We consider the $k$-layer pointer jumping problem in the one-way multi-party number-on-the-forehead communication model. In this problem, the input is a layered directed graph with each vertex having outdegree $1$, shared amongst $k$ players: Player~$i$ knows all layers {\em except} the $i$th. The players must communicate, in the order $1,2,\ldots,k$, ... more >>>