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(3): huh? by Brian Smith)

Or, to fit the problem a little better, what if she had 9 pairs of red and green gloves (so 8 red and 1 green, or 7 red and 2 green...)?  Then she would draw 10 rights to guarantee a blue right, and then 10 lefts to guarantee a blue left.  Ok, that's only 20.  The 21st is just redundant.

The point is, I do agree that you can say there is no limit to the number of pairs of gloves she could have, just a limit on the arrangement.

Posted by nikki on 2004-06-03 18:19:20