Question 178
A set consisting of at least two distinct positive integers is called *centenary* if its greatest element is $100$. We will consider the average of all numbers in a centenary set, which we will call the average of the set. For example, the average of the centenary set $\{1, 2, 20, 100\}$ is $\frac{123}{4}$ and the average of the centenary set $\{74, 90, 100\}$ is $88$.
Determine all integers that can occur as the average of a centenary set.
Determine all integers that can occur as the average of a centenary set.