In a certain town of population 2n + 1, all relations are reciprocal: If Person 1 knows Person 2, then Person 2 knows Person 1. For any set A that consists of n citizens, there’s some person among the remaining n + 1 who knows everyone in A. Prove that there’s some citizen of the town who knows all the others.
This problem was proposed by Ashay Burungale of Satara, Maharashtra, India, in the November 2008 issue of American Mathematical Monthly
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