Epistemic Planning in Network Muddy Children Puzzle
The basic story of the puzzle is as follows. Three children have muddy faces,
and each can see the others' faces, but not his own. A teacher announces to the
children: \at least one of you has a muddy face". Then he asks: \Do you know
whether your face is muddy or not? If so, raise your hand". No child raises a
hand. Then, after some time, the teacher asks the same question, and again
no child raises a hand. Some more time passes, and when asked the question a
third time, each child raises his hand.