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 Different solution? by Jer)

Uhh.. No offense, but you've proven nothing. Your hypothetical situation does not match the given situation at all. The problem states that there is a minimum number of gloves that she needs to draw. For your situation, there is no minimum.

Also, this isn't a hypothetical situation. It's a real situation so there can't be an infinite number of gloves. You can argue that there may be a large number of gloves, but it is still finite. Of course, the minimum number of gloves is a function of that number.

In essense, all you've shown is that in your situation, there is no minimum or maximum, which is true. But your situation is far from the problem.

Posted by np_rt on 2004-06-03 14:56:40