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I have a problem to solve but I am in need of your help.

Subjects with equal sums:

Prove that for every set $A$ which consists of $10$ double digit natural numbers( numbers among $10, \ldots, 99$), there are always two different subsets of $A$ that its elements have the same sum.

Thank you very much

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    Hint: how many different values can the sum of the elements of a subset of $A$ take, and how many different subsets of $A$ are there?2012-01-03

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