Editing Groupoid (section)

=== Puzzles ===

While puzzles such as the [[Rubik's Cube]] can be modeled using group theory (see [[Rubik's Cube group]]), certain puzzles are better modeled as groupoids.<ref>[https://www.crcpress.com/An-Introduction-to-Groups-Groupoids-and-Their-Representations/Ibort-Rodriguez/p/book/9781138035867 An Introduction to Groups, Groupoids and Their Representations: An Introduction]; Alberto Ibort, Miguel A. Rodriguez; CRC Press, 2019.</ref>

The transformations of the [[fifteen puzzle]] form a groupoid (not a group, as not all moves can be composed).<ref>Jim Belk (2008) [https://cornellmath.wordpress.com/2008/01/27/puzzles-groups-and-groupoids/ Puzzles, Groups, and Groupoids], The Everything Seminar</ref><ref>[http://www.neverendingbooks.org/the-15-puzzle-groupoid-1 The 15-puzzle groupoid (1)] {{Webarchive|url=https://web.archive.org/web/20151225220110/http://www.neverendingbooks.org/the-15-puzzle-groupoid-1 |date=2015-12-25 }}, Never Ending Books</ref><ref>[http://www.neverendingbooks.org/the-15-puzzle-groupoid-2 The 15-puzzle groupoid (2)] {{Webarchive|url=https://web.archive.org/web/20151225210035/http://www.neverendingbooks.org/the-15-puzzle-groupoid-2 |date=2015-12-25 }}, Never Ending Books</ref> This [[Group action (mathematics)#Variants and generalizations|groupoid acts]] on configurations.