  We study the continuous version of a hyperbolic rescaling of a discrete game,
called open mancala. The resulting PDE turns out to be a singular transport
equation, with a forcing term taking values in $\{0,1\}$, and discontinuous in
the solution itself. We prove existence and uniqueness of a certain formulation
of the problem, based on a nonlocal equation satisfied by the free boundary
dividing the region where the forcing is one (active region) and the region
where there is no forcing (tail region). Several examples, most notably the
Riemann problem, are provided, related to singularity formation. Interestingly,
the solution can be obtained by a suitable vertical rearrangement of a
multi-function. Furthermore, the PDE admits a Lyapunov functional.
