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 re(2): Different solution? by Charlie)

Your whole assumption relies on the fact that you get color C first. What if the one you choose is not color C? This example of yours does not work because there is no guarantee that she will get color C first. Even if it's highly likely, you cannot say the minimum is 21.

Posted by np_rt on 2004-06-04 12:12:27