Number patterns, step by step

A number pattern hides a rule, and finding it is early algebra in disguise.

The question

5, 17, ?, 41, 53

517?4153
517?4153
517?4153
517?4153
517294153
  1. Find the rule first, from two numbers you can actually see — never from the gap.
  2. 5 to 17 is + 12. One pair is a guess, though — check it against another.
  3. 41 + 12 = 53, so the rule holds. Two pairs agreeing is what turns a guess into the rule.
  4. Now apply it to the gap: 17 + 12 = 29.
  5. Check it against the number already after the gap: 29 + 12 = 41, which is what is there. The missing number is 29.

How it works.

  1. 01

    Find the rule first, from two numbers you can actually see — never from the gap.

  2. 02

    5 to 17 is + 12. One pair is a guess, though — check it against another.

  3. 03

    41 + 12 = 53, so the rule holds. Two pairs agreeing is what turns a guess into the rule.

  4. 04

    Now apply it to the gap: 17 + 12 = 29.

  5. 05

    Check it against the number already after the gap: 29 + 12 = 41, which is what is there. The missing number is 29.