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 The odds stay unchanged (Posted on 2004-06-17)
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?

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 re: generalisation ==> author's remarks | Comment 17 of 21 |
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

 Posted by Ady TZIDON on 2004-06-20 11:00:07

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