The transformations of the fifteen puzzle form a groupoid (not a group, as not all moves can be composed).Jim Belk (2008) Puzzles, Groups, and Groupoids, The Everything SeminarThe 15-puzzle groupoid (1) , Never Ending BooksThe 15-puzzle groupoid (2) , Never Ending Books This groupoid acts on configurations.
tHe tRansfoRMatiONs OF the FifteeN puzZle FoRm a gROupOid (noT a Group, as nOt all moves can bE composEd).jiM Belk (2008) PUZzLes, gRouPs, And GrouPoids, the eveRYthinG seminaRTHe 15-pUzZLe grOUpoiD (1) , never enDiNg bookSThE 15-PUZzlE gRouPOId (2) , neVer enDinG bOoks this grOupoiD Acts On cONfigURAtiONs.