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: huh? by Erik O.)

I still don't understand why if there are 10,000 pairs of one color that you can be SURE that with 21 gloves they won't all be that color. - me

"If you have 10,000 pairs of red gloves and you draw 20 right handed red gloves from the drawer, the 21st glove you draw (left handed of course) could be one of the other colors." - Erik

That's exactly my point! If you pick 20 right-handed red gloves then a green left-handed glove you won't have a match! If there were 10,000 red, 10 blue & 10 green, then you would need to pick 10,012 gloves, because the first 10,000 could all be red, the next 10 could all be blue, (all of the same hand) and if you pick another one of the same hand it would have to be green. Then, if you look for a glove of the opposite hand you are guaranteed a match because with 10,011 gloves of the same hand you are sure to have every color.

Posted by Danny on 2004-06-03 18:03:49