  We investigate a special variant of chip-firing, in which we consider an
infinite set of rooms on a number line, some of which are occupied by
violinists. In a move, we take two violinists in adjacent rooms, and send one
of them to the closest unoccupied room to the left and the other to the closest
unoccupied room to the right. We classify the different possible final states
from repeatedly performing this operation. We introduce numbers $R(N,\ell,x)$
that count labeled recursive rooted trees with $N$ vertices, $\ell$ leaves, and
the smallest rooted path ending in $x$. We describe the properties of these
numbers and connect them to permutations. We conjecture that these numbers
describe the probabilities ending with different final states when the moves
are chosen uniformly.
