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?

Those of you who are wondering why the maximum number of pairs can't be 10,000+ seem to be misreading the puzzle.

The puzzle asks, what is the maximum number of pairs of gloves that Sharon can have so that she can be assured of a match by grabbing only 21 gloves from the drawer?

Obviously 10,000 is much too large a number because you could draw 20 right handed gloves from the pool of 10,000 same colored gloves, and then your 21st draw (a left handed glove) could be one of the other colors.

Posted by Erik on 2004-06-03 19:21:25