A man wears socks of two colours - black and brown. He has...

It is given that he has socks of 2 colours& only.

It is obvious that if he only takes out one sock then he can’t have a matching pair (since by definition a pair is 2 socks).

If he takes out 2 socks, he could select 2 that are the same colour, but he could also select one of each colour — which is not a matching pair. Therefore, 2 socks are not enough to& guarantee& that he will have a matching pair

If he takes out 3 socks then there are 2 scenarios — the first being that the first two socks he selects are matching. The second is that the first two socks he picks don’t match (without loss of generality we can assume the first is black& and the second is brown) - in this case, the next sock he selects must make a pair, since if it is black it will make a pair with the first sock, and if it is brown it will make a pair with the second sock.

Thus, we have shown that 3 socks will guarantee a pair.&