×

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 ago

Sort by:

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 $$100$$? · 1 year, 10 months ago