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Back to Class Notes (M326)

The Socks problem (from Dr. Lynch)

Because you are leaving your house before dawn this morning and you do not want to disturb your spouse any moe than you have to, you have put the clothes you plan to wear in the living room. When the alarm rings, you shut it off quickly and quietly slip out of bed.  Then you realize that you have forgotten to put any socks out with your other clothes.

Your socks are in the top drawer of your dresser and you don't care which color socks you wear today so long as they match. The problem is that the socks in that drawer are not joined in pairs; they are all loose.  You do know, however, that there are 15 black socks, 12 brown socks, 9 gray socks, and 6 blue socks in the drawer.

You don't want to turn on the light to find a matched pair, so you have to take a bunch of single socks out into the living room to find your pair.  You want to take as few as possible, but you need a matched pair.  The color does not matter.  What is the minimum number of socks you need to take out of that drawer to guarantee yourself a matched pair?

When you think you have the best answer, devise a way of explaining it to others so as to convince them that you have solved the problem correctly.