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A drawer contains 10 black and 10 brown socks which are all mixed up. What is the smallest number of socks to be taken from the drawer to decide without seeing them, to be sure that there is atleast one pair of socks of the same colour?

A drawer contains 10 black and 10 brown socks which are all mixed up. What is the smallest number of socks to be taken from the drawer to decide without seeing them, to be sure that there is atleast one pair of socks of the same colour? Correct Answer 3

Given,

10 black shoes and 10 brown socks

Suppose a person choose black socks in first turn 

In the second turn, he can either choose black or brown socks, suppose he choose brown socks 

In the third turn, he can choose either black socks or brown socks

Now, he has at least a pair of black socks or brown socks in 3 turns

∴ The smallest number of socks to be taken from the drawer to decide that there is atleast one pair of socks of the same colour is 3

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