What is the minimum number of randomly chosen people needed

What is the minimum number of randomly chosen people needed in order to be sure that at least four of them were born in the same month?

Solution

You could have 12 people, one born in each month, that would not have any pair born in the same month.

If you have minimum number of randomly chosen people 15, though, you can assign one born in 11 months and in the 12th month you can choose 4 born.

hnece minimum number of randomly chosen people needed in order = 15.