ARC Challenge

Puzzle ID: 007bbfb7

Reasoning

Initial Observation:

In the first example, it looks like each square in the input becomes more zoomed out in the output.

Verification Step 1:
• Check: example 2, example 3, example 4, example 5.
• It looks like this holds true.
Initial Rule Formulation:
Each square in the input becomes more zoomed out in the output.
Refinement Process:

This isn't enough information to solve the test case, since I don't have an exact mapping. To obtain the mapping, I need to figure out exactly how the "zooming out" works.

Pattern Discovery:

Let me try to map each square in the input to the set of "zoomed out" squares in the output.

Wait, it looks like I can lay one square in the input on top of a 3x3 sub-grid in the output.

Verification Step 2:
• Question: Is this true for all squares?
• Answer: Yes, it is.
• Supporting Evidence: Input is a 3x3 grid, and output is a 9x9 grid.
• Additional Check: example 2, example 3, example 4, example 5.
• Result: True for all examples.
Refined Rule:
Each square in the input maps to a 3x3 sub-grid in the output.
Deduction:

Since each input square maps to a 3x3 sub-grid, and the input is 3x3, the output must be 9x9:

• Input dimensions: 3x3
• Each square expands to: 3x3
• Therefore output dimensions: 3*3 x 3*3 = 9x9
What about color?

Starting with square (1,2) in the input (orange):

• Maps to sub-grid (1:3,4:6) in output
• NOT a match - (1,4) and (1,6) are black in output
• Check square (2,2) - pattern holds
• Check all orange squares - pattern holds
Working Hypothesis:
Each square in the input maps to a 3x3 sub-grid in the output. Color-wise, (1,1) and (1,3) remain black.
Hypothesis Testing:
• Test Case: example 2
Result:
The rule fails example 2.
Failure Analysis:

It fails because the wrong squares are black. My hypothesis is wrong, but the rule remains correct, yet too general.

Critical Investigation:

What makes examples 1 and 2 different? Why are different squares black for both?

I'm not sure. Let me look at the other examples.

Wait a minute. In example 3, I can see in the first 3x3 sub-grid, the pattern of black squares is exactly the pattern in the input.

Wait a minute, the entire 3x3 sub-grid is the exact same as the input 3x3 grid.

This is a surprising result. Let me see if it holds true for all examples.

Check: example 1, example 2, example 4, example 5.

It looks like the rule holds true for all examples. This is enough information to solve the test case.

Final Rule:
Each 3x3 sub-grid in the output is the same as the input 3x3 grid.
Test Output:
Test Output