Solution to puzzle of white tailed cats
The following solution is reproduced from Prof Ian Stewart’s book “Cabinet of Mathematical Curiosities”.
Answer:
Suppose that there are c cats, of which w have white tails. There are 
ordered pairs of distinct cats, and 
ordered pairs of white tailed cats. (You can choose the first cat of the pair in c ways, but the second in only 
ways since you have used up one cat. Ditto for white tailed cats. By ordered, what is meant is choosing first cat A and then cat B is considered to be different from B first and then A. If you don’t like that, then both formulae have to be halved — with the same result.)
This means that the probability of both cats having white tails is 
and this must be 1/2. Therefore, 
with c and w being whole numbers. The smallest solution is 
, and 
. The next smallest turns out to be 
and 
. Since Ms Smith has fewer than 20 cats, she must have 4 cats, of which three have white tails.
More fun later,
Nalin Pithwa
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