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. Copyright 2024 Published by Elsevier Inc.
