Mathematics Number Puzzle Extension Puzzle – Langford Problem

This is a great problem to extend KS3 learners!!

Langford problem: 1 , 1 ,2, 2 ,3, 3

rearrange the numbers so that the 1s are 1 apart, 2s are 2 apart and 3s are 3 apart

Solution: 3 1 2 1 3 2


Now try for:  1,1,2,2,3,3,4,4

Now try for: 1,1,2,2,3,3,4,4,5,5,6,6,7,7

Only works when last digit is 4n or 4n-1

Would love to know your views once you have tried it!


Posted in Lesson starters, Mathematics, Number
One comment on “Mathematics Number Puzzle Extension Puzzle – Langford Problem
  1. Tyler Warfel says:

    I gave this to my Algebra class today. We got the answers for 4 and 7 but are trying to think through WHY it works for 4n and 4n-1 and doesn’t work for other numbers.

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