1. The pigeonhole principle states that given a function, f, from the set X to the set Y, where n(X) > n(Y), there must be at least two elements in the domain that have the same image in the co-domain.
Here let X be the set of students and Y be the set of grades. There are 101 possible grades, so n(Y) = 101. Therefore, in order for the pigeonhole principle to apply we need at least 102 students.