GPT4o, 2024-dec-20

---

# ARC Puzzle

```json
{"train":[{"input":[[9,1,4],[9,1,4],[2,1,1]],"output":[[9,1,4],[9,1,4],[2,1,1],[2,1,1],[9,1,4],[9,1,4]]},{"input":[[4,8,4],[7,6,7],[8,7,8]],"output":[[4,8,4],[7,6,7],[8,7,8],[8,7,8],[7,6,7],[4,8,4]]},{"input":[[7,7,7],[9,5,5],[5,1,7]],"output":[[7,7,7],[9,5,5],[5,1,7],[5,1,7],[9,5,5],[7,7,7]]},{"input":[[2,6,9],[2,6,9],[2,9,2]],"output":[[2,6,9],[2,6,9],[2,9,2],[2,9,2],[2,6,9],[2,6,9]]}],"test":[{"input":[[2,9,2],[8,5,2],[2,2,8]]}]}
```

The `test.output` is not provided, and it's up to you to solve it.

# Task A 

Think step by step.
- What does all the inputs have in common.
- What does all the outputs have in common.
- What does input/outputs have in common.
- Identify what transformation is happening from input to output.
- Verify that the transformation rules work on all input/output pairs.

# Task B

Go ahead and solve this ARC puzzle.

# Task C

Convert the `test.output` data to json format.

The section must contain only the json data wrapped in three back quotes, like this:
```json
[[1,2,3],[4,5,6]]
```

---

Task A: Step-by-step Analysis

1. Commonalities in Inputs
	•	Each input is a 3x3 grid of numbers.
	•	The rows in the grid may repeat, but there is no consistent pattern in how the numbers are arranged.

2. Commonalities in Outputs
	•	Each output starts with the original input grid.
	•	The grid is then mirrored or repeated vertically to form a 6x3 grid.
	•	Specifically, the output is structured as:
Input Grid + Reversed Input Grid.

3. Input and Output Relationship
	•	The transformation rule involves duplicating the grid vertically and appending its reverse (top to bottom).

4. Transformation Rule

For any given 3x3 grid:
	1.	Duplicate the grid.
	2.	Reverse the rows of the duplicated grid.
	3.	Append the reversed grid below the original grid.

5. Verification of Rule
	•	Applying this rule to each train input produces the corresponding train output.
	•	The transformation is consistent and works for all provided examples.

Task B: Solve the Test Case

Using the transformation rules:
	1.	The given test input is:

[[2,9,2],[8,5,2],[2,2,8]]


	2.	Reverse the rows to get:

[[2,2,8],[8,5,2],[2,9,2]]


	3.	Append the reversed rows below the original grid to form the output:

[[2,9,2],[8,5,2],[2,2,8],[2,2,8],[8,5,2],[2,9,2]]

Task C: test.output in JSON Format

[[2,9,2],[8,5,2],[2,2,8],[2,2,8],[8,5,2],[2,9,2]]
