  Let G be a graph with a distribution of pebbles on its vertices. A pebbling
move consists of removing two pebbles from one vertex and placing one pebble on
an adjacent vertex. The optimal pebbling number of G is the smallest number of
pebbles which can placed on the vertices of G such that, for any vertex v of G,
there is a sequence of pebbling moves resulting in at least one pebble on v. We
determine the optimal pebbling number for several classes of induced subgraphs
of the square grid, which we call staircase graphs.
