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Problem 3

Part of 1978 Bulgaria National Olympiad

Problems(1)

5 people sitting around table

Source: Bulgaria 1978 P3

6/17/2021
On the name day of a man there are 55 people. The men observed that of any 33 people there are 22 that knows each other. Prove that the man may order his guests around circular table in such way that every man have on its both side people that he knows.
N. Nenov, N. Hazhiivanov
combinatorics