Question

A drawer contains 22 black socks and 22 white socks. If the light is off and Matt reaches into the drawer to get his​ socks, what is the minimum number of socks he must pull out in order to be sure that he has a matching​ pair?

Answer 1

Answer: At least 3

Explanation:

Lets solve this problem by the pidgeon hole principle. Suppose that Matt pulls out 2 socks, if he gets a matching pair then he is done and that's it. But now suppose that he gets one black sock and one white sock, if he then pulls out a third sock it will be either white or black, in either case he would have gotten with a 100% certainty a matching pair, since he already has a black and a white sock. So the minimum number to ensure he gets a matching pair is 3 socks.