An Open Pouring Problem

Authors Fabian Frei, Peter Rossmanith, David Wehner

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Author Details

Fabian Frei
  • Department of Computer Science, ETH Zürich, Switzerland
Peter Rossmanith
  • Department of Computer Science, RWTH Aachen, Germany
David Wehner
  • Department of Computer Science, ETH Zürich, Switzerland


We would like to thank the anonymous reviewers who carefully read this paper for their detailed feedback.

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Fabian Frei, Peter Rossmanith, and David Wehner. An Open Pouring Problem. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 14:1-14:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We analyze a little riddle that has challenged mathematicians for half a century. Imagine three clubs catering to people with some niche interest. Everyone willing to join a club has done so and nobody new will pick up this eccentric hobby for the foreseeable future, thus the mutually exclusive clubs compete for a common constituency. Members are highly invested in their chosen club; only a targeted campaign plus prolonged personal persuasion can convince them to consider switching. Even then, they will never be enticed into a bigger group as they naturally pride themselves in avoiding the mainstream. Therefore each club occasionally starts a campaign against a larger competitor and sends its own members out on a recommendation program. Each will win one person over; the small club can thus effectively double its own numbers at the larger one’s expense. Is there always a risk for one club to wind up with zero members, forcing it out of business? If so, how many campaign cycles will this take?

Subject Classification

ACM Subject Classification
  • Theory of computation → Theory and algorithms for application domains
  • Theory of computation → Representations of games and their complexity
  • Pitcher Pouring Problem
  • Water Jug Riddle
  • Water Bucket Problem
  • Vessel Puzzle
  • Complexity
  • Die Hard


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