000K utf8 1100 $c2008 1500 ger 2050 urn:nbn:de:hbz:464-20210204-154030-9 2051 10.17185/duepublico/73803 3000 Törner, Günter 4000 Kein Kinderspiel$dDas Fünfzehner-Schiebepuzzle [Törner, Günter] 4209 The puzzle is a popular topic for books on recreational mathematics, most of which use it as an example to illustrate the consequences of even and odd permutations. Most references to the 15-puzzle explain the impossibility of obtaining odd permutations, and many state the classical result that every even permutation is indeed possible, however complete proofs are rare. Indeed, the famous mathematicians Herstein and Kaplansky wrote in 1978 that no really easy proof seems to be known. Archer’s (1999) paper set out to rectify that deficiency. Central to this is the algebraic result that the group An with n = 15 is generated by the consecutive 3-cycles which has to be justified by suitable placements in the puzzle. We adopted Archer‘s idea, modified his enumeration and implemented a cyclic numbering of the cells where the beginning and the end of the path is the blank cell. Using this method we are able to prove the classical result rather quickly. Further, we generalize the structure of the puzzle and make clear how the result can be extended to suitable polygonal graphs. 4209 Über das Fünfzehner-Schiebepuzzle, das nun wahrlich mehr als ein Kinderspiel ist und viel mit handfester Mathematik zu tun hat, berichtet der Beitrag von Günter Törner. 4950 https://doi.org/10.17185/duepublico/73803$xR$3Volltext$534 4950 https://nbn-resolving.org/urn:nbn:de:hbz:464-20210204-154030-9$xR$3Volltext$534 4961 https://duepublico2.uni-due.de/receive/duepublico_mods_00073803 5051 510