MathDB

8

Part of 2005 Korea Junior Math Olympiad

Problems(1)

study groups between 6 students

Source: KJMO 2005 p8

5/1/2019
A group of 66 students decided to make study groups and service activity groups according to the following principle: Each group must have exactly 33 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 88.
combinatorics