Question 14
A set $\mathcal{S}$ of distinct positive integers has the following property: for every integer $x$ in $\mathcal{S},$ the arithmetic mean of the set of values obtained by deleting $x$ from $\mathcal{S}$ is an integer. Given that $1$ belongs to $\mathcal{S}$ and that $2002$ is the largest element of $\mathcal{S},$ what is the greatest number of elements that $\mathcal{S}$ can have?