MEPX
Chapter 10 of 10All chapters
  1. 1Finding the rule
  2. 2Arithmetic sequences
  3. 3Geometric sequences
  4. 4Sequences worth knowing
  5. 5Primes and factors
  6. 6Writing the nth term
  7. 7Patterns from shapes
  8. 8Recursive rules
  9. 9Patterns outside mathematics
  10. 10Solving pattern puzzles

Chapter 10 of 10

Solving pattern puzzles

Tests and interviews.

A strategy

Try differences, then ratios, then the position number itself, then alternating rules, then sums of previous terms. Most puzzle sequences are one of those five.

  • Watch for two interleaved sequences alternating with each other.
  • If a term breaks the pattern, question your rule before questioning the puzzle.

Honesty about ambiguity

Strictly, any finite list can continue in infinitely many ways. These puzzles ask for the simplest rule that fits, which is a convention rather than a mathematical fact.