1
$\begingroup$

Let $S = \{1,2,3,4,5,6,7,8,9\}$. Prove that every subset of $S$ with $6$ or more elements must contain two numbers whose difference is equal to $5$.

  • 0
    @AlexBecker Thank you.2012-01-11

1 Answers 1

1

Well, your set can be broken into 4 subsets of 2 (with one element left over) such that the difference of the 2 elements is 5. Can you take it from there?

  • 0
    Well, that was stupid of me. Fixed.2012-01-11