Sample Question #262 (brainteaser)

[This is a classic brainteaser question]

You get up in the wee hours of the morning and it’s still dark outside. You’re too lazy to turn on the lights and you can’t see a thing, but you open a drawer where you keep your socks. You have 10 red socks, 10 blue socks, 10 white socks, and 10 black socks, but they’re all mixed up in the drawer.

How many socks in the minimum do you need to take out of the drawer to ensure you get at least one pairing?

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ANSWER

Since there are 4 colors, you just take out 5 stocks to ensure you get at least one pair of the same color.

Bonus question: what if the number of socks of each color are different, say, 10 red socks, 2 blue socks, 5 white socks, and 30 black socks. Would the answer be the same?

[This question is almost always asked with an equal number of socks for each color.]

Maybe it will be helpful to mention that this is related to the pigeonhole principle. If you have n pigeons in m holes where n>m, there is at least one hole with more than one pigeon. By analogy the total number of socks is n and the number of colors is m. One needs to pick at least m+1 socks to ensure at least a pair of the same color.

Monad, you’re absolutely right, this is an application of the pigeon hole principle.

-brett

Quant Career:usually there’s a left and a right sock. At least mine come this way (you can look carefully at a brand new pair of sock). Which means the answer is 21. Q.E.D. -Yanis