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Putnam 2010 A1

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December 6, 2010
Putnamceiling functionpigeonhole principlefloor functioncollege contestsPutnam easy

Problem Statement

Given a positive integer n,n, what is the largest kk such that the numbers 1,2,…,n1,2,\dots,n can be put into kk boxes so that the sum of the numbers in each box is the same?
[When n=8,n=8, the example {1,2,3,6},{4,8},{5,7}\{1,2,3,6\},\{4,8\},\{5,7\} shows that the largest kk is at least 3.]
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