MathDB

A club of

11

people has a committee. At every meeting of the committee a new committee is formed which differs by

1

person from its predecessor (either one new member is included or one member is removed). The committee must always have at least three members and , according to the club rules, the committee membership at any stage must differ from its membership at every previous stage. Is it possible that after some time all possible compositions of the committee will have already occurred?
(S. Fomin , Leningrad)

(220) 4

Problems(1)