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.
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.
Official Evidence
| Official feature | What it means |
|---|---|
| 5 by 5 grid | Only five letters are possible |
| Letters A to E | Each row and column contains each letter once |
| Cell marked with ? | You usually need only one target cell |
| 20 tasks | Practise in full sets |
| 25 minutes | Train toward 75 seconds per task |
| No notes | Learn mental elimination |
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The task rewards disciplined scanning. Students who randomly inspect the whole grid often lose time.
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.
Worked Example
Think Mile original example:
| Row | C1 | C2 | C3 | C4 | C5 |
|---|---|---|---|---|---|
| R1 | A | B | C | D | E |
| R2 | B | C | D | E | A |
| R3 | C | D | ? | A | B |
| R4 | D | E | A | B | C |
| R5 | E | A | B | C | D |
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Question: What is ?
Row 3 contains C, D, A, B. The only missing letter is E.
Answer: E
Common Traps
| Trap | Why it happens | Fix |
|---|---|---|
| Scanning every cell | The grid looks like a full puzzle | Focus on the row and column of ? |
| Forgetting column rule | Students solve only by row | Always check both row and column |
| Reusing a letter | A candidate fits the row but already appears in the column | Cross-check before answering |
| Chained deduction panic | The answer is not immediate | Solve a nearby easier cell first |
| Working-memory overload | Students try to remember the full grid | Use short mental sets: "row missing B/E, column blocks E" |
| Sudoku assumptions | Students look for 3 by 3 boxes | dMAT Latin Squares use row and column constraints, not Sudoku boxes |
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Think Mile Original Practice
These are original practice grids, not official dMAT questions.
Easy
What letter belongs in ?
| Row | C1 | C2 | C3 | C4 | C5 |
|---|---|---|---|---|---|
| R1 | A | B | C | D | E |
| R2 | B | C | D | E | A |
| R3 | C | D | E | A | B |
| R4 | D | E | A | B | C |
| R5 | E | A | B | ? | D |
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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 ?
| Row | C1 | C2 | C3 | C4 | C5 |
|---|---|---|---|---|---|
| R1 | A | C | E | B | D |
| R2 | B | D | A | C | E |
| R3 | C | E | B | D | A |
| R4 | D | A | C | E | B |
| R5 | ? | B | D | A | C |
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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 ?
| Row | C1 | C2 | C3 | C4 | C5 |
|---|---|---|---|---|---|
| R1 | A | _ | C | D | E |
| R2 | _ | C | D | E | A |
| R3 | C | D | E | A | _ |
| R4 | D | E | A | _ | C |
| R5 | E | A | _ | C | ? |
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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 ?
| Row | C1 | C2 | C3 | C4 | C5 |
|---|---|---|---|---|---|
| R1 | A | B | _ | D | E |
| R2 | B | _ | D | E | A |
| R3 | _ | D | E | A | B |
| R4 | D | E | A | B | _ |
| R5 | E | A | B | _ | ? |
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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)
Working-Memory Techniques
Because notes are not allowed, use mental compression:
| Situation | Mental phrase |
|---|---|
| Row has A, C, D | "row missing B/E" |
| Column has B, D, E | "column missing A/C" |
| Candidate must satisfy both | "overlap is C" |
| Need chained deduction | "solve column five first" |
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Do not silently stare at the grid. Name the missing set in your head.
Timed Practice Plan
| Stage | Practice | Target |
|---|---|---|
| Day 1 | 10 easy row-only tasks | 95% accuracy |
| Day 2 | 10 column-only tasks | 95% accuracy |
| Day 3 | 15 row-plus-column tasks | Under 90 seconds each |
| Day 4 | 10 chained tasks | No guessing |
| Day 5 | 20 mixed tasks | 25 minutes |
| Week 2 | Mix with Figure Sequences and Mathematical Equations | Full Core rhythm |
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Accuracy first, then speed. If you guess too early, you train the wrong habit.
Free Learning Path
| Step | Resource | Expected time | dMAT connection |
|---|---|---|---|
| Learn the official task | Official dMAT preparation material on d-mat.de | 20-30 min | Actual task rules |
| Practise similar grid logic | ThePuzzleLabs logic grid puzzles | 30-45 min | Elimination and deduction |
| Add Sudoku-style elimination | Any simple 4 by 4 or 5 by 5 Sudoku/Latin-square practice source | 20-30 min | Candidate elimination |
| Return to timed dMAT format | 20 Latin Square tasks in 25 minutes | 25 min | Exam rhythm |
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Logic grid puzzles are not the same as Latin Squares, but they train the same elimination discipline.
Official vs Think Mile Recommendation
| Officially shown | Think Mile recommendation |
|---|---|
| 5 by 5 grid with letters A to E | Memorise the five-letter candidate set |
| One occurrence per row and column | Always check both row and column |
| 20 tasks in 25 minutes | Train toward 75 seconds per item |
| No notes | Use mental missing-set phrases |
| Some tasks require other cells first | Practise chained deductions |
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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.
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.
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