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?
If I'm interpretting the question correctly, the maximum number of pairs of gloves would be 20.
If Sharon pulls out all 20 right handed gloves, then the 1 lefthanded glove she pulls out will match one of the others.
This assumes that the process of pulling gloves out is not random.

Posted by Erik
on 20040603 08:46:25 