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 $5$.
Prove every subset will contain two numbers whose difference is equal to $5$
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elementary-number-theory
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1@Q123 I suggest you look up the [pigeonhole principle](http://en.wikipedia.org/wiki/Pigeonhole_principle). – 2012-01-11
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4welcome 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 you – 2012-01-11
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0@AlexBecker Thank you. – 2012-01-11