A Fourier approach to Levine's hat puzzle

2025/03/12 by Steven Heilman, Omer Tamuz, Heilman, Steven +1 · 1 citation
Engineering · Mathematics · #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Probability (math.PR) #Sports Dynamics and Biomechanics

paper · pdf · doi:10.48550/arxiv.2503.09042

openalex publication_date 2025/03/12 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

We consider Lionel Levine's notorious hat puzzle with two players. Each player has a stack of hats on their head, and each hat is chosen independently to be either black or white. After observing only the other player's hats, players simultaneously choose one of their own hats. The players win if both chosen hats are black. In this note, we observe an upper bound on the probability of success, using Chang's lemma, a result in Boolean harmonic analysis.

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