Sharon has a number of pairs of gloves of identical design, but of several (at least three) different colors. She has at least three pairs of each color. In the dark she can distinguish the handedness of a glove, but not its color. Unfortunately, she keeps the gloves jumbled up in a drawer in an unlit cellar.

Sharon knows that if she takes out 21 gloves, in the dark, she can be sure of getting at least one pair.

What is the maximum number of pairs of gloves that she could have?

1. Is it possible that Sharon can be certain with only 20 gloves and picking out another one just makes her more certain?

2. IS there a real answer? As in a specific number between 28 and infinity?

If the answer to 1 is yes then the answer to 2 could be no. IOW, there could be no limit to how many gloves she can have and this is all just a trick question. You may be right, there could be another method of picking gloves that can yield a higher answer. But I DO know THIS for certain. Whatever method you use, you need to be certain you have at least one specific color of glove of at least one hand (for ex. "I know I have at least one green left glove...") and at least one glove of the other hand. You need to be certain of at least THAT much.

I'll sleep on it again tonight!

Edited on June 4, 2004, 4:28 pm

Posted by Danny on 2004-06-04 16:14:46