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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0@AlexBecker Thank you. – 2012-01-11
1 Answers
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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?
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0Well, that was stupid of me. Fixed. – 2012-01-11