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arXiv · 2511.22392

Muddy Waters

Hans van Ditmarsch
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Abstract

In the 2013 Advent calender of the Berlin Mathematics Research Center MATH+, Gerhard Woeginger presents a novel hat problem with an uncommon initial announcement. Although the information given is insufficient for the hat bearers to learn their colour, they are informed that the colours have been chosen so that they can learn their colour. We formalize this announcement in public announcement logic and in an extension of public announcement logic with fixpoints.

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Hans van Ditmarsch. 2025-11-27. Muddy Waters. https://doi.org/10.4204/eptcs.437.33

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