PROBLEM 3 FOR RMO 2011
A set is reciprocally whole if its elements are distinct integers greater than 1 and
the sum of the reciprocals of all those elements is exactly 1. Find a set S, as small
as possible, that contains two reciprocally whole subsets, I and J, which are distinct
but not necessarily disjoint (meaning they may share elements, but they may not be
the same subset). Prove that no set with fewer elements than S can contain two
reciprocally whole subsets.
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