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ASU 493 All Soviet Union MO 1989 n bird-nests in a forest, change nests

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August 13, 2019
combinatoricscombinatorial geometry

Problem Statement

One bird lives in each of nn bird-nests in a forest. The birds change nests, so that after the change there is again one bird in each nest. Also for any birds A,B,C,DA, B, C, D (not necessarily distinct), if the distance AB<CDAB < CD before the change, then AB>CDAB > CD after the change. Find all possible values of nn.
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