Double Counting
There are 10001 students at an university. Some students join together to form several clubs (a student may belong to different clubs). Some clubs join together to form several societies (a club may belong to different societies). There are a total of k societies. Suppose that the following conditions hold:
i.) Each pair of students are in exactly one club.
ii.) For each student and each society, the student is in exactly one club of the society.
iii.) Each club has an odd number of students. In addition, a club with {2m+1} students (m is a positive integer) is in exactly m societies.
Find all possible values of k.
The answer is 5000.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
0 solutions
No explanations have been posted yet. Check back later!