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DOI: 10.4230/LIPIcs.FUN.2016.22
URN: urn:nbn:de:0030-drops-58661
URL: http://drops.dagstuhl.de/opus/volltexte/2016/5866/
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Langerman, Stefan ; Uno, Yushi

Threes!, Fives, 1024!, and 2048 are Hard

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Abstract

We analyze the computational complexity of the popular computer games Threes!, 1024!, 2048 and many of their variants. For most known versions expanded to an m*n board, we show that it is NP-hard to decide whether a given starting position can be played to reach a specific (constant) tile value.

BibTeX - Entry

@InProceedings{langerman_et_al:LIPIcs:2016:5866,
  author =	{Stefan Langerman and Yushi Uno},
  title =	{{Threes!, Fives, 1024!, and 2048 are Hard}},
  booktitle =	{8th International Conference on Fun with Algorithms (FUN 2016)},
  pages =	{22:1--22:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-005-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{49},
  editor =	{Erik D. Demaine and Fabrizio Grandoni},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5866},
  URN =		{urn:nbn:de:0030-drops-58661},
  doi =		{10.4230/LIPIcs.FUN.2016.22},
  annote =	{Keywords: algorithmic combinatorial game theory}
}

Keywords: algorithmic combinatorial game theory
Seminar: 8th International Conference on Fun with Algorithms (FUN 2016)
Issue Date: 2016
Date of publication: 25.05.2016


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