a Binairo puzzle.
**Binairo Puzzle Rules:**
1. Each cell must contain either a 0 or a 1.
2. There can be no more than two consecutive identical numbers in any row or column (e.g., 000 or 111 are not allowed).
3. Each row and each column must contain an equal number of 0s and 1s.
4. No two rows can be identical, and no two columns can be identical.
The red squares represent 1 and the blue squares represent 0.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle. Each cell is represented by 0 or 1.
Option A:
```
0 0 1 1 0 0 1 1
1 1 0 1 0 1 0 0
1 1 0 0 1 0 1 0
0 0 1 1 0 1 0 1
0 1 0 0 1 1 0 1
1 1 0 1 0 0 1 0
1 0 1 0 1 1 0 0
0 0 1 0 1 0 1 1
```
Option B:
```
0 0 1 1 0 0 1 1
1 1 0 1 0 1 0 0
1 1 0 0 1 0 1 0
0 0 1 1 0 0 0 1
0 1 0 0 1 1 0 1
1 1 0 1 0 0 1 0
1 0 1 0 1 1 0 0
0 0 1 0 1 0 1 1
```
Option C:
```
0 0 1 1 0 0 1 1
0 0 0 1 0 1 0 0
1 1 0 0 1 0 1 0
0 0 1 1 0 1 0 1
0 1 0 0 1 1 0 1
1 1 0 1 0 0 1 0
1 0 1 0 1 1 0 0
0 0 1 0 1 0 1 1
```
Option D:
```
0 0 1 1 0 0 1 1
1 1 0 1 0 1 0 0
1 1 0 0 1 0 1 0
0 0 1 1 0 1 0 1
0 1 0 0 1 1 0 1
0 0 1 0 1 0 1 1
1 0 1 0 1 1 0 0
0 0 1 0 1 0 1 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>You need to solve a Sudoku puzzle of size 9x9.
**Sudoku Puzzle Rules (9x9 grid):**
1. **The Grid:** The grid is a 9x9 square, further divided into each 3x3 subgrid (non-overlapping regions).
2. **The Goal:** Fill all empty cells in the grid with digits from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must appear exactly once in:
a. Each row.
b. Each column.
c. Each 3x3 subgrid.
4. **Given Numbers:** The puzzle starts with some cells already filled with digits. These are your clues.
5. **Solving:** Use logic to deduce the correct digit for each empty cell based on the given numbers and the rules.
Option A:
```
6 2 4 1 3 5 8 7 9
3 5 9 6 7 8 2 1 4
8 1 7 2 9 4 3 5 6
1 9 2 4 6 7 5 3 8
4 8 3 5 2 9 7 6 1
7 6 5 3 5 1 9 4 2
2 7 6 9 4 3 1 8 5
9 3 1 8 8 6 4 2 7
5 4 8 7 1 2 6 9 3
```
Option B:
```
9 4 5 1 3 2 7 8 6
1 6 8 5 7 4 9 2 3
2 7 3 9 6 8 4 1 5
3 1 4 8 2 5 6 7 9
6 2 9 3 1 7 8 5 4
5 8 7 6 4 9 1 3 2
7 5 6 2 9 1 3 4 8
8 9 1 4 5 3 2 6 7
4 3 2 7 8 6 5 9 1
```
Option C:
```
6 2 4 1 3 5 8 7 9
3 8 9 6 7 5 2 1 4
8 1 7 2 9 4 3 5 6
1 9 2 4 6 7 5 3 8
4 8 3 5 2 9 7 6 1
7 6 5 3 8 1 9 4 2
2 7 6 9 4 3 1 8 5
9 3 1 8 5 6 4 2 7
5 4 8 7 1 2 6 9 3
```
Option D:
```
6 2 4 1 3 5 8 7 9
3 5 9 6 7 8 2 1 4
8 1 7 2 9 4 3 5 6
1 9 2 4 6 7 5 3 8
4 8 3 5 2 9 7 6 1
7 6 5 3 8 1 9 4 2
2 7 6 9 4 3 1 8 5
9 3 1 8 5 6 4 2 7
5 4 8 7 1 2 6 9 3
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
D
|
|
<image>Now you are asked to solve a new ARC puzzle. You are given up to three example pairs of ARC grids, each showing an input state and its correct output state. You should learn the transformation rules from these examples. Below these training examples is a new test input grid. Four candidate outputs labeled A, B, C, and D are provided in the lower half of the image. Select the single letter whose output grid correctly completes the test input according to the same transformation rules. After your thinking process, respond only with the chosen letter enclosed in \boxed{}.
|
D
|
|
<image>You need to solve a Binairo puzzle.
**Binairo Puzzle Rules:**
1. Each cell must contain either a 0 or a 1.
2. There can be no more than two consecutive identical numbers in any row or column (e.g., 000 or 111 are not allowed).
3. Each row and each column must contain an equal number of 0s and 1s.
4. No two rows can be identical, and no two columns can be identical.
The red squares represent 1 and the blue squares represent 0.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle. Each cell is represented by 0 or 1.
Option A:
```
1 0 1 0 0 1
0 0 1 1 0 1
0 1 0 1 0 1
0 1 0 1 0 1
1 0 1 0 1 0
0 1 0 1 1 0
```
Option B:
```
1 0 1 0 0 1
0 0 1 1 0 1
1 1 0 0 1 0
0 1 0 1 0 1
0 0 1 0 1 0
1 1 0 1 1 0
```
Option C:
```
1 0 1 0 0 1
0 0 1 1 0 0
1 1 0 0 1 0
0 1 0 1 0 0
1 0 1 0 1 0
0 1 0 1 1 0
```
Option D:
```
1 0 1 0 0 1
0 0 1 1 0 1
1 1 0 0 1 0
0 1 0 1 0 1
1 0 1 0 1 0
0 1 0 1 1 0
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
D
|
|
<image>You need to solve a 7x7 Kakuro puzzle.
**Kakuro Puzzle Rules (7x7 Grid):**
1. **Grid:** The grid is a 7x7 square, containing blank cells and clue cells.
2. **Objective:** Fill all blank cells with numbers from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must satisfy the following conditions:
a. The sum of the digits in each horizontal block must equal the clue value for that block.
b. The sum of the digits in each vertical block must equal the clue value for that block.
(Note: No digit can be repeated within the same horizontal or vertical block, although this wasn't explicitly in the original Chinese, it's a standard Kakuro rule and crucial for solving. Adding it for clarity.)
4. **Clues:** Clue cells display the required sum for the adjacent horizontal or vertical block of blank cells.
5. **Solving:** Use logic to deduce the correct digit for each blank cell based on the clue values.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.Option A:
```
3 6 2 7 1 8 9
7 5 9 1 2 4 8
1 9 6 4 7 2 5
5 8 7 6 3 1 2
8 7 1 2 5 6 3
2 1 3 5 8 7 4
4 5 8 3 6 9 7
```
Option B:
```
3 6 2 7 1 8 9
5 3 9 1 2 4 8
1 9 6 4 7 2 5
5 8 7 6 3 1 2
8 7 1 2 5 6 3
2 1 3 5 8 7 4
4 5 8 3 6 9 7
```
Option C:
```
3 6 2 7 1 8 9
7 3 9 1 2 4 8
1 9 6 4 7 2 5
5 8 7 6 3 1 2
8 7 1 2 5 6 3
2 1 3 5 8 7 4
4 5 8 3 6 9 7
```
Option D:
```
3 6 2 7 1 8 9
7 3 9 1 2 4 8
1 9 6 4 7 2 5
5 8 7 6 3 1 2
8 7 1 1 5 6 3
2 1 3 5 8 7 4
4 5 8 3 6 9 7
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>You need to solve this Killer Sudoku puzzle.
Fill the grid so that each row, column, and box has unique digits.
In each colored cage, the sum of digits equals the given number, and digits do not repeat.
Option A:
```
2 1 4 3
3 4 2 1
4 3 1 2
1 2 3 4
```
Option B:
```
2 1 4 3
1 2 3 4
4 3 1 2
3 4 2 1
```
Option C:
```
2 1 4 3
4 3 1 2
1 2 3 4
3 4 2 1
```
Option D:
```
1 2 3 4
2 1 4 3
4 3 1 2
3 4 2 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>Now you are asked to solve a new ARC puzzle. You are given up to three example pairs of ARC grids, each showing an input state and its correct output state. You should learn the transformation rules from these examples. Below these training examples is a new test input grid. Four candidate outputs labeled A, B, C, and D are provided in the lower half of the image. Select the single letter whose output grid correctly completes the test input according to the same transformation rules. After your thinking process, respond only with the chosen letter enclosed in \boxed{}.
|
A
|
|
<image>Now you are asked to solve a new ARC puzzle. You are given up to three example pairs of ARC grids, each showing an input state and its correct output state. You should learn the transformation rules from these examples. Below these training examples is a new test input grid. Four candidate outputs labeled A, B, C, and D are provided in the lower half of the image. Select the single letter whose output grid correctly completes the test input according to the same transformation rules. After your thinking process, respond only with the chosen letter enclosed in \boxed{}.
|
C
|
|
<image>You need to solve a Sudoku puzzle of size 9x9.
**Sudoku Puzzle Rules (9x9 grid):**
1. **The Grid:** The grid is a 9x9 square, further divided into each 3x3 subgrid (non-overlapping regions).
2. **The Goal:** Fill all empty cells in the grid with digits from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must appear exactly once in:
a. Each row.
b. Each column.
c. Each 3x3 subgrid.
4. **Given Numbers:** The puzzle starts with some cells already filled with digits. These are your clues.
5. **Solving:** Use logic to deduce the correct digit for each empty cell based on the given numbers and the rules.
Option A:
```
4 8 6 2 1 3 5 7 9
1 7 2 6 5 9 3 8 4
9 3 5 7 4 8 6 1 2
2 1 7 4 9 6 8 5 3
6 4 8 5 3 7 9 2 1
3 5 9 1 8 2 7 4 6
7 2 3 8 6 1 4 9 5
5 9 1 3 7 4 2 6 5
8 6 4 9 2 5 1 3 7
```
Option B:
```
4 8 6 2 1 3 5 7 9
1 7 2 6 5 9 3 8 4
9 3 5 7 4 8 6 1 2
5 1 7 4 9 6 8 5 3
6 4 8 5 3 7 9 2 1
3 5 9 1 8 2 7 4 6
7 2 3 8 6 1 4 9 5
2 9 1 3 7 4 2 6 8
8 6 4 9 2 5 1 3 7
```
Option C:
```
4 8 6 2 1 3 5 7 9
1 7 2 6 5 9 3 8 4
9 3 5 7 4 8 6 1 2
2 1 7 4 9 6 8 5 3
6 4 8 5 3 7 9 2 1
3 5 9 1 8 2 7 4 6
7 8 3 2 6 1 4 9 5
5 9 1 3 7 4 2 6 8
8 6 4 9 2 5 1 3 7
```
Option D:
```
4 8 6 2 1 3 5 7 9
1 7 2 6 5 9 3 8 4
9 3 5 7 4 8 6 1 2
2 1 7 4 9 6 8 5 3
6 4 8 5 3 7 9 2 1
3 5 9 1 8 2 7 4 6
7 2 3 8 6 1 4 9 5
5 9 1 3 7 4 2 6 8
8 6 4 9 2 5 1 3 7
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
D
|
|
<image>Ready for a Futoshiki puzzle?
Q: What size is this puzzle?
A: It's a 8×8 grid.
Q: What numbers do I use?
A: Use the digits 1 through 8.
Q: What are the main rules?
A: Each number appears once per row and once per column.
Q: What do the inequality signs mean?
A: '>' means greater than, '<' means less than, '^' means top is less, 'v' means top is greater.
Q: How many numbers are already filled in?
A: There are 28 numbers given as clues. Empty cells show '*'.
Now, which option correctly completes the puzzle?
**Available Solutions:**
--- A ---
```
7 1 6 2 5 8 4 3
6 3 2 5 8 7 1 4
3 7 4 6 1 2 5 8
5 6 3 8 2 4 7 1
4 5 7 3 6 1 8 2
2 4 8 1 3 5 6 7
8 2 1 7 7 6 3 5
1 8 5 4 4 3 2 6
```
--- B ---
```
7 1 6 2 5 8 4 7
6 3 2 5 8 3 1 4
3 7 4 6 1 2 5 8
5 6 3 8 2 4 7 1
4 5 7 3 6 3 8 2
2 4 8 1 2 5 6 7
8 3 1 4 7 6 1 5
1 8 5 7 4 3 2 6
```
--- C ---
```
1 7 6 2 8 5 4 3
6 3 2 5 8 7 1 4
3 7 4 6 1 2 5 8
5 6 3 8 2 4 7 1
4 5 7 3 6 1 8 2
2 4 8 1 3 5 6 7
8 2 1 4 7 6 3 5
1 8 5 7 4 3 2 6
```
--- D ---
```
7 1 6 2 5 8 4 3
6 3 2 5 8 7 1 4
3 7 4 6 1 2 5 8
5 6 3 8 2 4 7 1
4 5 7 3 6 1 8 2
2 4 8 1 3 5 6 7
8 2 1 4 7 6 3 5
1 8 5 7 4 3 2 6
```
Submit your answer as \boxed{X} where X is the letter of the correct option.
|
D
|
|
<image>You are a Nonogram player. You need to fill in cells in a grid based on numbers at the side of the grid.
**Nonogram Rules:**
1. For each row or column, the numbers indicate the lengths of consecutive filled cells in that row/column.
2. For example, '2 3' means there are two blocks of filled cells - first 2 cells, then 3 cells, with at least one empty cell between them.
3. '0' means the row/column is completely empty.
**Row hints:** 3, 5, 3, 4, 4, 4 1, 8, 2 5, 1 6, 8, 7, 5
**Column hints:** 8, 8 1, 7 3, 2 9, 1 6, 6, 7, 6, 2, 0, 0, 0
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.
Option A:
```
e s s s e e e e e e e e
s s s s s e e e e e e e
s s s e e e e e e e e e
s s s s e e e e e e e e
s s s s e e e e e e e e
s s s s e e s e e e e e
s s s s s s s s e e e e
s s e s s s s s e e e e
s e s s s s s s e e e e
e s s s s s s s s e e e
e e s s s s s s s e e e
e e e s s s s s e e e e
```
Option B:
```
e s s s e e e e e e e e
s s s s s e e e e e e e
s s s e e e e e e e e e
s s s s s e e e e e e e
s s s s e e e e e e e e
s s s s e e s e e e e e
s s s s s s s s e e e e
s s e s s s s s e e e e
s e s s s s s s e e e e
e s s s s s s s s e e e
e e s s s s s s s e e e
e e e s s s s s e e e e
```
Option C:
```
e s s s e e e e e e e e
s s s s s e e e e e e e
s s s e e e e e e e e e
s s s s e e e e e e e e
s s s s e e e e e e e e
s s s s e e e e e e e e
s s s s s s s s e e e e
s s e s s s s s e e e e
s e s s s s s s e e e e
e s s s s s s s s e e e
e e s s s s s s e e e e
e e e s s s s s e e e e
```
Option D:
```
e s s s e e e e e e e e
s s s s s e e e e e e e
s s s e e e e e e e e e
s s s s e e e e e e e e
s s s s e e e e e e e e
s s s s e e s e e e e e
s s s s s s s s e e e e
s s e s s s s s e e e e
s e s s s s s s e e e e
e s s s s s e s s e e e
e e s s s s s s s e e e
e e e s s s s s e e e e
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>Now you are asked to solve a new ARC puzzle. You are given up to three example pairs of ARC grids, each showing an input state and its correct output state. You should learn the transformation rules from these examples. Below these training examples is a new test input grid. Four candidate outputs labeled A, B, C, and D are provided in the lower half of the image. Select the single letter whose output grid correctly completes the test input according to the same transformation rules. After your thinking process, respond only with the chosen letter enclosed in \boxed{}.
|
C
|
|
<image>You need to solve a 5x5 Kakuro puzzle.
**Kakuro Puzzle Rules (5x5 Grid):**
1. **Grid:** The grid is a 5x5 square, containing blank cells and clue cells.
2. **Objective:** Fill all blank cells with numbers from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must satisfy the following conditions:
a. The sum of the digits in each horizontal block must equal the clue value for that block.
b. The sum of the digits in each vertical block must equal the clue value for that block.
(Note: No digit can be repeated within the same horizontal or vertical block, although this wasn't explicitly in the original Chinese, it's a standard Kakuro rule and crucial for solving. Adding it for clarity.)
4. **Clues:** Clue cells display the required sum for the adjacent horizontal or vertical block of blank cells.
5. **Solving:** Use logic to deduce the correct digit for each blank cell based on the clue values.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.Option A:
```
9 1 7 5 8
1 8 2 7 9
6 7 4 1 2
2 5 9 3 1
8 3 1 2 7
```
Option B:
```
9 1 7 -1 8
1 8 2 7 9
6 7 4 1 2
2 5 9 3 1
8 3 1 2 7
```
Option C:
```
9 1 7 5 8
1 8 2 7 9
6 7 4 1 2
2 5 9 3 1
8 3 1 5 7
```
Option D:
```
9 1 7 5 8
1 8 2 7 9
6 7 4 1 2
2 5 9 3 1
8 3 1 2 3
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>You need to solve a Binairo puzzle.
**Binairo Puzzle Rules:**
1. Each cell must contain either a 0 or a 1.
2. There can be no more than two consecutive identical numbers in any row or column (e.g., 000 or 111 are not allowed).
3. Each row and each column must contain an equal number of 0s and 1s.
4. No two rows can be identical, and no two columns can be identical.
The red squares represent 1 and the blue squares represent 0.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle. Each cell is represented by 0 or 1.
Option A:
```
1 0 0 1 0 1
1 0 0 1 1 0
0 1 1 0 1 0
1 0 1 0 0 1
0 1 0 1 1 0
0 1 1 0 0 1
```
Option B:
```
1 0 0 1 0 1
1 0 0 1 1 0
0 1 1 0 0 1
1 0 1 0 0 1
0 1 0 1 1 0
0 1 1 0 0 1
```
Option C:
```
1 0 0 1 0 1
1 0 0 1 1 0
0 1 1 0 1 0
1 0 1 0 0 0
0 1 0 1 1 0
0 1 1 0 0 1
```
Option D:
```
1 0 0 1 0 1
1 0 0 1 1 0
0 1 1 0 1 0
1 0 1 1 0 1
0 1 0 1 1 0
0 1 1 0 0 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
1 1 0 0 0
1 0 1 0 0
1 1 0 0 0
1 1 0 1 0
1 0 1 1 1
```
Option B:
```
1 1 0 0 0
1 0 1 0 0
1 1 0 0 0
1 1 0 1 0
1 1 1 1 1
```
Option C:
```
1 1 0 0 0
1 0 1 0 0
1 0 1 0 0
1 1 0 1 0
1 1 1 1 1
```
Option D:
```
1 1 0 0 0
1 0 0 0 0
1 1 0 0 0
1 1 0 1 0
1 1 1 1 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>Now you are asked to solve a new ARC puzzle. You are given up to three example pairs of ARC grids, each showing an input state and its correct output state. You should learn the transformation rules from these examples. Below these training examples is a new test input grid. Four candidate outputs labeled A, B, C, and D are provided in the lower half of the image. Select the single letter whose output grid correctly completes the test input according to the same transformation rules. After your thinking process, respond only with the chosen letter enclosed in \boxed{}.
|
C
|
|
<image>You need to solve a Binairo puzzle.
**Binairo Puzzle Rules:**
1. Each cell must contain either a 0 or a 1.
2. There can be no more than two consecutive identical numbers in any row or column (e.g., 000 or 111 are not allowed).
3. Each row and each column must contain an equal number of 0s and 1s.
4. No two rows can be identical, and no two columns can be identical.
The red squares represent 1 and the blue squares represent 0.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle. Each cell is represented by 0 or 1.
Option A:
```
0 0 1 0 1 0 1 1
1 1 0 1 0 0 1 0
1 0 0 1 0 1 0 1
0 1 1 0 1 1 0 0
0 1 0 0 1 0 1 1
1 0 1 1 0 0 1 0
1 1 0 0 1 1 0 0
0 0 1 1 0 1 0 1
```
Option B:
```
0 0 1 0 1 0 1 1
1 1 0 1 0 0 1 0
1 0 0 1 0 1 0 1
1 1 0 0 1 1 0 0
0 1 0 0 1 0 1 1
1 0 1 1 0 0 1 0
1 1 0 0 1 1 0 0
0 0 1 1 0 1 0 1
```
Option C:
```
0 0 1 0 1 0 1 1
1 1 0 1 0 0 1 0
1 0 0 1 0 1 0 1
0 1 1 0 1 1 0 0
0 1 0 0 1 0 1 1
1 0 1 1 0 0 1 0
1 1 0 0 1 1 0 0
0 0 1 1 1 1 0 1
```
Option D:
```
1 0 1 1 1 0 1 1
1 1 0 1 0 0 1 0
1 0 0 1 0 1 0 1
0 1 1 0 1 1 0 0
0 1 0 0 1 0 1 1
1 0 1 1 0 0 1 0
1 1 0 0 1 1 0 0
0 0 1 1 0 1 0 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>You are a Star Battle player. You have to place stars on the grid such that each row, column, and region contains exactly one star. Additional rule is: stars cannot touch each other, not even diagonally.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.
Option A:
```
s s e e e e e e e e e e
e e e e e e e s e e e e
e s e e e e e e e e e e
e e e s e e e e e e e e
e e e e e s e e e e e e
e e e e e e e e e e s e
e e s e e e e e e e e e
e e e e s e e e e e e e
e e e e e e s e e e e e
e e e e e e e e e s e e
e e e e e e e e e e e s
e e e e e e e e s e e e
```
Option B:
```
s e e e e e e e e e e e
e e e e e e e s e e e e
e s e e e e e e e e e e
e e e s e e e e e e e e
e e e e e s e e e e e e
e e e e e e e e e e s e
e e s e e e e e e e e e
e e e e s e e e e e e e
e e e e e e s e e e e e
e e e e e e e e e s e e
e e e e e e e e e e e s
e e e e e e e e s e e e
```
Option C:
```
s e e e e e e e e e e e
e e e e e e e s e e e e
e s e e e e s e e e e e
e e e s e e e e e e e e
e e e e e s e e e e e e
e e e e e e e e e e s e
e e s e e e e e e e e e
e e e e s e e e e e e e
e e e e e e s e e e e e
e e e e e e e e e s e e
e e e e e e e e e e e s
e e e e e e e e s e e e
```
Option D:
```
s e e e e e e e e e e e
e e e e e e e s e e e e
e s e e e e e e e e e e
e e e s e e e e e e e e
e e e e e s e e e e e e
e e e e e e e e e e s e
e e s e e e e e e e e e
s e e e s e e e e e e e
e e e e e e s e e e e e
e e e e e e e e e s e e
e e e e e e e e e e e s
e e e e e e e e s e e e
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 1 1
1 0 0 0 0 1 0 0 1 1 1
0 1 1 1 1 0 0 0 0 1 1
1 1 1 1 1 0 0 1 0 1 0
0 0 1 0 1 0 0 0 1 1 1
0 0 1 0 0 0 0 0 0 1 1
0 0 0 1 1 0 0 0 0 0 1
0 0 0 1 0 0 0 0 0 0 1
0 1 1 1 0 0 0 0 0 1 0
1 1 1 0 0 1 1 1 1 1 1
```
Option B:
```
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 1 0
1 0 0 1 0 1 0 0 1 1 1
0 1 1 1 1 0 0 0 0 1 1
0 1 1 1 1 0 0 1 0 1 0
0 0 1 0 1 0 0 0 1 1 1
0 0 1 0 0 0 0 0 0 1 1
0 0 0 0 1 0 0 0 0 0 1
0 0 0 1 0 0 0 0 0 0 1
0 1 1 1 0 0 0 0 0 1 0
0 1 0 0 0 1 1 1 1 1 1
```
Option C:
```
0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 1 0
1 0 0 0 0 1 0 0 1 1 1
0 1 1 1 1 0 0 0 0 1 1
0 1 1 1 1 0 0 1 0 1 0
0 0 1 0 1 0 0 0 1 1 1
0 0 1 0 0 0 0 0 0 1 1
0 0 0 1 1 0 0 0 0 0 1
0 0 0 1 0 0 0 0 0 0 1
0 1 1 1 0 0 0 0 0 1 0
0 1 1 0 0 1 1 1 1 1 1
```
Option D:
```
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 1 0
1 0 0 0 0 1 0 0 1 1 1
0 1 1 1 1 0 0 0 0 1 1
0 1 1 1 1 0 0 1 0 1 0
0 0 1 0 1 0 0 0 1 1 1
0 0 1 0 0 0 0 0 0 1 1
0 0 0 1 1 0 0 0 0 0 1
0 0 0 1 0 0 0 0 0 0 1
0 1 1 1 0 0 0 0 0 1 0
0 1 1 0 0 1 1 1 1 1 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
D
|
|
<image>You need to solve a Binairo puzzle.
**Binairo Puzzle Rules:**
1. Each cell must contain either a 0 or a 1.
2. There can be no more than two consecutive identical numbers in any row or column (e.g., 000 or 111 are not allowed).
3. Each row and each column must contain an equal number of 0s and 1s.
4. No two rows can be identical, and no two columns can be identical.
The red squares represent 1 and the blue squares represent 0.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle. Each cell is represented by 0 or 1.
Option A:
```
0 1 1 0
0 0 1 1
1 1 0 1
1 0 0 1
```
Option B:
```
1 1 1 0
1 0 1 1
0 1 0 0
0 0 0 1
```
Option C:
```
0 1 1 0
0 1 1 1
1 1 0 0
1 0 0 1
```
Option D:
```
0 1 1 0
0 0 1 1
1 1 0 0
1 0 0 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
D
|
|
<image>You need to solve a Binairo puzzle.
**Binairo Puzzle Rules:**
1. Each cell must contain either a 0 or a 1.
2. There can be no more than two consecutive identical numbers in any row or column (e.g., 000 or 111 are not allowed).
3. Each row and each column must contain an equal number of 0s and 1s.
4. No two rows can be identical, and no two columns can be identical.
The red squares represent 1 and the blue squares represent 0.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle. Each cell is represented by 0 or 1.
Option A:
```
1 1 0 1 0 0 1 0
1 1 0 0 1 0 1 0
0 0 1 1 0 1 0 1
1 1 0 0 1 0 0 1
0 0 1 0 0 1 1 0
0 1 0 0 1 1 0 1
1 0 1 1 0 0 1 0
0 0 1 0 1 1 0 1
```
Option B:
```
1 1 0 1 0 0 1 0
1 1 0 0 1 0 1 0
0 0 1 1 0 1 0 1
1 1 0 0 1 0 0 1
0 0 1 1 0 1 1 0
1 0 1 1 0 0 1 0
1 0 1 1 0 0 1 0
0 0 1 0 1 1 0 1
```
Option C:
```
1 1 0 1 0 0 1 0
1 1 0 0 1 0 1 0
0 0 1 1 0 1 0 1
0 1 0 0 1 0 0 1
0 0 1 1 0 1 1 0
0 1 0 0 1 1 0 1
1 0 1 1 0 0 1 0
0 0 1 0 1 1 0 1
```
Option D:
```
1 1 0 1 0 0 1 0
1 1 0 0 1 0 1 0
0 0 1 1 0 1 0 1
1 1 0 0 1 0 0 1
0 0 1 1 0 1 1 0
0 1 0 0 1 1 0 1
1 0 1 1 0 0 1 0
0 0 1 0 1 1 0 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
D
|
|
<image>You need to solve a Binairo puzzle.
**Binairo Puzzle Rules:**
1. Each cell must contain either a 0 or a 1.
2. There can be no more than two consecutive identical numbers in any row or column (e.g., 000 or 111 are not allowed).
3. Each row and each column must contain an equal number of 0s and 1s.
4. No two rows can be identical, and no two columns can be identical.
The red squares represent 1 and the blue squares represent 0.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle. Each cell is represented by 0 or 1.
Option A:
```
0 1 0 1
1 1 0 0
0 0 1 1
1 0 0 0
```
Option B:
```
0 1 0 1
0 1 0 0
1 0 1 1
1 0 1 0
```
Option C:
```
0 1 0 1
1 1 0 0
0 0 1 1
1 0 1 0
```
Option D:
```
0 1 0 0
1 1 0 0
0 0 1 0
1 0 1 0
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
0 0 0 0 0 0 0
1 1 1 0 0 0 0
0 0 1 0 0 1 1
1 0 0 0 0 0 0
0 0 0 1 1 1 1
1 1 1 0 1 0 1
1 1 1 1 1 0 0
```
Option B:
```
0 0 0 0 0 0 0
0 1 1 0 0 0 0
0 1 1 0 0 0 1
0 0 0 0 0 0 0
0 0 0 1 0 1 1
1 1 1 0 1 0 1
1 1 1 1 1 0 0
```
Option C:
```
0 0 0 0 0 0 0
1 1 1 0 0 0 0
0 0 1 0 0 0 1
0 0 0 0 0 0 0
0 0 0 1 0 1 1
1 1 1 0 1 0 1
1 1 1 1 1 0 0
```
Option D:
```
0 0 0 0 0 0 0
1 1 1 0 0 0 1
0 0 1 1 0 0 1
0 0 0 0 0 0 0
0 1 0 1 0 1 1
1 1 1 0 1 0 1
1 1 1 1 1 0 0
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>Now you are asked to solve a new ARC puzzle. You are given up to three example pairs of ARC grids, each showing an input state and its correct output state. You should learn the transformation rules from these examples. Below these training examples is a new test input grid. Four candidate outputs labeled A, B, C, and D are provided in the lower half of the image. Select the single letter whose output grid correctly completes the test input according to the same transformation rules. After your thinking process, respond only with the chosen letter enclosed in \boxed{}.
|
B
|
|
<image>You need to solve a 8x8 Kakuro puzzle.
**Kakuro Puzzle Rules (8x8 Grid):**
1. **Grid:** The grid is a 8x8 square, containing blank cells and clue cells.
2. **Objective:** Fill all blank cells with numbers from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must satisfy the following conditions:
a. The sum of the digits in each horizontal block must equal the clue value for that block.
b. The sum of the digits in each vertical block must equal the clue value for that block.
(Note: No digit can be repeated within the same horizontal or vertical block, although this wasn't explicitly in the original Chinese, it's a standard Kakuro rule and crucial for solving. Adding it for clarity.)
4. **Clues:** Clue cells display the required sum for the adjacent horizontal or vertical block of blank cells.
5. **Solving:** Use logic to deduce the correct digit for each blank cell based on the clue values.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.Option A:
```
7 8 5 3 6 4 1 2
4 9 3 9 1 2 7 5
6 1 2 8 4 9 3 7
2 4 1 5 9 3 8 6
3 7 9 4 5 6 2 8
9 5 4 7 3 8 6 1
1 3 6 2 7 5 4 9
5 2 7 6 8 1 9 3
```
Option B:
```
7 8 5 3 6 4 1 2
4 6 3 9 1 2 7 5
6 1 2 8 4 9 3 7
2 4 1 4 9 3 8 6
3 7 9 4 5 6 2 8
9 5 4 7 3 8 6 1
1 3 6 2 7 5 4 9
5 2 7 6 8 1 9 3
```
Option C:
```
7 8 5 3 6 4 1 2
4 6 3 9 1 2 7 5
6 1 2 8 4 9 3 7
2 4 1 5 9 3 8 6
3 7 9 4 5 6 2 8
9 5 4 7 3 8 6 1
1 3 6 2 7 5 4 9
5 2 7 6 8 1 9 3
```
Option D:
```
7 8 5 3 6 4 8 2
4 6 3 9 1 2 7 5
6 1 2 8 4 9 3 7
2 4 1 5 9 3 8 6
3 7 9 4 5 6 2 8
9 5 4 7 3 8 6 1
1 3 6 2 7 5 4 9
5 2 7 6 8 1 9 3
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>Let's solve this Futoshiki puzzle together!
Here's what you need to know:
- Fill in the empty cells (marked with *) with numbers from 1 to 4
- Each row must have all different numbers (1 through 4)
- Each column must have all different numbers (1 through 4)
- Pay attention to the inequality signs!
- '>' means the left number is bigger than the right
- '<' means the left number is smaller than the right
- '^' means the top number is smaller than the bottom
- 'v' means the top number is bigger than the bottom
The puzzle already has 12 numbers filled in to help you get started.
Which option shows the correct solution?
**Available Solutions:**
--- A ---
```
1 4 2 3
3 3 4 2
2 2 3 1
4 1 1 4
```
--- B ---
```
1 4 2 3
4 1 3 2
4 2 3 1
3 2 1 4
```
--- C ---
```
1 4 2 3
3 1 4 2
4 2 3 1
2 3 1 4
```
--- D ---
```
1 4 2 3
2 2 4 2
4 3 3 1
1 3 1 4
```
Submit your answer as \boxed{X} where X is the letter of the correct option.
|
C
|
|
<image>You need to solve a Sudoku puzzle of size 9x9.
**Sudoku Puzzle Rules (9x9 grid):**
1. **The Grid:** The grid is a 9x9 square, further divided into each 3x3 subgrid (non-overlapping regions).
2. **The Goal:** Fill all empty cells in the grid with digits from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must appear exactly once in:
a. Each row.
b. Each column.
c. Each 3x3 subgrid.
4. **Given Numbers:** The puzzle starts with some cells already filled with digits. These are your clues.
5. **Solving:** Use logic to deduce the correct digit for each empty cell based on the given numbers and the rules.
Option A:
```
1 4 5 3 2 6 7 8 9
7 2 6 1 8 9 4 5 3
3 8 9 5 4 6 2 6 1
2 3 4 8 7 1 5 9 6
5 1 8 6 9 4 3 7 2
6 9 7 2 3 5 1 4 8
9 5 1 4 6 2 8 3 7
4 6 3 7 1 8 9 2 5
8 7 2 9 5 3 6 1 4
```
Option B:
```
1 4 5 3 2 6 7 8 9
7 2 6 1 8 9 4 5 3
3 8 9 5 4 7 2 6 1
2 3 4 8 7 1 5 9 6
5 1 8 6 9 4 3 7 2
6 9 7 2 3 5 1 4 8
9 5 1 4 6 2 8 3 7
4 6 3 7 1 8 9 2 5
8 7 2 9 5 3 6 1 4
```
Option C:
```
8 1 5 2 3 4 7 6 9
7 9 6 5 1 8 2 3 4
4 3 2 6 7 9 1 8 5
1 2 7 8 4 3 5 9 6
3 6 9 1 2 5 8 4 7
5 8 4 9 6 7 3 2 1
9 4 3 7 5 2 6 1 8
6 5 8 3 9 1 4 7 2
2 7 1 4 8 6 9 5 3
```
Option D:
```
1 4 5 3 2 6 7 8 9
7 2 6 1 8 9 4 5 3
3 8 9 5 4 7 2 6 1
2 3 4 8 7 1 5 9 6
5 1 8 6 9 4 3 7 2
6 9 7 2 3 5 1 4 8
9 5 1 4 6 2 8 3 7
2 6 3 7 1 8 9 2 5
8 7 4 9 5 3 6 1 4
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You need to solve a Sudoku puzzle of size 9x9.
**Sudoku Puzzle Rules (9x9 grid):**
1. **The Grid:** The grid is a 9x9 square, further divided into each 3x3 subgrid (non-overlapping regions).
2. **The Goal:** Fill all empty cells in the grid with digits from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must appear exactly once in:
a. Each row.
b. Each column.
c. Each 3x3 subgrid.
4. **Given Numbers:** The puzzle starts with some cells already filled with digits. These are your clues.
5. **Solving:** Use logic to deduce the correct digit for each empty cell based on the given numbers and the rules.
Option A:
```
3 4 6 2 1 7 5 9 8
1 8 2 3 5 9 6 7 4
7 5 9 4 6 8 1 2 3
2 7 5 8 4 3 9 1 6
8 1 3 1 2 6 7 4 5
6 9 4 9 7 5 3 8 2
4 3 7 6 8 1 2 5 9
9 2 1 5 3 4 8 6 7
5 6 8 7 9 2 4 3 1
```
Option B:
```
3 4 6 2 1 7 5 9 8
1 8 2 3 5 9 6 7 4
7 5 9 4 6 8 1 2 3
2 7 5 8 4 3 9 1 6
8 1 3 9 2 6 7 4 5
6 9 4 1 7 5 3 8 2
4 3 7 6 8 1 2 5 9
9 2 1 5 3 4 8 6 7
5 6 8 7 9 2 4 3 1
```
Option C:
```
3 5 6 2 1 7 5 9 8
1 8 2 3 5 9 6 7 4
7 4 9 4 6 8 1 2 3
2 7 5 8 4 3 9 1 6
8 1 3 9 2 6 7 4 5
6 9 4 1 7 5 3 8 2
4 3 7 6 8 1 2 5 9
9 2 1 5 3 4 8 6 7
5 6 8 7 9 2 4 3 1
```
Option D:
```
3 4 6 9 1 7 5 9 8
1 8 2 3 5 2 6 7 4
7 5 9 4 6 8 1 2 3
2 7 5 8 4 3 9 1 6
8 1 3 9 2 6 7 4 5
6 9 4 1 7 5 3 8 2
4 3 7 6 8 1 2 5 9
9 2 1 5 3 4 8 6 7
5 6 8 7 9 2 4 3 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>## Futoshiki Grid Configuration Task
### Objective
Determine the valid number placement from the given options.
### System Parameters
- Grid dimensions: 4×4
- Value domain: {1, 2, ..., 4}
- Pre-filled cells: 9
- Empty cell notation: '*'
### Constraint Specifications
1. Row constraint: ∀ row r, values(r) = {1, 2, ..., 4}
2. Column constraint: ∀ column c, values(c) = {1, 2, ..., 4}
3. Inequality constraints: All specified relations must hold
- Horizontal: '>' (left > right), '<' (left < right)
- Vertical: '^' (top < bottom), 'v' (top > bottom)
### Task
Select the configuration that satisfies all constraints.
(A) Solution:
```
3 4 2 1
3 2 4 1
4 1 3 2
1 2 4 3
```
(B) Solution:
```
3 4 2 1
2 3 1 4
4 1 3 2
1 2 4 3
```
(C) Solution:
```
3 4 1 2
2 3 1 4
4 1 3 2
1 2 3 4
```
(D) Solution:
```
2 4 4 1
3 3 1 4
4 1 3 2
1 2 2 3
```
Which option is correct? Answer with A, B, C, or D in \boxed{}.
|
B
|
|
<image>You need to solve a Binairo puzzle.
**Binairo Puzzle Rules:**
1. Each cell must contain either a 0 or a 1.
2. There can be no more than two consecutive identical numbers in any row or column (e.g., 000 or 111 are not allowed).
3. Each row and each column must contain an equal number of 0s and 1s.
4. No two rows can be identical, and no two columns can be identical.
The red squares represent 1 and the blue squares represent 0.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle. Each cell is represented by 0 or 1.
Option A:
```
1 1 0 1 0 1 0 0
1 0 1 0 0 1 0 1
0 0 1 0 1 0 1 1
1 1 0 1 0 0 1 0
0 1 1 0 1 1 0 0
1 0 0 1 0 0 1 1
0 0 1 0 1 1 0 1
0 1 0 1 1 0 1 0
```
Option B:
```
1 1 0 1 0 1 0 0
1 0 1 0 0 1 0 1
0 0 1 0 1 0 1 1
1 1 0 1 0 0 1 0
0 1 1 0 0 1 0 0
1 0 0 1 0 0 1 1
0 0 1 0 0 1 0 1
0 1 0 1 1 0 1 0
```
Option C:
```
1 1 0 1 0 1 0 0
1 0 1 0 0 1 0 1
0 0 1 0 1 0 1 1
1 1 0 1 0 0 1 0
0 1 0 0 0 1 0 0
1 0 0 1 0 0 1 1
0 0 1 0 1 1 0 1
0 1 0 1 1 0 1 0
```
Option D:
```
1 1 0 1 0 0 1 0
1 0 1 0 0 1 0 1
0 0 1 0 1 0 1 1
1 1 0 1 0 0 1 0
0 1 1 0 1 1 0 0
1 0 0 1 0 0 1 1
0 0 1 0 1 1 0 1
0 1 0 1 1 0 1 0
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>Now you are asked to solve a new ARC puzzle. You are given up to three example pairs of ARC grids, each showing an input state and its correct output state. You should learn the transformation rules from these examples. Below these training examples is a new test input grid. Four candidate outputs labeled A, B, C, and D are provided in the lower half of the image. Select the single letter whose output grid correctly completes the test input according to the same transformation rules. After your thinking process, respond only with the chosen letter enclosed in \boxed{}.
|
A
|
|
<image>**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Which of the following cells has water?
A: (2,0)
B: (4,1)
C: (1,1)
D: (3,1)
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
D
|
|
<image>You are a Nonogram player. You need to fill in cells in a grid based on numbers at the side of the grid.
**Nonogram Rules:**
1. For each row or column, the numbers indicate the lengths of consecutive filled cells in that row/column.
2. For example, '2 3' means there are two blocks of filled cells - first 2 cells, then 3 cells, with at least one empty cell between them.
3. '0' means the row/column is completely empty.
**Row hints:** 0, 0, 0, 3, 3 2, 2 2 3, 6 3, 7 3, 7 3, 5 2, 1 2 3, 3
**Column hints:** 8, 7, 2 5, 5, 5, 4, 2, 0, 0, 4 2, 8, 8
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.
Option A:
```
e e e e e e e e e e e e
e e e e e e e e e e e e
e e e e e e e e e e e e
s s s e e e e e e e e e
s s s e e e e e e e s s
s s e e s s e e e s s s
s s s s s s e e e s s s
s s s s s s s e e s s s
s s s s s s s e e s s s
s s s s s e e e e e s s
s e s s e e e e e s s s
e e e e e e e e e s s s
```
Option B:
```
e e e e e e e e e e e e
e e e e e e e e e s e e
e e e e e e e e e e e e
s s s e e e e e e e e e
s s s e e e e e e e s s
s s e e s s e e e s s s
s s s s s s e e e s s s
s s s s s s s e e s s s
s s s s e s s e e s s s
s s s s s e e e e e s s
s e s s e e e e e s s s
e e e e e e e e e s s s
```
Option C:
```
e e e e e e e e e e e e
e e e e e e e e e e e e
e e e e e e e e e e e e
s s s e e e e e e e e e
s s s e e e e e e e s s
s s e e s s e e e s s s
s s s s s s e e e s s s
s s s s s s s e e s s s
s s s s s s s e e s s s
s s s s s e e e e e s s
s e s s e e e e e s s s
e e e s e s e e e s s s
```
Option D:
```
e e e e e e e e e e e e
e e e e e e e e e e e e
e e e e e e e e e e e e
s s s e e e e e e e e e
s s s e e e e e e e s s
s s e e s s e e e s s s
s s s s e s e e e s s s
s s s s s s s e e s s s
s s s s s s s e e s s s
s s s s s e e e e e s s
s e s s e e e e e s s s
e e e e e e e e e s s s
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
1 1 0 1 0 0
1 0 0 0 0 0
1 0 1 0 0 1
1 0 0 1 1 1
0 0 0 1 1 1
1 0 1 1 1 1
```
Option B:
```
1 1 0 1 0 0
1 0 0 0 0 0
1 0 1 0 1 1
1 0 1 0 1 1
0 0 0 1 1 1
1 0 1 1 1 1
```
Option C:
```
1 1 0 1 1 0
1 0 0 0 0 0
1 0 1 0 1 1
1 0 1 0 1 1
0 0 0 1 1 0
1 0 1 1 1 1
```
Option D:
```
1 1 0 1 0 0
1 0 0 0 0 0
1 0 1 0 1 1
1 0 1 0 1 1
0 0 0 1 1 0
1 0 1 1 1 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Is cell ((1, 5)) filled with water?
A: Yes
B: No
Please provide your answer as a single letter (A or B) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
1 1 0 0 0 0
1 1 0 0 0 1
1 1 0 1 0 0
1 1 1 1 1 1
1 1 1 1 1 0
1 1 1 1 1 0
```
Option B:
```
1 0 0 1 0 0
1 1 0 0 0 1
1 1 0 1 0 0
1 1 1 1 1 1
1 1 1 1 1 0
1 1 1 1 1 1
```
Option C:
```
1 0 0 1 0 0
1 1 0 0 0 1
1 1 0 1 0 0
1 1 1 1 1 1
0 1 1 1 0 0
1 0 1 1 1 1
```
Option D:
```
1 0 1 1 0 0
1 1 0 0 0 1
1 1 0 1 0 0
1 1 1 1 1 1
1 1 1 1 1 0
1 1 1 1 1 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You need to solve a Sudoku puzzle of size 9x9.
**Sudoku Puzzle Rules (9x9 grid):**
1. **The Grid:** The grid is a 9x9 square, further divided into each 3x3 subgrid (non-overlapping regions).
2. **The Goal:** Fill all empty cells in the grid with digits from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must appear exactly once in:
a. Each row.
b. Each column.
c. Each 3x3 subgrid.
4. **Given Numbers:** The puzzle starts with some cells already filled with digits. These are your clues.
5. **Solving:** Use logic to deduce the correct digit for each empty cell based on the given numbers and the rules.
Option A:
```
5 7 3 2 1 4 6 8 9
2 4 8 6 9 5 7 1 3
1 6 9 3 8 7 2 4 5
7 9 5 4 3 6 8 2 1
3 1 4 7 2 8 5 9 6
8 2 6 1 5 9 3 7 4
9 3 1 5 7 2 4 6 8
4 8 7 9 6 3 1 5 2
6 5 2 8 4 1 9 3 7
```
Option B:
```
8 9 5 2 1 3 6 7 4
3 6 1 4 7 9 2 5 8
4 7 2 5 8 6 3 9 1
6 4 9 1 2 5 7 8 3
2 3 7 6 9 8 4 1 5
1 5 8 3 4 7 9 6 2
5 8 6 9 3 2 1 4 7
7 2 4 8 6 1 5 3 9
9 1 3 7 5 4 8 2 6
```
Option C:
```
5 7 3 2 4 1 6 8 9
2 4 8 6 9 5 7 1 3
1 6 9 3 8 7 2 4 5
7 9 5 4 3 6 8 2 1
3 1 4 7 2 8 5 9 6
8 2 6 1 5 9 3 7 4
9 3 1 5 7 2 4 6 8
4 8 7 9 6 3 1 5 2
6 5 2 8 4 1 9 3 7
```
Option D:
```
3 7 1 2 5 4 8 9 6
6 4 9 1 8 3 2 7 5
5 8 2 6 7 9 3 4 1
1 2 6 5 4 8 9 3 7
4 9 3 7 6 2 5 1 8
7 5 8 9 3 1 4 6 2
2 6 5 3 9 7 1 8 4
9 1 4 8 2 6 7 5 3
8 3 7 4 1 5 6 2 9
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Which of the following cells has water?
A: (1,0)
B: (8,7)
C: (8,5)
D: (2,7)
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
0 0 0 1 0 0
1 1 0 0 0 0
1 1 0 0 1 1
1 0 0 0 1 0
1 0 1 1 1 1
1 1 1 0 1 1
```
Option B:
```
0 0 0 1 0 0
1 1 0 0 0 0
1 1 0 0 1 1
1 0 0 0 1 0
0 1 0 0 1 1
1 1 1 0 1 1
```
Option C:
```
0 0 0 1 0 0
1 1 0 0 0 0
1 1 0 0 1 1
1 0 0 0 1 0
1 0 0 1 1 1
1 1 1 1 1 1
```
Option D:
```
0 0 0 1 0 0
1 1 0 0 0 0
1 1 0 0 1 1
1 0 0 0 1 0
1 0 0 1 1 1
1 1 1 0 1 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
D
|
|
<image>You need to solve a 4x4 Kakuro puzzle.
**Kakuro Puzzle Rules (4x4 Grid):**
1. **Grid:** The grid is a 4x4 square, containing blank cells and clue cells.
2. **Objective:** Fill all blank cells with numbers from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must satisfy the following conditions:
a. The sum of the digits in each horizontal block must equal the clue value for that block.
b. The sum of the digits in each vertical block must equal the clue value for that block.
(Note: No digit can be repeated within the same horizontal or vertical block, although this wasn't explicitly in the original Chinese, it's a standard Kakuro rule and crucial for solving. Adding it for clarity.)
4. **Clues:** Clue cells display the required sum for the adjacent horizontal or vertical block of blank cells.
5. **Solving:** Use logic to deduce the correct digit for each blank cell based on the clue values.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.Option A:
```
3 2 5 7
6 9 7 4
1 4 8 5
5 6 5 1
```
Option B:
```
3 2 5 7
6 9 7 4
1 4 8 5
5 6 4 1
```
Option C:
```
3 2 5 7
6 9 7 4
11 4 8 5
5 6 4 1
```
Option D:
```
3 2 5 7
6 -1 7 4
1 4 8 5
5 6 4 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>Futoshiki 4×4. Fill 1-4. No repeats in rows/cols.
Inequalities: > greater, < less, ^ up<down, v up>down
Given: 4 numbers (* = empty)
Choose the correct solution.
(A) Solution:
```
1 2 3 4
3 2 4 1
4 3 2 1
2 4 1 3
```
(B) Solution:
```
1 4 3 4
3 1 1 2
3 3 2 4
2 2 1 4
```
(C) Solution:
```
1 2 3 4
3 1 4 2
4 3 2 1
2 1 4 3
```
(D) Solution:
```
1 2 3 4
3 1 4 2
4 3 2 1
2 4 1 3
```
Identify the valid solution. Put your answer choice (A/B/C/D) in \boxed{}.
|
D
|
|
<image>You need to solve a Light Up puzzle.
**Puzzle Rules:**
1. A bulb (`s`) illuminates its entire row and column until blocked by a wall.
2. Numbered walls must have exactly that many bulbs adjacent (up/down/left/right).
3. Bulbs cannot illuminate each other.
Below is the puzzle (walls shown in the image). Fill bulbs (`s`) and empty cells (`e`) to satisfy the rules.
Option A:
```
s e e w
w e s e
e e e e
e s w s
```
Option B:
```
s e s w
w e s e
s e e e
e s w s
```
Option C:
```
s e e w
w e s e
s e e e
e s w s
```
Option D:
```
e e e w
w e s e
s e e e
e s w s
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
C
|
|
<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
0 0 1 0 0 0
0 0 0 0 0 1
0 1 1 0 1 1
1 0 0 0 0 1
1 0 1 0 0 1
0 1 1 1 0 0
```
Option B:
```
0 0 0 0 0 0
0 0 0 0 0 1
0 1 1 0 1 1
1 0 0 0 0 1
1 0 1 0 1 1
0 1 1 1 0 0
```
Option C:
```
0 0 0 0 0 0
0 0 0 0 0 1
0 1 1 0 1 1
1 0 0 0 0 1
1 1 1 0 0 1
0 0 1 1 0 0
```
Option D:
```
0 0 0 0 0 0
0 0 0 0 0 1
0 1 1 0 1 1
1 0 0 0 0 1
1 0 1 0 0 1
0 1 1 1 0 0
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
D
|
|
<image>You are a Nonogram player. You need to fill in cells in a grid based on numbers at the side of the grid.
**Nonogram Rules:**
1. For each row or column, the numbers indicate the lengths of consecutive filled cells in that row/column.
2. For example, '2 3' means there are two blocks of filled cells - first 2 cells, then 3 cells, with at least one empty cell between them.
3. '0' means the row/column is completely empty.
**Row hints:** 4, 5, 3, 0, 0
**Column hints:** 3, 3, 3, 2, 1
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.
Option A:
```
s e s e e
s s s s s
s s s e s
e e e e e
e e e e e
```
Option B:
```
s s s s e
s s s s s
s s s e e
e e e e e
e e e e e
```
Option C:
```
s s s e e
s s s s s
s s s e e
e e e e e
e e e e e
```
Option D:
```
s s s s e
s s e s s
s s s e e
e e e e e
e e s e e
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
0 0 0 0
0 1 1 1
1 1 1 1
1 1 1 1
```
Option B:
```
0 0 0 0
0 1 1 1
1 0 1 1
1 1 1 1
```
Option C:
```
0 0 0 0
0 1 1 1
0 1 1 1
1 1 1 1
```
Option D:
```
1 0 0 0
0 1 1 1
1 1 1 1
1 1 1 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
1 0 0 0 0
1 0 0 0 0
1 1 0 0 1
1 1 0 1 1
1 1 1 1 1
```
Option B:
```
1 0 0 0 0
1 0 0 0 0
1 1 0 0 1
1 1 0 1 1
0 1 1 1 1
```
Option C:
```
1 0 0 0 0
1 0 0 0 1
1 1 0 0 1
1 0 0 1 1
0 1 1 1 1
```
Option D:
```
1 0 1 0 0
1 0 0 0 0
1 1 0 0 1
1 1 0 1 1
1 1 1 1 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>You need to solve a Light Up puzzle.
**Puzzle Rules:**
1. A bulb (`s`) illuminates its entire row and column until blocked by a wall.
2. Numbered walls must have exactly that many bulbs adjacent (up/down/left/right).
3. Bulbs cannot illuminate each other.
Below is the puzzle (walls shown in the image). Fill bulbs (`s`) and empty cells (`e`) to satisfy the rules.
Option A:
```
e e s e w s e w
s e e e w e s e
e e e s e w e e
e s w e e w e s
w w s w s e w e
s e e e w s e e
e s w e e e s e
w e s e e w e w
```
Option B:
```
e e s e w s e w
s e e e w e s e
e e e s e w e e
e s w e e w e s
w w s w s e w e
s e e e e s e e
e s w e e e s e
w e s e e w e w
```
Option C:
```
e e s e w s e w
s e e e w e s e
s e e s e e e e
e s w e e w e s
w w s w s e w e
s e e e w s e e
e s w e e e s e
w e s e e w e w
```
Option D:
```
e e s e w s e w
s e e e w e s e
e e e s e w e e
e s w e e w e s
w w s w s e w e
s e s e w s s e
e s w s e e s e
w e s e e w e e
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>You need to solve a Binairo puzzle.
**Binairo Puzzle Rules:**
1. Each cell must contain either a 0 or a 1.
2. There can be no more than two consecutive identical numbers in any row or column (e.g., 000 or 111 are not allowed).
3. Each row and each column must contain an equal number of 0s and 1s.
4. No two rows can be identical, and no two columns can be identical.
The red squares represent 1 and the blue squares represent 0.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle. Each cell is represented by 0 or 1.
Option A:
```
1 0 0 1 0 0 1 1
1 0 1 1 0 0 1 0
0 1 0 0 1 1 0 1
0 1 0 0 1 0 1 1
1 0 1 1 0 1 0 0
1 0 1 0 1 0 0 1
0 1 0 1 0 1 1 0
0 1 1 0 1 1 0 0
```
Option B:
```
1 0 0 1 0 0 1 1
1 0 1 1 0 0 1 0
0 1 0 0 1 1 0 1
0 1 0 0 1 0 1 1
1 0 1 1 0 1 0 0
1 0 1 1 1 0 0 1
0 1 0 1 0 1 1 0
0 1 1 0 1 1 0 0
```
Option C:
```
1 0 0 1 0 0 1 1
1 0 1 1 0 0 1 1
0 1 0 0 1 1 0 0
0 1 0 0 1 0 1 0
1 0 1 1 0 1 0 1
1 0 1 0 1 0 0 1
0 1 0 1 0 1 1 0
0 1 1 0 1 1 0 0
```
Option D:
```
1 0 0 1 0 0 1 1
1 1 1 1 0 0 1 0
0 1 0 0 1 1 0 1
0 1 0 0 1 0 1 1
1 1 1 1 0 1 0 0
1 0 1 0 1 0 0 1
0 1 0 1 0 1 1 0
0 1 1 0 1 1 0 0
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>Now you are asked to solve a new ARC puzzle. You are given up to three example pairs of ARC grids, each showing an input state and its correct output state. You should learn the transformation rules from these examples. Below these training examples is a new test input grid. Four candidate outputs labeled A, B, C, and D are provided in the lower half of the image. Select the single letter whose output grid correctly completes the test input according to the same transformation rules. After your thinking process, respond only with the chosen letter enclosed in \boxed{}.
|
C
|
|
<image>You need to solve an Aquarium puzzle.
**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Option A:
```
0 0 0 1 1
0 0 0 0 0
0 1 1 1 1
0 0 1 1 0
1 1 0 1 1
```
Option B:
```
0 0 0 1 0
0 0 0 0 0
0 1 1 1 1
0 1 1 1 0
1 1 0 1 1
```
Option C:
```
0 0 0 1 1
0 0 0 0 0
0 1 1 1 1
0 1 1 1 0
1 1 0 1 1
```
Option D:
```
0 0 0 1 1
1 0 0 0 0
0 1 1 1 1
0 0 1 1 0
1 1 0 1 1
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
Which of the following cells has water?
A: (2,0)
B: (3,0)
C: (1,3)
D: (0,1)
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You need to solve a Light Up puzzle.
**Puzzle Rules:**
1. A bulb (`s`) illuminates its entire row and column until blocked by a wall.
2. Numbered walls must have exactly that many bulbs adjacent (up/down/left/right).
3. Bulbs cannot illuminate each other.
Below is the puzzle (walls shown in the image). Fill bulbs (`s`) and empty cells (`e`) to satisfy the rules.
Option A:
```
e e s e
e e e s
s e s w
e s w s
```
Option B:
```
e e s e
e e e s
s e e w
e s w s
```
Option C:
```
e e s e
s e e s
s e e w
e s w s
```
Option D:
```
e e s s
e e e s
s e e w
e s w s
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>Now you are asked to solve a new ARC puzzle. You are given up to three example pairs of ARC grids, each showing an input state and its correct output state. You should learn the transformation rules from these examples. Below these training examples is a new test input grid. Four candidate outputs labeled A, B, C, and D are provided in the lower half of the image. Select the single letter whose output grid correctly completes the test input according to the same transformation rules. After your thinking process, respond only with the chosen letter enclosed in \boxed{}.
|
D
|
|
<image>You are a Star Battle player. You have to place stars on the grid such that each row, column, and region contains exactly one star. Additional rule is: stars cannot touch each other, not even diagonally.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.
Option A:
```
s e e e e e e e
e e s e e e e e
e e e e s e e e
e s e e e e e e
e e e e e e s e
e e e s e e e e
e e e e e s e e
e e e e e e e s
```
Option B:
```
s e e e e e e e
e e s e e e e e
e e e e s e e e
s s e e e e e e
e e e e e e e e
e e e s e e e e
e e e e e s e e
e e e e e e e s
```
Option C:
```
s s e e e e e e
e e s e e e e e
e e e e s e e e
e s e e e e e e
e e e e e e s e
e e e s e e e e
e e e e e s e e
e e e e e e e s
```
Option D:
```
s e e e e e e e
e e s e e e e e
e e e e s e e e
e e e e e e e e
e e e e e e s e
e e e s e s e e
e e e e e s e e
e e e e e e e s
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>**Aquarium Puzzle Rules:**
1. **The Grid:** The grid is divided into several regions called "tanks" by the thick colored (red) lines.
2. **The Goal:** Your goal is to fill some cells in the grid with "water".
3. **Water Levels:** Within each tank, water must settle at a uniform level. This means: if a cell is filled with water, all cells directly below it *within the same tank* must also be filled, down to the bottom of that tank.
4. **Clues:** The numbers outside the grid indicate how many cells *in total* must be filled with water in that specific row (numbers on the left) or column (numbers on the top).
5. **Solving:** Use the numbers as clues to figure out which cells must be filled with water, ensuring that the water level rule within each tank is followed, until all numbers are satisfied.
How many cells are filled with water in total?
A: 57
B: 56
C: 55
D: 54
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
D
|
|
<image>You need to solve a 4x4 Kakuro puzzle.
**Kakuro Puzzle Rules (4x4 Grid):**
1. **Grid:** The grid is a 4x4 square, containing blank cells and clue cells.
2. **Objective:** Fill all blank cells with numbers from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must satisfy the following conditions:
a. The sum of the digits in each horizontal block must equal the clue value for that block.
b. The sum of the digits in each vertical block must equal the clue value for that block.
(Note: No digit can be repeated within the same horizontal or vertical block, although this wasn't explicitly in the original Chinese, it's a standard Kakuro rule and crucial for solving. Adding it for clarity.)
4. **Clues:** Clue cells display the required sum for the adjacent horizontal or vertical block of blank cells.
5. **Solving:** Use logic to deduce the correct digit for each blank cell based on the clue values.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.Option A:
```
4 5 7 2
3 7 5 1
9 8 1 3
6 1 8 9
```
Option B:
```
4 5 7 2
3 7 5 1
9 8 2 3
6 1 8 9
```
Option C:
```
4 5 7 2
9 7 5 1
9 8 2 3
6 1 8 9
```
Option D:
```
4 5 7 2
3 7 1 1
9 8 2 3
6 1 8 9
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>Now you are asked to solve a new ARC puzzle. You are given up to three example pairs of ARC grids, each showing an input state and its correct output state. You should learn the transformation rules from these examples. Below these training examples is a new test input grid. Four candidate outputs labeled A, B, C, and D are provided in the lower half of the image. Select the single letter whose output grid correctly completes the test input according to the same transformation rules. After your thinking process, respond only with the chosen letter enclosed in \boxed{}.
|
C
|
|
<image>You need to solve a 4x4 Kakuro puzzle.
**Kakuro Puzzle Rules (4x4 Grid):**
1. **Grid:** The grid is a 4x4 square, containing blank cells and clue cells.
2. **Objective:** Fill all blank cells with numbers from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must satisfy the following conditions:
a. The sum of the digits in each horizontal block must equal the clue value for that block.
b. The sum of the digits in each vertical block must equal the clue value for that block.
(Note: No digit can be repeated within the same horizontal or vertical block, although this wasn't explicitly in the original Chinese, it's a standard Kakuro rule and crucial for solving. Adding it for clarity.)
4. **Clues:** Clue cells display the required sum for the adjacent horizontal or vertical block of blank cells.
5. **Solving:** Use logic to deduce the correct digit for each blank cell based on the clue values.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle.Option A:
```
2 1 8 9
5 7 2 4
11 6 5 2
7 3 9 6
```
Option B:
```
8 1 8 9
5 7 2 4
3 6 5 2
7 3 9 6
```
Option C:
```
2 1 8 9
4 7 2 4
3 6 5 2
7 3 9 6
```
Option D:
```
2 1 8 9
5 7 2 4
3 6 5 2
7 3 9 6
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
D
|
|
<image>You need to solve this Killer Sudoku puzzle.
Fill the grid so that each row, column, and box has unique digits.
In each colored cage, the sum of digits equals the given number, and digits do not repeat.
Option A:
```
4 2 3 1
2 3 1 4
1 4 2 3
3 1 4 2
```
Option B:
```
4 2 3 1
3 1 4 2
1 4 2 3
2 3 1 4
```
Option C:
```
2 3 1 4
3 1 4 2
1 4 2 3
4 2 3 1
```
Option D:
```
4 2 3 1
1 4 2 3
3 1 4 2
2 3 1 4
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You need to solve a Binairo puzzle.
**Binairo Puzzle Rules:**
1. Each cell must contain either a 0 or a 1.
2. There can be no more than two consecutive identical numbers in any row or column (e.g., 000 or 111 are not allowed).
3. Each row and each column must contain an equal number of 0s and 1s.
4. No two rows can be identical, and no two columns can be identical.
The red squares represent 1 and the blue squares represent 0.
Your task is to choose the correct grid configuration from the options below that represents the solution to the puzzle. Each cell is represented by 0 or 1.
Option A:
```
1 1 0 1 0 1 0 0
1 1 0 0 1 1 0 0
0 0 1 0 1 0 1 1
1 1 0 1 0 0 1 0
0 0 1 1 0 1 0 1
0 1 1 0 1 0 1 1
1 0 1 1 0 0 1 0
0 0 1 0 1 1 0 1
```
Option B:
```
1 1 0 1 0 1 0 0
1 1 0 0 1 1 0 0
0 0 1 0 1 0 1 1
1 1 0 1 0 0 1 0
0 0 1 1 0 1 0 1
0 1 0 0 1 0 1 1
1 0 1 1 0 0 1 0
0 0 1 0 1 1 0 1
```
Option C:
```
1 1 0 1 0 1 0 0
1 1 0 0 1 1 1 0
0 0 1 0 1 0 1 1
1 1 0 1 0 0 1 0
0 0 1 1 0 1 1 1
0 1 0 0 1 0 1 1
1 0 1 1 0 0 1 0
0 0 1 0 1 1 0 1
```
Option D:
```
1 1 0 1 0 1 0 1
1 1 0 0 1 1 0 1
0 0 1 0 1 0 1 0
1 1 0 1 0 0 1 1
0 0 1 1 0 1 0 0
0 1 0 0 1 0 1 1
1 0 1 1 0 0 1 0
0 0 1 0 1 1 0 0
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
B
|
|
<image>You need to solve a Sudoku puzzle of size 9x9.
**Sudoku Puzzle Rules (9x9 grid):**
1. **The Grid:** The grid is a 9x9 square, further divided into each 3x3 subgrid (non-overlapping regions).
2. **The Goal:** Fill all empty cells in the grid with digits from 1 to 9.
3. **Constraints:** Each digit (1 to 9) must appear exactly once in:
a. Each row.
b. Each column.
c. Each 3x3 subgrid.
4. **Given Numbers:** The puzzle starts with some cells already filled with digits. These are your clues.
5. **Solving:** Use logic to deduce the correct digit for each empty cell based on the given numbers and the rules.
Option A:
```
5 9 2 1 4 3 7 8 6
8 7 6 2 9 5 1 3 4
4 1 3 6 7 8 2 9 5
1 2 5 8 3 4 9 6 7
6 4 9 7 5 2 8 1 3
7 3 8 9 6 1 4 5 2
9 8 7 5 2 6 3 4 1
2 6 4 3 1 9 5 7 8
3 5 1 4 8 7 6 2 9
```
Option B:
```
5 9 2 1 4 3 7 8 6
8 7 6 2 9 5 1 3 4
4 1 3 6 7 8 2 9 5
1 2 5 8 3 4 9 6 7
6 4 9 7 5 2 8 1 3
7 3 1 9 6 8 4 5 2
9 8 7 5 2 6 3 4 1
2 6 4 3 1 9 5 7 8
3 5 1 4 8 7 6 2 9
```
Option C:
```
5 9 2 1 4 3 7 8 6
8 7 6 2 9 5 1 3 4
4 1 3 6 7 8 2 9 5
1 2 5 8 3 4 9 6 7
6 4 9 7 8 2 8 1 3
7 3 8 9 6 1 4 5 2
9 8 7 5 2 6 3 4 1
2 6 4 3 1 9 5 7 8
3 5 1 4 8 7 6 2 9
```
Option D:
```
5 9 2 1 4 3 7 8 6
2 7 6 2 9 5 1 3 4
4 1 3 6 7 8 2 9 5
1 2 5 8 3 4 9 6 7
6 4 9 7 5 2 8 1 3
7 3 8 9 6 1 4 5 2
9 8 7 5 2 6 3 4 1
2 6 4 3 1 9 5 7 8
3 5 1 4 8 7 6 2 9
```
Please provide your answer as a single letter (A, B, C, or D) in \boxed{} corresponding to the correct option.
|
A
|
|
<image>🔢 FUTOSHIKI PUZZLE 🔢
How to Play:
Fill the 12×12 grid with numbers!
Your Tools:
📝 Numbers to use: 1, 2, ..., 12
🎯 Starting clues: 25 numbers already placed
❓ Empty spaces: marked with *
The Rules:
✓ Each row needs all numbers 1-12 (no repeats!)
✓ Each column needs all numbers 1-12 (no repeats!)
✓ Follow the inequality signs:
• > means "bigger than"
• < means "smaller than"
• ^ means "top is smaller"
• v means "top is bigger"
Which grid shows the winning solution?
Option A:
```
2 11 7 10 1 9 8 4 3 12 6 5
2 11 6 5 7 3 1 10 9 8 4 12
9 4 2 7 6 11 12 1 10 5 3 8
8 3 9 6 4 1 5 7 2 12 11 10
7 1 5 12 10 8 3 9 11 2 6 4
10 9 3 1 5 7 4 6 12 11 8 2
1 12 4 3 9 2 6 11 8 10 5 7
5 10 11 2 8 4 9 12 6 3 7 1
12 5 1 9 2 6 11 8 4 7 10 3
3 7 12 8 11 5 10 2 1 4 9 6
4 6 8 11 12 10 7 3 5 1 2 9
6 8 10 4 3 12 2 5 7 9 1 11
```
Option B:
```
11 2 7 10 1 9 8 4 3 6 12 5
2 11 6 5 7 3 1 10 9 8 4 12
9 4 2 7 6 11 12 1 10 5 3 8
8 3 9 6 4 1 5 7 2 12 11 10
7 1 5 12 10 8 3 9 11 2 6 4
10 9 1 1 12 7 4 6 12 11 8 2
1 12 4 3 9 2 6 11 8 10 5 7
5 10 11 2 8 4 9 12 6 3 7 1
12 5 3 9 2 6 11 8 4 7 10 3
3 7 12 8 11 5 10 2 1 4 9 6
4 6 8 11 5 10 7 3 5 1 2 9
6 8 10 4 3 12 2 5 7 9 1 11
```
Option C:
```
11 2 7 10 1 9 8 4 3 6 12 5
2 11 6 5 7 3 1 10 9 8 4 12
9 4 2 7 6 11 12 1 10 5 3 8
8 3 9 6 4 1 5 7 2 12 11 10
7 1 5 12 10 8 3 9 11 2 6 4
10 9 3 1 5 7 4 6 12 11 8 2
1 12 4 3 9 2 6 11 8 10 5 7
5 10 11 2 8 4 9 12 6 3 7 1
12 5 1 9 2 6 11 8 4 7 10 3
3 7 12 8 11 5 10 2 1 4 9 6
4 6 8 11 12 10 7 3 5 1 2 9
6 8 10 4 3 12 2 5 7 9 1 11
```
Option D:
```
11 2 7 10 1 9 8 4 3 6 12 5
2 11 6 5 7 3 1 10 9 8 4 12
9 4 2 7 6 11 12 1 10 5 3 8
8 3 9 6 4 1 5 7 2 12 11 10
7 1 5 12 10 8 3 9 11 2 6 4
10 9 3 1 5 7 4 6 12 11 8 2
1 12 4 3 9 2 6 11 8 10 5 7
5 10 11 2 8 4 9 12 6 1 7 3
12 5 1 9 2 6 11 8 4 7 10 3
3 7 12 8 11 5 10 2 1 4 9 6
4 6 8 7 12 10 11 3 5 1 2 9
6 8 10 4 3 12 2 5 7 9 1 11
```
Select the correct solution and respond with the letter (A, B, C, or D) in \boxed{}.
|
C
|
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