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Consider the n×n square Q=[0,n]×[0,n]. Using the pigeonhole theorem prove that, if S is a set...

Consider the n×n square Q=[0,n]×[0,n].

Using the pigeonhole theorem prove that, if S is a set of n+1 points contained in Q then there are two distinct points p,q∈S such that the distance between pand q is at most 2–√.

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