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?

(In reply to Shame on me! by Brian Smith)

Well, that certainly changes a lot!

Anyway, since Brian Smith has made himself clear, on to improvement of the original strategy.  Here's my proposal.

3 pairs of red, 13 pairs of green, 13 pairs of blue, 29 total pairs.

Take 4 left and 17 right.  You are guaranteed a right of both green and blue, and a left of green or blue.

Now, does this really work?  Is there a way to be guaranteed a pair with 20 gloves?  Is there a better way?

Posted by Tristan on 2004-06-04 20:42:08