  An ordered triple $(s,p,n)$ is called admissible if there exist two different
multisets $X=\{x_1,x_2,\dotsc,x_n\}$ and $Y=\{y_1,y_2,\dotsc,y_n\}$ such that
$X$ and $Y$ share the same sum $s$, the same product $p$, and the same size
$n$. We first count the number of $n$ such that $(s,p,n)$ are admissible for a
fixed $s$. We also fully characterize the values $p$ such that $(s,p,n)$ is
admissible. Finally, we consider the situation where $r$ different multisets
are needed, instead of just two. This project is also related to John Conway's
wizard puzzle from the 1960s.
