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dMAT Latin Squares: the rules

A Latin Square of size n uses n symbols, and each appears exactly once in every row and every column. That is the whole rule, and everything else follows from it as a consequence rather than as a separate rule to learn.

What follows from the rule

  • Every row contains every symbol, so a row missing one symbol has exactly one cell for it.
  • The same holds for columns.
  • A symbol placed in a cell is eliminated from the rest of that row and that column at once.
  • A row with one empty cell is always immediately solvable.

The fourth is the one to look for first on any grid: an almost-complete row or column is a free placement, and free placements are what start the cascade.

What is not a rule

  • There is no diagonal constraint unless the item states one.
  • There is no box constraint — that belongs to Sudoku, not to a plain Latin Square.
  • Symbols have no order; they are labels, so letters or shapes behave exactly like numbers.

Importing a Sudoku box rule is a real error for candidates who have practised on Sudoku. Read what the item states; a dMAT grid may add a constraint, and it may not.

The rules — FAQs

2 questions

Not unless the item says so. The base rule covers rows and columns only.

No. They are labels, so shapes and letters behave the same as digits.

More latin squares question types

Sources

Written from the test board's own published material and checked on 1 October 2026.

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