  Given an initial configuration of pebbles on a graph, one can move pebbles in
pairs along edges, at the cost of one of the pebbles moved, with the objective
of reaching a specified target vertex. The pebbling number of a graph is the
minimum number of pebbles so that every configuration of that many pebbles can
reach any chosen target. The pebbling threshold of a sequence of graphs is
roughly the number of pebbles so that almost every (resp. almost no)
configuration of asymptotically more (resp. fewer) pebbles can reach any chosen
target. In this paper we find the pebbling threshold of the sequence of squares
of cliques, improving upon an earlier result of Boyle and verifying an
important instance of a probabilistic version of Graham's product conjecture.
