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Non-verbal reasoning: shape codes and pattern rules

Learn the method for cracking two-part shape codes, spotting the shared rule in a group of figures, and finding the odd one out reliably instead of guessing.

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Lesson overview

Non-verbal reasoning — codes, odd-one-out and similarities

Most 11+ non-verbal reasoning questions test the same underlying skill: spot a RULE from examples, then apply it to a new case. Shape-code questions usually give you a rule with two independent parts (for example, the outer shape and the shading of an inner shape) — each part of the code is controlled by a different feature. 'Odd one out' and 'similarities' questions work the other way round: you're given several figures and have to work out what rule connects most of them before you can tell which one breaks it.

Two-part codes have two independent rules

A pentagon with a black inner shape is coded 'pb'. A square with a white inner shape is coded 'sw'.

'pb''sw'
First letterOuter shape

p = pentagon, s = square, c = circle, t = triangle

Second letterInner shading

b = black, w = white, g = grey, s = striped

Work out each letter's rule separately — don't try to guess the whole code at once.

Confirm the rule with a second example before trusting it

One example could match more than one rule by coincidence. A second example that fits the same rule confirms it's genuinely correct.

RiskyGuessing a rule from just one coded example
SafeChecking the same rule works for at least two examples before applying it

Real 11+ shape-code questions always give you at least two or three worked examples for exactly this reason -- use all of them.

Odd one out: find the shared rule first

Four of these five figures share a rule (same outer shape); one figure breaks it. Which one is the odd one out?

ABCDE
Step 1Look at every figure and describe each one in words
Step 2Find what most of them have in common -- that's the rule
Step 3Test each figure against the rule -- the one that fails is the answer

Here every figure has the same grey circle inside, and four are pentagons -- D is the odd one out because it's a square. Never assume the odd one out is whichever figure 'looks' different at a glance -- test every figure against the rule you found.

Worked example — cracking a shape code

A triangle with a grey inner shape is coded 'tg'. A triangle with a striped inner shape is coded 'ts'. A square with a grey inner shape is coded 'sg'. What is the code for a circle with a black inner shape?

'tg''ts''sg'?
From the first two examplesThe first letter changes only when the OUTER SHAPE changes (t stays for triangle in both)
From examples 1 and 3The second letter changes only when the SHADING changes (g stays for grey in both)
  1. Compare the two triangle examples (tg, ts): the outer shape (triangle) is the same, so the first letter 't' means triangle.
  2. The shading changed from grey to striped, and the second letter changed from g to s -- so g = grey, s = striped.
  3. Compare the two grey examples (tg, sg): the shading (grey) is the same, so the second letter 'g' means grey -- confirmed.
  4. The outer shape changed from triangle to square, and the first letter changed from t to s -- so s (first letter) = square.
  5. Now apply the rule to a NEW figure: circle with a black inner shape. We haven't seen circle or black yet, but the same two-letter structure applies: first letter for the outer shape, second for the shading.
  6. If c = circle and b = black (following the same pattern as the other letters), the code is 'cb'.

Try it

Use the method: find each letter's rule from at least two examples, then apply it.

Question 1

A square with a black inner shape is coded 'sb'. A circle with a white inner shape is coded 'cw'. A square with a white inner shape is coded 'sw'. What does the first letter of the code represent?

'sb''cw''sw'
Question 2

Using the rule from Q1 (s = square, and shading letters b = black, w = white), what would a square with a white inner shape be coded as?

?
Question 3

Five figures are shown. Four are regular polygons (all sides and angles equal); one is an irregular quadrilateral. What rule connects the four that belong together?

ABCDE
Question 4

True or false: if a rule matches just ONE coded example, that's enough to trust it completely. Answer 'true' or 'false'.

Question 5

You're finding the odd one out among five figures. What should you do FIRST?

Common mistakes

Watch for these when working through the lesson.

  • Trying to work out the whole code at once instead of one letter at a time.
  • Trusting a rule after checking only one example, rather than confirming it with a second.
  • In odd-one-out questions, picking the figure that 'looks' different rather than testing every figure against the actual shared rule.
  • Mixing up which letter position stands for which feature (shape vs. shading) when a code has more than one part.

Related topics

These ideas fit closely with this lesson.

  • Spatial reasoning: cube nets and block counting
  • 2D and 3D shape properties
  • Sequences and pattern rules

Practice next

Ready for real questions?

This lesson builds the method for shape codes, odd-one-out and similarities. Head to 11+ Prep practice for real non-verbal reasoning questions with adaptive difficulty and scaffolded hints when you get one wrong.