Latin Squares for dMAT: Rules and Practice

Latin Squares is one of the three dMAT Core Module subtests. It looks similar to Sudoku, but the official dMAT task is smaller and uses letters instead of numbers.

In the official task type, you see a 5 by 5 grid using the letters A, B, C, D, and E. Each letter may appear only once in each row and only once in each column. Your job is to identify the letter that belongs in the cell marked with a question mark.

The official preparation material gives 20 Latin Square tasks in 25 minutes, so your target is about 75 seconds per task.

Read this after the dMAT structure guide, and use it with the dMAT preparation guide.

Last reviewed: 1 August 2026. This article uses the official dMAT preparation material for format and rule understanding. All practice questions below are Think Mile original and are not official dMAT questions.

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Direct Answer

Latin Squares tests constraint reasoning. You need to decide which letter is missing by checking:

• the row containing the question mark;
• the column containing the question mark;
• other cells that can be solved first;
• chained deductions when the answer is not immediate.

It is not a mathematics test. It is a logic and working-memory task.

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Official Evidence

The task rewards disciplined scanning. Students who randomly inspect the whole grid often lose time.

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Concept Lesson: The Elimination Method

Use this process.

Step 1: List row exclusions mentally

If the row with ? already contains A, C, D, and E, then the answer must be B.

This is the fastest case.

Step 2: List column exclusions mentally

If the column with ? already contains B, C, D, and E, then the answer must be A.

This is also fast.

Step 3: Combine row and column

If the row excludes A and C, and the column excludes B and D, the only remaining letter may be E.

Step 4: Solve an easier cell first

Sometimes the ? cell has two possible letters. In that case, find another empty cell in the same row or column that has only one possibility. Solve it, then return to the question mark.

Step 5: Avoid full-grid solving

You are not trying to complete the whole puzzle unless needed. You are trying to answer one marked cell quickly.

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Worked Example

Think Mile original example:

Question: What is ?

Row 3 contains C, D, A, B. The only missing letter is E.

Answer: E

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Common Traps

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Think Mile Original Practice

These are original practice grids, not official dMAT questions.

Easy

What letter belongs in ?

A. A
B. B
C. C
D. E

Solution:
Row 5 contains E, A, B, and D. The missing letter is C.
Answer: C

Medium

What letter belongs in ?

A. A
B. B
C. D
D. E

Solution:
Column 1 contains A, B, C, D. The missing letter is E.
Row 5 also contains B, D, A, C, so E is the only missing row letter.
Answer: D

Difficult

What letter belongs in ?

A. A
B. B
C. D
D. E

Solution:
Look at column 5. It contains E, A, blank, C, and ?. The missing letters in column 5 are B and D.

Look at row 5. It contains E, A, blank, C, and ?. The missing letters in row 5 are B and D.

So ? is either B or D. We need a chained deduction.

Check row 3: C, D, E, A, blank. The missing letter is B. Therefore R3C5 = B.

Now column 5 contains E, A, B, C, and ?. The only missing letter is D.

Answer: C (D)

Harder Chained Item

What letter belongs in ?

A. A
B. C
C. D
D. E

Solution:
Row 5 contains E, A, B, blank, and ?, so the missing letters are C and D.

Column 5 contains E, A, B, blank, and ?, so the missing letters are C and D. Still ambiguous.

Check row 4: D, E, A, B, blank. The missing letter is C, so R4C5 = C.

Now column 5 contains E, A, B, C, and ?. The only missing letter is D.

Answer: C (D)

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Working-Memory Techniques

Because notes are not allowed, use mental compression:

Do not silently stare at the grid. Name the missing set in your head.

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Timed Practice Plan

Accuracy first, then speed. If you guess too early, you train the wrong habit.

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Free Learning Path

Logic grid puzzles are not the same as Latin Squares, but they train the same elimination discipline.

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Official vs Think Mile Recommendation

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Frequently Asked Questions

Is Latin Squares the same as Sudoku?
It is similar, but dMAT Latin Squares use row and column constraints with letters. Do not look for 3 by 3 Sudoku boxes.

Do I need math for this section?
No. It is logic and elimination, not calculation.

Should I complete the whole grid?
Only if necessary. Your goal is to answer the ? cell.

What is the fastest method?
Check the row of ?, check the column of ?, find the overlap of remaining letters, and solve a nearby easier cell only if needed.

What should I study next?
Use How to Read dMAT Academic Passages for General Academic Module passage strategy.

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Source note: This article was reviewed against the official dMAT preparation material and the official dMAT preparation page. Think Mile is not affiliated with APS India or g.a.s.t.; all practice grids here are original.