Joe keeps all his socks in one drawer. he has 7 blue docks and 9 brown socks. if he reaches in the drawer without looking, what is the least number of socks he can take out to be sure of getting a pair of the same color?

The least number of socks Joe can take out to be sure of getting a pair of the same color is 3 socks.

Solution:

Given, Joe keeps all his socks in one drawer.  

He has 7 blue docks and 9 brown socks.  

He reaches in the drawer without looking,  

We have to find what is the least number of socks he can take out to be sure of getting a pair of the same color?

Total number of socks in the drawer = 9 + 7 = 16.

Now, he has to pick atleast 2 socks to get a pair.  

Here, two condition arises, if the two picked socks are same colour and two picked socks are different colour.

In 1st condition, he has a pair of same colour, so our condition satisfied.

In 2nd condition, he has different pair, and he has pick another sock, then, the 3rd will pair with any one of the already picked socks, then, he will have a pair.

So, in total, without looking, to be sure that he got a pair he has to pick 3 socks.

Hence, he has to pick 3 socks.