Free dMAT Latin squares practice — 20 timed tasks, no login.

01How this mock test works

Generated fresh, checked for one valid answer.

Every 5×5 grid is built in your browser the moment you reach it, so no two runs are the same and there is nothing to memorise. Before a task is shown, the generator proves two things: that exactly one letter can legally sit in the marked cell, and that the cell can be reached by a chain of forced deductions. The chain it found is the working you read afterwards.

02Format and timing

What the Latin squares subtest actually asks.

03Worked examples

Four grids, solved in the order a solver actually works.

These four are fixed, so you can read them before committing to a timed run. Each one shows the grid, the answer, and the chain of forced cells that gets there — starting with the cell that is forced first, which is the move the whole subtest rewards. They get harder as you go down.

1. 01

   Start from the row that is nearly full

   medium

   The fastest opening move is almost never at the marked cell. Scan for a row or column with only one or two gaps — that is where a letter is forced, and the letter you place there is what unlocks the next gap.

   B

   E

   D

   B

   D

   A

   C

   E

   B

   The marked cell R3C1 is B.

   How you get there

   1. 1Row 4 is missing B and D; column 4 already has D, so R4C4 is B.
   2. 2Row 4 is missing only D, so R4C1 is D.
   3. 3In column 1, B fits only R3C1 — every other open cell in that column is in a row that already has B.
2. 02

   A full column names the letter it is missing

   medium

   A column holding four letters is missing exactly one. Place it without checking anything else, then look at what that placement does to the rows it crosses.

   B

   C

   E

   A

   A

   D

   C

   B

   E

   A

   The marked cell R4C2 is B.

   How you get there

   1. 1Column 1 is missing only D, so R5C1 is D.
   2. 2In column 4, D fits only R4C4 — every other open cell in that column is in a row that already has D.
   3. 3Row 4 is missing only B, so R4C2 is B.
3. 03

   When nothing is forced, ask where a letter can go

   high

   Sometimes no cell has only one candidate. Flip the question: take one letter and ask which cells in a row could hold it. If four of the five are blocked by their columns, the fifth is forced.

   C

   D

   A

   B

   D

   C

   E

   C

   A

   The marked cell R1C4 is D.

   How you get there

   1. 1Row 5 is missing B and D; column 3 already has B, so R5C3 is D.
   2. 2Column 2 is missing A, B and E; row 2 already has A and B, so R2C2 is E.
   3. 3Row 2 is missing C and D; column 5 already has C, so R2C5 is D.
   4. 4In row 1, D fits only R1C4 — every other open cell in that row is in a column that already has D.
4. 04

   Chaining the where-can-it-go move

   high

   The hardest tasks need that same move several times over. Each placement blocks a column, which forces the next letter, which blocks another column. This is the deduction depth the high-difficulty tasks are built to test.

   A

   E

   B

   A

   E

   A

   E

   B

   A

   The marked cell R3C5 is A.

   How you get there

   1. 1In row 5, E fits only R5C2 — every other open cell in that row is in a column that already has E.
   2. 2In column 3, E fits only R3C3 — every other open cell in that column is in a row that already has E.
   3. 3In row 5, B fits only R5C1 — every other open cell in that row is in a column that already has B.
   4. 4In row 3, B fits only R3C2 — every other open cell in that row is in a column that already has B.
   5. 5In row 3, A fits only R3C5 — every other open cell in that row is in a column that already has A.

04dMAT preparation

Four things that actually move your score.

• Find the forced cell, not the answer

  You are never asked to complete the grid. Look for the row or column with four letters filled in — that cell is forced, and filling it usually forces the next one. Chain those until the marked cell is covered.

• Work at 75 seconds a task

  20 tasks in 25 minutes is 75 seconds each. If a task has not opened up in about 40 seconds, it is usually cheaper to move on and come back with a fresh eye than to keep staring.

• Practise without writing anything

  The real dMAT allows no calculator, no rough paper and no notes. Doing this drill mentally from the start is the single biggest difference between a smooth exam and a slow one.

• Read the working, not just the answer

  After each task the deduction chain is shown in the order a solver actually used it. Reading that order is what makes the next grid faster to see.

05Practise offline

Install dmatgrid as an app.

Tasks are generated on your device, so once the app is installed the mock test runs with no internet at all — on a commute, in a queue, anywhere. It takes a few hundred kilobytes and still needs no account.

Installable as an app — use your browser's Install or Add to Home Screen option to practise offline.

Keep going

Next on dmatgrid

• Mathematical equationsThe other quick core subtest: integers 1–20, one solution per system.
• Figure sequencesContinue a series of matrices as the figures move, turn and recolour.
• Exam patternHow the modules fit together and how long each one runs.