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    Let T be a set of 11 natural numbers. Using the PHP, show that there are two elements t1,t2 in T (t1 does not equal t2) such that t2-t1 is divisible by 10.

    Can I just say that a set of natural numbers with different last digits can only have 10 elements so as the set has 11 elements 2 will have the same last digit so one minus the other will be divisible by 10.
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    Pretty much. Pigeonhole principle basically says that if you try to stick more than n pigeons in n holes, at least one hole will have more than one pigeon in it.
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    Yes
 
 
 
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Updated: November 15, 2008
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