One morning you wake to find the power is out and you'll need to dress in the dark.

You know you have eight black socks and twelve brown socks in your sock drawer. But you're not the most orderly person in the world and the socks are all jumbled up, so you can't tell one color from another in the dark.

What's the minimum number of socks you'll need to grab in order to ensure that you'll have two socks of the same color?


Solution to Dark Socks Puzzle

The answer is not nine or thirteen but only three. You don't care which color you end up with so long as at least two of the socks are the same. If you took only two socks, they might be of different colors. But if you took three, two of them would have to be the same because there are only two colors total.

The number of socks that need to be taken depends on the number of colors, not the number of socks of each color there are in the drawer. If the number of colors is c, then the number of socks needing to be taken is c+1. So if the drawer contains 36 differently colored socks all jumbled up, then you'd need to take out 36+1 or 37 socks. At least 2 of those 37 socks will be the same color.

If, on the other hand, you wanted 2 or more socks of the same specific color, then it would be different. In the original problem above, there are 8 black socks and 12 brown socks. To be absolutely certain of getting 2 or more black socks, you'd need to take 14 socks total. You'd have to allow for the (remote) possibility of pulling out all 12 brown socks before you managed to get 2 black socks. 12+2=14. Similarly, if you wanted to be sure of getting 2 brown socks, you'd have to take 8+2=10 socks total.