GridMewThe no-touch rule
Understand edge contact, corner contact and distant diagonal placements.
On this page
Check the immediate neighborhoodA long diagonal is differentTry the idea, then restore the full rulesApply the ideaOriginal exampleCheck your understanding✕ Touching — not allowed
✓ Apart — allowed
Original GridMew lesson · Updated 16 October 2026
Learning goal: Distinguish immediate diagonal contact from a long diagonal, then reapply the separate row, column and region quotas.
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.
Apply the idea to gm-5-0034
r2c3 means row 2, column 3, counting from the top left.
Region A in gm-5-0034 forces r1c1. Around this corner there are only three touching cells: r1c2, r2c1 and r2c2. The first cat also excludes more distant cells in row 1 and column 1, but those are quota exclusions rather than contact exclusions.
For comparison, r3c3 is two rows and two columns away from r1c1. Touching alone does not forbid that pair. This does not certify r3c3 as a solution cell: the original puzzle still has other cats, regional quotas and later deductions to consider.
A real step from gm-5-0034
region A has only one remaining candidate: row 1, column 1. Every other cell is excluded by earlier placements or deductions. Place the cat here.
Try the idea
Choose a second cell. This exercise checks touching only, not a complete arrangement.
Check your understanding
Does the cat at r1c1 exclude r3c3 merely because they lie on the same diagonal?
Show the explanation
No. Their row and column distances are both two. The no-touch rule only concerns immediate neighbors. You must still check every other constraint before placing a cat at r3c3.