Key idea. Count how many socks can be present without reaching three of a colour.

1. There are only two colours. Suppose each colour appears at most twice among the socks taken.

2. Then there could be at most \(2+2=4\) socks altogether.

3. We have taken five socks. Therefore one colour must appear at least three times.

Remember. The argument gives a guarantee even in the least favourable selection.