study groups between 6 students
Source: KJMO 2005 p8
May 1, 2019
combinatorics
Problem Statement
A group of students decided to make study groups and service activity groups according to the following
principle:
Each group must have exactly members. For any pair of students, there are same number of study groups
and service activity groups that both of the students are members.
Supposing there are at least one group and no three students belong to the same study group and service activity group, prove that the minimum number of groups is .