Latin Squares: A Strategy for the dMAT

A Latin Square is an n × n grid where every symbol appears exactly once in each row and each column. On the dMAT, your task is to complete the grid using logical elimination — no arithmetic, no guessing if you do it right.

Where to start

Do not start where the grid is empty. Start where it is most full. The row or column with the fewest blanks gives you the most constraints, which means the fewest possibilities.

The elimination loop

1. Pick the most constrained cell.
2. List which symbols are impossible there (already in that row or column).
3. Whatever remains is your candidate set. If only one remains, place it.
4. Repeat — every placement tightens the constraints elsewhere.

Avoiding the guessing spiral

If you reach a point where no cell has a single forced answer, resist guessing. Instead, look for a symbol that can only go in one place within a given row or column — the "hidden single". This almost always breaks the deadlock.

Latin Squares reward patience. One careful placement unlocks three more; one careless guess can invalidate the whole grid.

The Core Module includes graded Latin Square sets that build from 4×4 up, so the method becomes second nature before exam day.