  We study the set of possible configurations for a general kinetically
constrained model (KCM), a non monotone version of the $\mathcal{U}$-bootstrap
percolation cellular automata. We solve a combinatorial question that is a
generalization of a problem addressed by Chung, Diaconis and Graham in 2001 for
a specific one-dimensional KCM, the East model. Since the general models we
consider are in any dimension and lack the oriented character of the East
dynamics, we have to follow a completely different route than the one taken by
Chung, Diaconis and Graham. Our combinatorial result is used by Mar\^ech\'e,
Martinelli and Toninelli to complete the proof of a conjecture put forward by
Morris.
