  We introduce a particle model, that we call the $\textit{golf model}$.
Initially, on a graph $G$, balls and holes are placed at random on some
distinct vertices. Balls then move one by one, doing a random walk on $G$,
starting from their initial vertex and stopping at the first empty hole they
encounter, filling it. On finite graphs, under reasonable assumptions (if there
are more holes than balls, and if the Markov chain characterizing the random
walks is irreducible) a final configuration is reached almost surely. In the
paper, we are mainly interested in ${\bf H}^1$, the set of remaining holes. We
give the distribution of ${\bf H}^1$ on $\mathbb{Z}/n\mathbb{Z}$, and describe
a phase transition on the largest distance between two consecutive holes when
the number of remaining holes has order $\sqrt{n}$. We show that the model on
$\mathbb{Z}$ is well-defined when every vertex contains either a ball with
probability $d_{\sf b}$, a hole with probability $d_{\sf h}$, or nothing,
independently from the other vertices, as long as $d_{\sf b} \leq d_{\sf h}$,
and we describe the law of ${\bf H}^1$ in this case.
