dMdMAT Exam Prep
Core Module

Latin Squares

What this question type is

A 5×5 grid where each of the letters A–E appears exactly once in every row and every column. One cell is marked "?"; you work out which letter belongs there.

How to solve it

Look at the "?" cell's row and column. List which letters are already present. The row (or column) that is missing only one letter tells you the answer directly. If both leave two possibilities, cross-reference: the letter that's already used elsewhere in the column can't repeat, which narrows the row to a single option.

Worked example

The "?" sits in a row that already shows A, B, D and E. Only C is missing from that row, so the "?" must be C.

Try it yourself

0 of 3 solved
A
B
?
D
E
B
C
D
E
A
C
·
E
·
B
D
E
A
B
C
·
A
·
C
·
Place a letter

Why

Row 1 already contains A, B, D and E. The only letter missing from that row is C, so the ? must be C.

C
·
E
·
B
E
A
B
C
D
A
B
C
?
E
D
E
A
B
C
·
C
·
E
·
Place a letter

Why

The ? row already shows A, B, C and E, leaving only D unplaced, so the answer is D.

B
C
D
?
A
·
·
·
A
·
·
·
·
B
·
·
·
·
C
·
·
·
·
D
·
Place a letter

Why

Row 1 already contains B, C, D and A — only E is missing. You can confirm with the column, which also still needs E. So the ? is E.