The urinal problem

Authors:
Evangelos Kranakis;Danny Krizanc
Affiliations:
School of Computer Science, Carleton University, Ottawa, Ontario, Canada;Department of Mathematics and Computer Science, Wesleyan University, Middletown, CT
Venue:
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
Year:
2010

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Abstract

A man walks into a men's room and observes n empty urinals. Which urinal should he pick so as to maximize his chances of maintaining privacy, i.e., minimize the chance that someone will occupy a urinal beside him? In this paper, we attempt to answer this question under a variety of models for standard men's room behavior. Our results suggest that for the most part one should probably choose the urinal furthest from the door (with some interesting exceptions). We also suggest a number of variations on the problem that lead to many open problems.