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Latin Squares

Deduce the letter in the question-mark field of a 5 x 5 grid using only row and column elimination.

What the task asks

You are shown a 5 × 5 grid. Some fields already contain a letter and one field holds a question mark.

Each of the five letters appears exactly once in every row and exactly once in every column. Only the letters offered as responses can appear in the grid.

Decide which letter belongs in the question-mark field. Sometimes you can read it straight off its own row and column; sometimes you have to work out one or two other fields first.

Rules

  • Each letter appears exactly once in every row.
  • Each letter appears exactly once in every column.
  • Only the letters shown in the response row (A–E) appear anywhere in the grid.
  • The question-mark field is always determined by the letters already given, so you never have to guess or try a letter and backtrack.

Worked example 1: read it off directly

  • The question mark sits in a column that already contains A, C, D and E.

Solution. Four of the five letters are already in that column, so the only one left for the question mark is B. When the answer is this direct, check the row too, since either one alone can settle it.

Worked example 2: fill in a field first

  • Neither the question mark's own row nor its own column is missing just one letter.

Solution. Look for a different empty field that is fully determined, one where four of the five letters already appear across its row and column. Fill that in mentally, and it often completes the question mark's row or column, which then gives the answer. Harder questions chain several such steps together.

Timing

The subtest gives you 25 minutes for 20 grids, about 75 seconds each. Answer every question, since a guess costs nothing. No notes are allowed.

How this app presents it

  • The solver’s dependency chain is 2–3 deductions for Low, 4–6 for Medium and 7–16 for High. Medium and High reject direct single-letter shortcuts at the question mark; High starts with at least three possible target letters. These are independent difficulty bands, not an official exam calibration.
  • Every generated grid is solvable by pure elimination, so you never have to guess a letter and backtrack.

The other Core Module task types

  • Figure Sequences Work out the rule governing each figure in a 4 x 4 matrix series, then pick the next two matrices.
  • Mathematical Equations Find the whole number each letter stands for so every equation in the system holds at once.

This is an unofficial practice tool, not affiliated with or endorsed by g.a.s.t. or the TestDaF-Institut. The description above is written for this project; always check the official preparatory materials for the authoritative instructions.