### Brain Teasers

# Sock Drawer

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

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?

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.Hide Answer Show Answer

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## Comments

Why aren't they both 11?

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?

I misread the question, and was just showing it to my husband and realized my confusion. Thank you Fishmed.

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.

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.

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.

ahh yes i missed the "to make certain you have 2 of each" ty for clarifying

classic but fun

Pigeon hole principle.

Really easy, but fun.

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