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 2 questions to Brian
I did not realize it until now, but I forgot a sentence in the second paragraph:
Sharon knows that if she takes out 21 gloves, in the dark, she can be sure of getting at least one pair. If she only takes out 20 there is no guarantee of a match.
Without that statement, there existed a loophole which allowed infinity for an answer. Danny, thank you for helping me find that omission.