Left and Right are the same!

Ten red socks and ten blue socks are all mixed up in a dresser drawer. The 20 socks are exactly alike except for their color. The room is in pitch darkness and you want two matching socks. What is the smallest number of socks you must take out of the drawer in order to be certain that you have a pair that match?

Clarification: A matching pair means 2 2 socks of same color, they are exactly the same, so Left and Right are the same!

3 11 19 2 17 4 18 10

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3 solutions

Why two socks won't work?

With two socks, it is possible to have one red and one blue.

Why three socks work?

With three socks, there is always a matching pair since either you will have chosen three of the same color, or a matching pair and an odd one out.

Hence, the smallest number of socks you must take out of the drawer in order to be certain that you have a pair that match is 3 \boxed{3} .

How do you make sure that one will be for left foot and the other for the right foot? You can only assure that two socks will be of the same color.

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Sir, that is why I have stated that "Left and Right are the same"!

Vinayak Srivastava - 1 year ago
Mahdi Raza
Jun 2, 2020

By the pigeonhole principle, if we take out three socks, at least two of the socks will be of the same color. And there, we have a pair of same colors.

Thanks for answering my problem! Nice!

Vinayak Srivastava - 1 year ago
Aryan Sanghi
Jun 1, 2020

By pigeonhole principle if we take three socks, atleast two will be of same colour.

Try similar question here

Such a complex thing in such a simple problem? Nice!

Vinayak Srivastava - 1 year ago

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No, it is not a bit complex. When you'll read, you'll come to know.

Aryan Sanghi - 1 year ago

Try similar question by me here

Thanks for giving me an idea.

Aryan Sanghi - 1 year ago

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