The paper includes four main results for epistemic planning. The first result is a description of all public announcements that lead to complete elimination of initial uncertainty for at least one agent in a multi-agent system based on a popular Muddy Faces Puzzle. The second result is an
introduction of a new approach for graphical representation of a dynamic epistemic model. The third result is an introduction of a Network generalization of this puzzle and its new control problem. A network generalization: children have a given observability of each other’s faces. Part of this result is a developed software and a numerical solution of an optimization problem for dynamic epistemic problem. The forth result is a Threshold generalization of the Network generalization of nagent multi-agent Muddy Faces Puzzle. Threshold generalization: children react when they are certain that the number of muddy faces among them is greater than the arbitrary threshold. We found that a teacher can give more information about the muddy faces to the children but as a result a number of children who realize that their faces are muddy will decrease.