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?

Question

Mathematics

Isabell Arias

26 September, 00:35

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?

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Answers (1)

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Rylan Dennis · Answer 1

Answer: At least 3

Step-by-step 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.