MathDB

Suppose a class contains

100

students. Let, for

1\le i\le 100

, the

i^{\text{th}}

student have

a_i

many friends. For

0\le j\le 99

let us define

c_j

to be the number of students who have strictly more than

j

friends. Show that \begin{align*} & \sum_{i=1}^{100}a_i=\sum_{j=0}^{99}c_j \end{align*}

Problem Statement