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 $5$.

  • 1
    @Q123 I suggest you look up the [pigeonhole principle](http://en.wikipedia.org/wiki/Pigeonhole_principle).2012-01-11
  • 4
    welcome to MathSE. I see that you are relatively new here. So I wanted to let you know a few things about MathSE. We like to know what you've tried on a problem. These sort of pleasantries usually result in more and better answers. Finally, I should add that posting questions in the imperative (i.e. Compute all such, Prove that...) is considered rude by some of the members, so it would be nice of you to change that wording. Thank you2012-01-11
  • 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