On a certain island each of the inhabitants is a member of one of the two existing clubs.

The membership distribution is such that when two random people meet, the probability of those two belonging to the same club is equal to the probability of them belonging to distinct clubs.

When 100 newcomers arrive on the island and each enrolls in one of the two clubs, the distribution still retains this feature. How many people belong to either club?

I don't know yet if this is the only solution, but this one works:

Originally the island was uninhabited, then 100 people showed up with 45 members in Club Alpha and 55 members in Club Beta.

I'm still working on a non-zero solution.

Posted by Erik O. on 2004-06-17 15:13:39