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?

What is a pair? Just "two"? ... or two that go together as a left-and-right set?

If the gloves are reversible--inside-out, it doesn't matter: three gloves will provide two of the same color, just like socks.

But if the gloves are not reversible, and you need a usable pair, AND you know that the 12 are really 6 matched pairs and the 8 are really 4 matched pairs, then you need to pull out 11 to be sure of having a matching pair.

But with so many pairs, I'm sure Mr. Blue has lost some along the way, the same way socks get lost.  He probably has something like 7 brown gloves for one hand and 5 for the other, and 5 black gloves for one hand and 3 for the other.  If this is the case, the first 12 gloves he chooses could possibly be all 7 brown gloves for one hand and all 5 black gloves for one hand, so he'd need to take a 13th glove to be sure of getting a usable pair.

But there's nothing really guaranteeing that Mr. Blue has even one right-hand glove. Or, if all his brown gloves are left-handed and all his black gloves are right-handed, for example, there's no way of getting a matching pair.

So there's no way of being certain that he has a pair of gloves of the same color unless handedness doesn't count in defining a "pair", in which case the answer is 3.

Posted by Charlie on 2004-10-06 09:42:04