We model the story of the muddy children which is known in many versions. See for example~cite{Littlewood1953:amm},~cite[p.~24-30]{fagin1995reasoning} or~cite[p.~93-96]{DitHoekKooi2007:del}.

Our implementation treats the general case for \(n\) children out of which \(m\) are muddy, but we focus on the case of three children who are all muddy. As usual, all children can observe whether the others are muddy but do not see their own face. This is represented by the observational variables: Agent $1$ observes $p_2$ and $p_3$, agent $2$ observes $p_1$ and $p_3$ and agent $3$ observes $p_1$ and $p_2$.