History of the Muddy Children Puzzle
The Muddy Children Puzzle, a classic about knowledge and ignorance that inspired epistemic logic, has unclear origins. This paper traces its evolution through 200 years of logical and literary publications, discusses its many variations, and presents a novel hat puzzle involving self-reference.
[2606.13703] History of the Muddy Children Puzzle
[Submitted on 8 Jun 2026]
Title:History of the Muddy Children Puzzle
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Abstract:The Muddy Children Puzzle is a puzzle about knowledge and ignorance that has been inspiring for the development of epistemic logic. Who came up with it first? This is unclear. We trace the origin of the Muddy Children Puzzle through logical and literary publications over the past two centuries. The puzzle inspired a numerous variations such as involving numbers or coloured hats. We also present a novel hats puzzle involving self-reference.
Subjects:
Artificial Intelligence (cs.AI); General Literature (cs.GL); Logic in Computer Science (cs.LO)
Cite as: arXiv:2606.13703 [cs.AI]
(or arXiv:2606.13703v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2606.13703
arXiv-issued DOI via DataCite
Submission history
From: Hans van Ditmarsch [view email] [v1] Mon, 8 Jun 2026 07:45:05 UTC (2,701 KB)
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