A certain college class has 40 student whose age are in the

A certain college class has 40 student whose age are in the range of 17-34. You want to make a bet that at least x of the student are the same age. What is the largest value for that you can choose to be certain.

Solution

To be certain, there has to be x-1 of each age. Then, the next one will be the xth one of one of the ages.

There are 18 possible ages here (17-34).

Thus, we need at least 18(x-1) + 1 = 18x - 17. [ANSWER]