dMAT Latin Squares: Rules, Solving Method and Practice Questions

By the Yastudy Test Prep Team · Last updated 11 October 2026

Latin Squares is the third subtest of the dMAT Core Module. You see a 5×5 grid that is partly filled with letters, and each letter may appear only once in every row and every column. You find the letter that belongs in the field with the question mark. There are 20 tasks in 25 minutes.

How the task works

Some fields of the grid already contain letters. One empty field is marked with a question mark. Next to the grid you see the response options, and only those letters can appear anywhere in the grid.

With five rows, five columns and five letters, a completed grid has every letter exactly once in each row and exactly once in each column. That single rule is enough to work out the marked field.

Easy tasks can be solved by looking at the marked field alone. Harder ones need you to work out one or more other fields first, in your head, because you may not write in the grid.

Two checks that solve every task

1. Check the field: which letters are already used? Look along the row and down the column of the marked field. Every letter you find there is ruled out. If four different letters are ruled out, the fifth is your answer.
2. Check the letter: where else could it go? If step 1 leaves two or more candidates, take one candidate and ask where it could go in that row. If every other empty field in the row is blocked, because its column already has that letter, the candidate must go in the marked field. The same check works along the column.

If neither check settles it, a helper field is needed:

3. Find a helper field. Look for another empty field in the same row or column as the question mark that you can solve with step 1 or step 2. Fields in rows or columns that are nearly full are the best candidates.
4. Keep the helper in mind and repeat. With the helper letter placed, go back to step 1 for the marked field.

Worked example

In this grid, rows are counted from the top and columns from the left.

Tips for working without notes

• Count what is missing, not what is there. In a row with three letters, name the two that are missing. Two candidates are easier to hold than three facts.
• Go to the fullest line first. A row or column with four letters gives you a helper field for nothing.
• Hold one helper at a time. Say it to yourself as a short phrase, for example "row 2, column 5 is C", before you look for the next one.
• Use your finger or the mouse pointer as a marker. You may not write, but you can keep your place on the screen.
• Do not solve fields you do not need. Only fields in the row or column of the question mark matter, plus any field you need in order to solve one of those.

Practice questions

Solve each grid in your head, then open the answer. In the explanations, rows are counted from the top and columns from the left.

Common mistakes

• Checking only the row. The column rules out letters too. Always look both ways.
• Stopping at "two candidates". That is the moment for the second check, not for a guess.
• Trying to fill the whole grid. It is not needed and there is no time for it.
• Forgetting a helper. If you lose track, re-derive that one field. Do not restart the task.
• Running over time on a hard grid. Hard grids need several helpers. If you are past 90 seconds, choose between your remaining candidates and move on.

What to practise next

• Figure Sequences, the first Core subtest
• Mathematical Equations, the second Core subtest
• The timed dMAT sample test, which includes ten more Latin Squares