MathDB

493

Part of 1989 All Soviet Union Mathematical Olympiad

Problems(1)

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

Source:

8/13/2019
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.
combinatoricscombinatorial geometry