Putnam 2010 A1

Given a positive integer n, what is the largest k such that the numbers 1,2,...,n can be put into k boxes so that the sum of the numbers in each box is the same?

Putnam 2010 A1

Hint: I think it’s enough to see that n must be in one of the boxes, and to make k big, the sum in the boxes must be small. Therefore divide into two cases, for n odd and even, and the rest is easy.

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