14th International Mathematical Olympiad 1972 Problems & Solutions

A1.  Given any set of ten distinct numbers in the range 10, 11, ... , 99, prove that we can always find two disjoint subsets with the same sum. A2.  Given n > 4, prove that every cyclic quadrilateral can be dissected into n cyclic quadrilaterals. A3.  Prove that (2m)!(2n)! is a multiple of m!n!(m+n)! for any non-negative integers m and n. B1. 

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