  In this paper, we define a new parameter of a graph as a spin-off of the
pebbling number (which is the smallest $t$ such that every supply of $t$
pebbles can satisfy every demand of one pebble). This new parameter is the
singular pebbling number, the smallest $t$ such that a player can be given any
configuration of at least $t$ pebbles and any target vertex and can
successfully move pebbles so that exactly one pebble ends on the target vertex.
We also prove that the singular pebbling number of any graph on 3 or more
vertices is equal to its pebbling number, that the singular pebbling number of
the disconnected graph on two vertices is equal to its pebbling number, and we
find the singular pebbling numbers of the two remaining graphs, $K_1$ and
$K_2$, which are not equal to their pebbling numbers.
