HMMT 二月 2002 · GEN1 赛 · 第 4 题

英文原题

We call a set of professors and committees on which they serve a university if
(1) given two distinct professors there is one and only one committee on which they both
serve,
(2) given any committee, C , and any professor, P , not on that committee, there is exactly
one committee on which P serves and no professors on committee C serve, and
(3) there are at least two professors on each committee; there are at least two committees.
What is the smallest number of committees a university can have?