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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, 9 months 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 $$100$$?

- 2 years, 8 months ago