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 Better than 28. by Brian Smith)

The first 20 gloves Sharon draws out could all be for the same hand, but finally that the 21st glove pairs with one of the previous 20, so she has 20 pairs total -- if she had more pairs it would be possible for the 21 drawn to all be for the same hand. Sharon is working in the dark, so the colors can't really be important -- the information about colors only shows that there must be at least 9 pair, three pairs each of three different colors, and this is not contradicted by there being 20 pairs.

Posted by Richard on 2004-06-03 23:26:28