Friday, 11 February 2011

big list - Interesting applications of the Pigeon-hole Principle

I think the solutions of these questions are very interesting (by using pigeon-hole principle), first question is easy, but second question is more advanced:



1) For any integer n, There are infinite integer numbers with digits only 0 and 1 where
they are divisible to n.



2) For any sequence s=a1a2cdotsan, there is at least one k, such that 2k begin with s.

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