cs.AI · 2606.13703 Copy arXiv ID · Jun 8, 2026 Save History of the Muddy Children Puzzle Authors: Hans van Ditmarsch
Organizations: CNRS, France · IIT Kanpur, India
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.
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Adi Gabay, Gabriel Stanovsky, Liat Peterfreund
School of Computer Science and Engineering The Hebrew University of Jerusalem
Epistemic reasoning requires agents to infer the state of the world from partial observations and information about other agents' knowledge. Prior work evaluating LLMs on epistemic puzzles often frames failures as memorization rather than reasoning. We argue that this dichotomy is too coarse for newer models: memorization is a limiting case of pattern-based reasoning, where a model matches a task to a familiar template and applies the corresponding solution. We introduce a two-dimensional benchmark over DEL-style puzzles, separating narrative familiarity from inference complexity, allowing us to distinguish pattern-based from epistemic reasoning. We find that models are substantially more robust to surface form changes than prior work suggested, yet consistently struggle in asymmetric settings where familiar patterns no longer apply and success requires tracking fragmented epistemic states.