Question

Assume that a class consists only of students residing the 50 US states. Find the smallest number of students that must be enrolled in a class to guarantee that there are at least 5 students from the same state

Answer 1

If a class contains 4 students from each state, then there are 4•50=200 all such students. Then by Pigeonhole principle, to guarantee that there are at least 5 students from the same state the smallest number of students that must be enrolled in a class is 200+1=201.