Braingle: 'Sock Drawer' Brain Teaser

Sock Drawer

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

Puzzle ID:	#3445
Fun:	(2.29)
Difficulty:	(1.73)
Category:	Probability
Submitted By:	neo1
Corrected By:	MarcM1098

There are 10 socks of each of the following colors in a drawer: blue, green, red, yellow & white, for a total of 50 socks. If the socks are randomly distributed in the drawer (i.e. not in pairs or any other grouping), and you are blindfolded, what is the minimum number socks you must draw from the drawer in order to be certain you have at least 2 socks of the same color?

If you are in the same situation as in the preceding problem, how many socks must you draw from the drawer in order to be certain you have at least 2 socks of different colors?

Answer

The answer for the first part is 6 socks and the answer for the second part is 11.
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Comments

strathconn Jun 01, 2003	Why aren't they both 11?
fishmed Jul 23, 2003	Because there are only 5 colors, once you draw 6, you are guaranteed to have at least one match, even if the 1st 5 were not. Make sense?
strathconn Aug 13, 2003	I misread the question, and was just showing it to my husband and realized my confusion. Thank you Fishmed.
absy Dec 06, 2003	then 6 would be the max you would have to draw to have a match....not the minimum....you could get lucky and draw same colors on the first 2 draws.....right? so either i'm totally missing a link, or the question was perhaps worded wrong.
absy Dec 06, 2003	the problem wasn't worded wrong, but i think the answer is the wrong thing. its the max, not the min, like is asked for in the question, unless like i said, i'm totally missing a link.
fishmed Dec 09, 2003	You are right, but it really is the minimum in that if you draw less than 6, you might luck out and get a match sooner, but as the question stated, you are looking for the minimum that needs to be drawn to guarantee a match. As there are 5 different colors, if you draw six, there might be more than one match, but there is a definite guarantee of one. That's why you have to draw 6 as you don't know if you draw a match sooner.
absy Dec 09, 2003	ahh yes i missed the "to make certain you have 2 of each" ty for clarifying
brainjuice Mar 31, 2006	classic but fun
eyenowhour Jan 10, 2007	Pigeon hole principle.
KarateGirl098 Nov 12, 2009	Really easy, but fun.