dMAT Latin Squares: the tightest constraint

Finding it fast

1. Count the filled cells in each row and column.
2. Go to the fullest one.
3. If it has one empty cell, that placement is forced — take it.
4. If it has two, check whether either symbol is blocked by its column.

After each placement the counts change, so re-scan rather than continuing down a plan made before the grid changed.

Why it cascades

Every placement removes a possibility from a whole row and a whole column at once. On a partly filled grid that frequently creates a new forced cell immediately, which creates another. Grids that look difficult are usually two forced placements away from solving themselves.

This is the habit g.a.s.t. material points at as transferable: working from the tightest constraint is the same instinct that solves a data question or a logic problem, which is why practising on logic grids and Sudoku genuinely helps.