\begin{definition}[Definition:Josephus Problem]
Consider a collection of $n$ people in a circle.
Let them each be eliminated sequentially by counting out every $m$th person (closing the gap after each elimination).
For a given a number of people $n$, and a given step size $m$, the problem is to determine the initial position in the circle of the person who remains after all the others have been eliminated.
\end{definition}