People in clubs
Source: KoMaL A. 842
February 11, 2023
combinatoricskomal
Problem Statement
people live in a town, and they are members of some clubs (residents can be members of more than one club). No matter how we choose some (but at least one) clubs, there is a resident of the town who is the member of an odd number of the chosen clubs. Prove that the number of clubs is at most .Proposed by Dömötör Pálvölgyi, Budapest