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?

Nothing wrong with Gamer's generalisation, except

that the solution of the puzzle is significantly shorter.

Please comment when you will see the "official"

solution.

BTW to find squares described by M^2-N^2=100

You go (M+N)*(M-N)=100 AND LOOK FOR 2 EVEN FACTORS

TO ENSURE AN INTEGER SOLUTION

IT IS 10*10==> TRIVIAL 0;100

or

50*2===> 576;676

ady