An Open Pouring Problem
DROPS (Schloss Dagstuhl – Leibniz Center for Informatics)
Abstract
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?
Authors 3
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Affiliation as printed
Department of Computer Science, ETH Zürich, Switzerland
ETH Zurich, Zurich, Switzerland
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Affiliation as printed
Department of Computer Science, RWTH Aachen, Germany
RWTH Aachen University, Aachen, Germany
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Affiliation as printed
Department of Computer Science, ETH Zürich, Switzerland
ETH Zurich, Zurich, Switzerland
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