Mr. Blue has 12 brown gloves and 8 black gloves in a drawer in his closet. If he blindly pulls gloves from the drawer, what's the minimum number of gloves Mr. Blue will have to pick, to be certain he has a pair of gloves of the same color?

The key to this one is the pigeonhole principle. We have 2 colors of gloves, so if he picks 3 gloves, they cannot all be of different colors. Hence, he must have at least a pair of gloves of the same color. So 3 gloves suffices. If he only takes 2 gloves, the possibility exists that they will be of different colors. So 2 does not guarantee a color-coordinated pair. Hence, for certainty, he must pick 3 gloves.

Posted by Timothy on 2004-10-06 18:48:22