Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

A club of $n$ members is organized into four committees following two rules:

  • Each member belongs to exactly two committees, and

  • each pair of committees has exactly 1 member in common.

Find all possible values of $n$.

share|improve this question

1 Answer 1

up vote 4 down vote accepted

If each member must belong to two committees, he or she must be the member in common to those two committees. There are 6 pairs of committees, requiring 6 common memberships and therefore 6 members.

Any more members joining would give his or her two committees two common members.

Therefore, I would say only $n=6$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.