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?
@InProceedings{frei_et_al:LIPIcs.FUN.2021.14, author = {Frei, Fabian and Rossmanith, Peter and Wehner, David}, 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 = {Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.14}, 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} }
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