On infinite versions of the prisoner problem

TL;DR

This paper explores various infinite extensions of the classic 100 prisoner problem, focusing on the analysis of prisoner strategies, constraints, and conditions in an infinite setting, emphasizing analytical methods over combinatorics.

Contribution

It introduces and analyzes multiple infinite variants of the prisoner problem, providing new insights into strategies and constraints in infinite scenarios.

Findings

Different infinite versions are characterized and analyzed.

Analytical methods are used to derive solutions.

Insights into constraints and strategies in infinite settings.

Abstract

We investigate some versions of the famous 100 prisoner problem for the infinite case, where there are infinitely many prisoners and infinitely many boxes with labels. In this case, many questions can be asked about the admissible steps of the prisoners, the constraints they have to follow and also about the releasing conditions. We will present and analyze many versions and cases. In the infinite case, the solutions and methods require mainly analysis rather than combinatorics.