License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FUN.2021.14
URN: urn:nbn:de:0030-drops-127751
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Frei, Fabian ; Rossmanith, Peter ; Wehner, David

An Open Pouring Problem

LIPIcs-FUN-2021-14.pdf (3 MB)


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?

BibTeX - Entry

  author =	{Fabian Frei and Peter Rossmanith and David Wehner},
  title =	{{An Open Pouring Problem}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{14:1--14:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Martin Farach-Colton and Giuseppe Prencipe and Ryuhei Uehara},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-127751},
  doi =		{10.4230/LIPIcs.FUN.2021.14},
  annote =	{Keywords: Pitcher Pouring Problem, Water Jug Riddle, Water Bucket Problem, Vessel Puzzle, Complexity, Die Hard}

Keywords: Pitcher Pouring Problem, Water Jug Riddle, Water Bucket Problem, Vessel Puzzle, Complexity, Die Hard
Collection: 10th International Conference on Fun with Algorithms (FUN 2021)
Issue Date: 2020
Date of publication: 16.09.2020

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