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6

Part of 2017 Moscow Mathematical Olympiad

Problems(1)

Gangsters wars

Source: Moscow Math Olympiad 2017, Grade 11, P6

4/25/2017
There are 3636 gangsters bands.And there are war between some bands. Every gangster can belongs to several bands and every 2 gangsters belongs to different set of bands. Gangster can not be in feuding bands. Also for every gangster is true, that every band, where this gangster is not in, is in war with some band, where this gangster is in. What is maximum number of gangsters in city?
combinatorics