A Fourier approach to Levine's hat puzzle
Probability
2025-03-13 v1
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.
Keywords
Cite
@article{arxiv.2503.09042,
title = {A Fourier approach to Levine's hat puzzle},
author = {Steven Heilman and Omer Tamuz},
journal= {arXiv preprint arXiv:2503.09042},
year = {2025}
}