Pebble game

In mathematics and computer science, a pebble game is a type of mathematical game played by moving "pebbles" or "markers" on a directed graph. A variety of different pebble games exist. A general definition of pebbling is given below.

Graph pebbling: A certain number of pebbles are distributed among the vertices of an undirected graph; the goal is to move at least one to a particular target vertex. But to move one pebble to an adjacent vertex, another pebble at the same vertex must be discarded.

...
Wikipedia