The no-touch rule

Check the immediate neighborhood

Cats cannot share an edge or a corner. For a cat at row 3, column 3, the neighboring positions are rows 2–4 and columns 2–4, excluding its own cell. All eight are unavailable because of touching, even when their region colors differ.

At the edge of a board there are fewer neighboring cells, but the same test applies. The separate row, column and region rules still rule out more distant cells in those groups. No-touch checks never replace the other quotas.

A long diagonal is different

A cat at row 1, column 1 does not touch one at row 3, column 3: a complete row and column lie between their positions. This pair passes the touching test. They would still be illegal if their regions were the same.

By contrast, row 1, column 1 and row 2, column 2 meet at a corner. They are forbidden neighbors. Judge the distance between the cells, not the direction of an imaginary diagonal line running through the board.

Try the idea, then restore the full rules

The small interactive exercise below tests touching alone. Select a second position, check it, and compare an immediate diagonal neighbor with a distant diagonal cell. It is intentionally not a full puzzle solution.

When you return to a real board, apply all four tests to every cat. Remembering that distinction prevents a common error: using a correct adjacency observation as if it had also checked rows, columns and regions.

A real step from gm-5-0001

Try the idea

Choose a second cell. This exercise checks touching only, not a complete arrangement.