pigeonhole principle clarification Would the following statement be applicable to the pigeonhole principle? Or can I simply do $100 \times 50 = 5000$? 
What is least amount of students in a school to guarantee that there are
at least 100 students from the same state?

The minimum number to guarantee that would be $99\cdot 50+1=4951$. If you had fewer, say $4950$, then there's the possibility that there are exactly $99$ students from each state. Any one additional student from any state is enough at this point.
