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If you have 14 brown socks and 14 blue socks and 14 black socks how many must you remove without looking to be sure to have a matched pair?
Wiki User
∙ 15y ago
You need to remove four socks without looking in order to have a matched pair. Here is the explanation: We have three distinct sets of socks: brown, blue and black. Look at each set as a bin, and consider choosing a sock from this set as placing a ball in the respective bin. If we place three balls, it is possible to have one ball in each bin, so we get no matched pair. Now, if we place four balls, we have to have two balls in at least one bin, corresponding to a matched pair. This makes for four socks we must choose to be sure we have a matched pair. This is a special case of the pigeonhole principle (please see related link).
Wiki User
∙ 15y ago
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