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Odd one out: reasoning by exclusion

The question is never what is different. It is what four of them share.

Part of the MatrixMind maths, science and reasoning guide · updated 13 October 2026

An odd-one-out puzzle shows five or six figures and asks which one does not belong. It sounds like the easiest format on any test, and it produces more arguments than any other, because in almost every set there is more than one defensible answer.

That is not sloppy design. It is the puzzle. Your job is not to find a difference — differences are everywhere — but to find the rule that the largest group shares, and then name the figure that breaks it.

Turn the question around

Beginners look at each figure and ask what is unusual about it. That produces a list of five different oddities and no answer, because every figure in a well-made set is unusual in some way.

Strong solvers ask the opposite question: what do four of these have in common? There is normally exactly one property shared by four and missing from the fifth, and once you have named that property the answer falls out immediately.

The reversal matters because it changes what you are searching for. Looking for differences is an open-ended search with no stopping condition. Looking for a shared rule has a clear finish: you have either found something four of them do, or you have not.

Run the attributes as a checklist

Same list as sequences, used differently. For each property, sort the figures into groups and see whether a four-one split appears:

A set with two defensible answers, and one correct one
1. triangle, filled 4. pentagon, filled 2. square, filled 5. hexagon, empty 3. circle, filled

By shading, 5 is the odd one — four are filled, one is not. By edges, 3 is the odd one — four have straight sides, one is curved. Both are real four-one splits, so the set is ambiguous as written and a real test would not ship it. When you meet something like this, look at which property the rest of the test has been using; papers are internally consistent far more often than they are random.

The traps built into these

The obvious difference is usually a decoy

If one figure is glaringly different — much larger, a different colour, rotated wildly — treat it with suspicion rather than relief. Designers put loud differences in because they are cheap distractors. The real rule is usually quieter: side counts, symmetry, an element that appears three times in four figures and twice in the fifth.

Categories you brought with you

People group by familiar categories rather than visual properties — separating shapes into 'ones I know the name of' and 'ones I do not', or grouping by what the figures resemble. Abstract reasoning tests are specifically built to be language-free, so any rule that depends on a shape having a name is almost certainly not the intended one.

Stopping at the first split you find

Having found a property where four match and one does not, check the remaining attributes anyway. If you find a second valid split, you have either misread one figure or picked up a decoy, and it is worth thirty seconds to work out which.

A tiebreaker that works. If two splits both look valid, prefer the one based on a property you can count — sides, elements, lines of symmetry — over one based on a judgement like 'looks rounder'. Test writers prefer countable rules because they are unarguable, which is exactly why they use them.

When nothing splits four-one

Occasionally you will check every attribute and find nothing. Three things to try before guessing:

  1. Look at combinations. The rule may be a pair: 'filled AND curved'. Four figures satisfy both, one satisfies only one of them.
  2. Look at relationships inside each figure rather than the figure as a whole — is the small shape always inside the large one, always touching, always in the same corner?
  3. Count something you have not counted. Intersections, enclosed regions, line ends. Enclosed regions in particular catch people out constantly.

If all that fails, eliminate whatever you can and choose. An answer produced by ruling out three options is a far better bet than an unbacked guess, and on a timed paper the minute you save is worth more than the mark you might lose.

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