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Given two positive integers $n, m$, let $A$ be a multiset of $n$ integers taken from { $ 1,2,\cdots, m$ }, and $B$ be a multiset of $m$ integers taken from { $1,2,\cdots,n$ }.

Is it always possible to choose two nonempty subsets from $A$ and $B$ respectively, such that their sums are equal?

I cannot either prove or disprove it. Trying some examples made me conjecture that it is true.

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This is the problem A4 in the 54th Putnam exam. I guess you can find a solution here… I also suggest as a better forum to discuss questions at this level. – Gjergji Zaimi Feb 22 '10 at 11:50
I see. Thanks for your reply. – Zeyu Feb 22 '10 at 13:53

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