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Let $A = \{1,2,3,\ldots,99\}$.
Let $S$ be a subset of $A$ with $10$ elements.
Show that there exist two disjoint subsets of $S$ such that sum of their elements is the same.

Example:
$S = \{1,4,7,9,67,70,83,85,90,97\}$ and we can choose $\{7,90\}$ and $\{97\}$ as two subsets of $S$ with sum of elements the same.

Theo Bendit
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Dritan Skarra
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    a similar problem: https://math.stackexchange.com/questions/1959331/prove-that-there-are-two-subsets-of-any-cardinality-10-subsets-of-1-2-dots-10?rq=1 – miracle173 Jul 05 '19 at 21:14

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