The Sock Problem

case 1: 1 white and 1 white

case 2: 1 black and 1 black

case 3: 1 black and 1 white

There is no problem in cases 1 and 2, the problem is in case 3. So we need to take at most 3 socks.

If you take 2 socks, one must be black and other must be white. If you take the 3rd sock you'll get black or white which makes a pair with any one of the 2 you took first.

But sometimes you may get 2 same color on the first 2 attempt, but you may not even get 2 same color in the first 2 attempt. But 3 makes sure you get a pair.

You can take a black sock then a white sock as the first two you pick. The next sock must either be black or white giving you a pair so the answer is:

$\boxed{3}$