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Proof note

Pick \(n\) integers from \(1\) to \(100\). Find with proof the minimum \(n\) such that for any set you choose of \(n\) integers in the range, this set may be divided into two disjoint subsets which have equal sums of elements.

Hint: Pigeons.

Note by Dylan Pentland
2 years, 1 month ago

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Well, for \(n\le 99\) you can always find a subset of \(\{1, 2, \ldots , 100\}\) such that the sum of the elements of the subset is odd, so I guess the answer is \(100\)? Daniel Liu · 2 years ago

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