Easy | Discrete Maths |

There are 10 black socks and 10 white socks (no left-right distinction) in the wardrobe. Your task is to draw the minimum number of socks at random to be sure you have a pair of a single color. How many socks should you draw?

Hint

Pigeonhole principle

Answer

3

Solution

This is the easiest example of a very powerful tool called the Pigeonhole principal, which says that if there are (N+1) pigeons to fit in N holes, atleast one hole will have 2 or more pigeons. Hence, if you pick 3 socks to come with 2 color categories, at least one category will have 2 or more socks, i.e. a pair is guaranteed with either red or black color.

Source: Common

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