The children are each told that they should step forward if they know that their own face is muddy.

A custodian tells the children that at least one of them has a muddy face. But, every child knows the state of all other children's faces. None of the children can determine the state of their own face themselves. The children consider it possible to have a muddy face. In other cases, hat puzzles are described in the context of wise men. In many variations, hat puzzles are described in the context of prisoners. Hat puzzles are induction puzzle variations that date back to as early as 1961. Muddy children puzzle is a variant of the well known wise men or cheating wives/husbands puzzles. The muddy children puzzle is the most frequently appearing induction puzzle in scientific literature on epistemic logic. Also, the inaction of a participant is a non-verbal communication of that participant's lack of knowledge, which then becomes common knowledge to all participants who observed the inaction. Also, usually, some kind of hint is given to suggest that the participants can trust each other's intelligence - they are capable of theory of mind (that 'every participant knows modus ponens' is common knowledge). Typical tell-tale features of these puzzles include any puzzle in which each participant has a given piece of information (usually as common knowledge) about all other participants but not themselves. Once the simplest case of the induction puzzle is solved, the whole puzzle is solved subsequently. According to the principle of induction, a solution to the simplest case makes the solution of the next complicated case obvious. Ī puzzle's scenario always involves multiple players with the same reasoning capability, who go through the same reasoning steps. Induction puzzles are logic puzzles, which are examples of multi-agent reasoning, where the solution evolves along with the principle of induction.

A color of his own