## 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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