A note on the problem of prisoners and hats

TL;DR

This paper formalizes the prisoners and hats puzzle, analyzing three variants to determine the existence of winning strategies through a comprehensive framework.

Contribution

It introduces a formal framework for the problem and fully characterizes three variants regarding the existence of winning strategies.

Findings

Complete characterization of three problem variants.

Identification of conditions for winning strategies.

Framework applicable to multiple problem variants.

Abstract

We study the famous mathematical puzzle of prisoners and hats. We introduce a framework in which various variants of the problem can be formalized. We examine three particular versions of the problem (each one in fact a class of problems) and completely characterize them as to (non)existence of winning strategies.