There are 100 black socks and 100 white socks mixed up in a drawer. If you have to pick socks blindly from the drawer, how many socks do you need to take out to be sure that you have a matching pair of socks?


Updated: Nov. 27, 2020 — Training Time: 1 Minute
Overseen by: Archangel Macsika

Topic: Data Science.

Difficulty: Easy.

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Objective: There are 100 black socks and 100 white socks mixed up in a drawer. If you have to pick socks blindly from the drawer, how many socks do you need to take out to be sure that you have a matching pair of socks?

Short Answer: 3 picks.

Full Solution

The question here requires us to find a matching pair of socks of either white or black, not a specific color.

Let B represent black and W represent white.

If we pick 2 socks blindly from the drawer as the minimum, the possibility of getting a pair is 50%.
Since we may arrive at either one of the combination: BB, BW, WB, WW.

On the other, if we pick 3 socks blindly from the drawer as the minimum, the possibility of getting a pair is 100%.
The combinations that come out from 3 picks can be BWW, BBW, BBB, WBB, WWB, WWW.
Therefore, picking a minimum of 3 socks means we can always pick a pair of socks with matching color from the drawer if we pick blindly.

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