Maths Olympiad · topic 14 of 33 · free

Number analogies and logical reasoning — Maths Olympiad practice

Number analogies give you pairs that follow one secret rule — add, multiply, multiply and add, square, or cube. Test your guess on every pair before you use it, because a rule that fits one pair can fail on the next.

How to solve it

One rule for every pair — “a rule that works for only one pair is a guess; it must work for all of them”

  1. Look at the first pair and guess a rule (add? multiply? multiply and add? square?).
  2. Test the guess on every other pair. If it fails, try another.
  3. Use the rule that works for all pairs on the new number.

Use it for: Analogy, number-relation and “find the missing number” reasoning questions.

Worked example: Every pair follows the same rule: 2 : 5, 4 : 9, 6 : 13. What is 7 : ? → 15

  1. Test “double and add 1”: 2 × 2 + 1 = 5, 4 × 2 + 1 = 9, 6 × 2 + 1 = 13 — it fits every pair.
  2. Use it on 7: 7 × 2 + 1 = 15.

Check: “Add 3” fits 2 : 5 but gives 4 : 7, not 9 — so it is the wrong rule, and only “double and add 1” fits all three ✓

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