Problem 1: A certain college class has 40 students whose ages are in the range of 17 - 34. You want to make a bet that at least x of the students are the same age. What is the largest value for x that you can choose to be certain.
Problem 2: How many integers from 100 through 999 must you pick randomly to be certain that at least two of them have a common digit? (For example, 256 and 513 have the common digit 5.)