dMAT mock testsCore · 03

dMAT Latin Squares

Latin Squares is the third subtest of the dMAT Core Module: 16 items in 20 minutes, the shortest of the three. Each item shows a partly filled 5×5 grid in which the letters A to E each appear exactly once in every row and exactly once in every column. One cell is marked, and you deduce which letter belongs in it. If you have done Sudoku the constraint will feel familiar, but the grids are smaller and the target is a single cell, so the whole item is usually two deductions rather than a full solve.

Items: 16
Time: 20 min
Per item: 75 sec

Format last checked against g.a.s.t. on 2 August 2026

How to approach latin squares

There is no syllabus to revise for this subtest, so preparation means having a routine you can run without thinking. This is the order that wastes the least time at 75 seconds an item.

1
Read the marked cell’s row first
List which of A–E the row already contains. If four are present, the fifth is your answer and the item is finished in one pass.
2
Confirm with the column
Do the same for the column through the marked cell. When both agree, you are certain. This second check costs a few seconds and catches the misread that would otherwise cost the mark outright.
3
When neither line is complete, cross off
Any letter appearing in either the row or the column is impossible in the marked cell. Eliminate from A–E and see what survives — often only one letter does, even when both lines have gaps.
4
Look for the shifted-row pattern
Many grids are built by shifting each row one position from the row above. Spotting that structure lets you fill the marked cell directly without scanning anything, and it is worth a deliberate half-second glance before you start eliminating.
5
Move on if the grid needs more than two deductions
At 75 seconds an item this subtest is generous, but only if you do not get drawn into solving the whole square. If the marked cell needs a chain of inferences, flag it and come back.

Latin Squares practice questions

Worked examples in the documented dMAT format, with the full reasoning underneath each one. Time yourself: 75 seconds per item is the pace the real clock allows.

These are practice questions written by AdmitVerse to the format g.a.s.t. publishes. They are not official or past dMAT papers — no past papers exist for this exam, since the first sitting is on 26 September 2026.

Q1 · Latin Squares
Each letter A–E appears exactly once in every row and every column. Which letter belongs in the cell marked ×?
```
A  B  C  D  E
B  C  D  E  A
C  ×  E  A  B
D  E  A  B  C
E  A  B  C  D
```
AA
BB
CD
DE
Solution: Read the row: C, ×, E, A, B — it is missing D. Confirm with the column: B, C, ×, E, A — also missing D. Both agree, so × is D. Checking one line is usually enough; checking the second is the cheap way to catch a slip.
Q2 · Latin Squares
Each letter A–E appears exactly once in every row and every column. Which letter belongs in the cell marked ×?
```
C  D  E  A  B
D  E  A  B  C
E  A  B  C  D
A  B  ×  D  E
B  C  D  E  A
```
AA
BB
CC
DE
Solution: The row reads A, B, ×, D, E — missing C. The column reads E, A, B, ×, D — also missing C. Answer: C. Notice the structure: every row is the row above shifted one place left. Once you spot that, the marked cell can be read straight off without scanning either line.
Q3 · Latin Squares
Each letter A–E appears exactly once in every row and every column. Which letter belongs in the cell marked ×?
```
A  C  E  B  D
C  E  B  D  A
E  B  ×  A  C
B  D  A  C  E
D  A  C  E  B
```
AA
BB
CC
DD
Solution: The row reads E, B, ×, A, C — missing D. The column reads E, B, ×, A, C as well — also missing D. Answer: D. This grid shifts by two positions rather than one, which is why it looks less orderly than the others; the row-and-column method is unaffected, which is the point of using it rather than pattern-spotting alone.

What costs people marks here

Solving the entire grid when only one cell is asked for.
Checking the row and stopping, then misreading a letter — the column check exists precisely to catch this.
Scanning the wrong column because the marked cell sits near the middle of the grid.
Not looking for the shifted-row structure first, and eliminating letter by letter when the answer was readable at a glance.
Treating this as the hard subtest. It has the fewest items and the same per-item allowance, so it is usually the best place to bank marks.

Know your pace before 26 September.

One exam date, one attempt, and no past papers. A timed mock is the only way to find out whether you are inside 75 seconds an item — free during early access.

Take a free Latin Squares mock