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. Muddy children puzzle is the most frequently appearing induction puzzle in scientific literature on epistemic logic. In February 2020, 437 hits on Google scholar mentioned the muddy children puzzle. Muddy children puzzle is a variant of the well known wise men or cheating wives/husbands puzzles. Hat puzzles are induction puzzle variations that date back to as early as 1961. In many variations, hat puzzles are described in the context of prisoners. In other cases, hat puzzles are described in the context of wise men. 12 Countably Infinite-Hat Variant without Hearing.13 Countably Infinite Hat Problem with Hearing.The children consider it possible to have a muddy face. None of the children can determine the state of their own face themselves. But, every child knows the state of all other children's faces. A custodian tells the children that at least one of them has a muddy face. Hereafter, the custodian starts to count and after every stroke, every muddy child has an opportunity to step forward. Let's assume that there just 2 children: Alice and Bob.
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