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 Solution? by Erik O.)

If she had 22 pairs of gloves and took out 20 right gloves and 1 left glove, she'd still be assured of having at least one of each color of right glove, and so of a match with whatever color the left one is.

Posted by Charlie on 2004-06-03 09:22:54