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?

i say there are at least 120 gloves, because is she took out at least one glove of each kind until she finally overlapped and took out another one, and there is a 1 in 6 chance that she took out a glove of each color so if it took 21 gloves for one to overlap then then the one in six is twenty in one-twenty.

Posted by becca on 2004-06-03 21:10:26