small groups created by 12 members in a club
Source: KJMO 2008 p8
May 2, 2019
combinatoricsSets
Problem Statement
There are members in a club. The members created some small groups, which satisfy the following:
- The small group consists of or people.
- Also, for two arbitrary members, there exists exactly one small group that has both members.
Prove that all members are in the same number of small groups.