Sock Search

In your bedroom, you have a drawer with 2 red, 4 yellow, 6 purple, 8 brown, 10 white, 12 green, 14 black, 16 blue, 18 grey, and 20 orange socks. It is dark in your bedroom so you cannot distinguish between the colors of the socks.

The question: How many socks do you need to take out of the drawer to be sure that you have at least three pairs of socks of the same color?

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Solution to: Sock Search

In the worst case in which you did not take three pairs of socks of the same color, you took 2 red socks, 4 yellow socks, and 5 of each of the other colors. That gives a total of 46 socks. Then if you take one more sock, you are sure to have 6 socks of at least one color. Therefore, you have to take 47 socks from the drawer to be sure that you have at least three pairs of socks of the same color.