Pattern guide

Cayley Table Questions

A Cayley table is the structural cousin of the Latin square. Two attributes vary together so that every (attribute-A, attribute-B) pair appears exactly once across the grid. The missing cell is the one pair the visible grid has not used.

What this pattern means

Two attributes (e.g. shape and rotation, or colour and fill) each take three values. The 3×3 grid uses every one of the 9 possible pairs exactly once. The missing cell is the only pair not yet visible.

How to spot it

  • Each row is Latin on each attribute independently AND the combined pairs are unique.
  • Two attributes vary together — never just one.
  • Counting visible pairs reveals exactly one combination unused.

Common visual signals

  • Three values per attribute, two attributes, nine visible cells.
  • Items often featured in premium Hard / Extremely Hard sets.
  • Pair uniqueness is the defining cue — not row-and-column uniqueness alone.

Step-by-step solving tactic

  1. 1List the nine possible (A, B) pairs.
  2. 2Cross off every pair that appears in a visible cell.
  3. 3The one remaining pair is the missing cell's content.
  4. 4Verify by checking that the row and column constraints are also satisfied.

Common traps

  • Confusing Cayley with Latin — Latin uniqueness applies per attribute, Cayley applies to the pair.
  • Missing that all nine pairs must be unique — solving on one attribute alone can give a wrong answer.
  • Three-attribute Cayley (Latin cube) is a harder cousin — check carefully.

Related patterns

Apply this pattern under timed conditions

Take the free 10-question matrix reasoning practice test — every question carries the cayley table pattern or another commonly tested mechanic.

Free test · 10 questions