Abstract
A puzzle called “M 13” J. H. Conway has described recently is explained. We report an implementation of the puzzle in the programming language Java. The program allows the human user to “play M 13” interactively (and to cheat by solving it automatically). The program is an example on how to bring to life a nice piece of discrete mathematics. In this sense it presents not only a didactical way of seeing “mathematics at work”, but also displays the stabilizer chain method developed by C. Sims to solve group theoretic puzzles, the most famous of which being Rubik's cube.
Similar content being viewed by others
References
T. Beth, D. Jungnickel, and H. Lenz, Design Theory, 2nd Edition, Cambridge University Press (1997), to appear.
G. Butler. Fundamental Algorithms for Permutation Groups, Lect. Notes in Comp. Sci., Springer-Verlag, New York 559 (1991).
J.H. Conway, M 13, Surveys in Combinatorics (1997). London Math. Soc. Lect. Note Series, 241 (1997).
S. Egner and M. Püschel, Solving Puzzles related to Permutation Groups, ISSAC Rostock (1998).
M13 — Messier's catalogue, June (today known as NGC 6205), Organizzazione Ricerche e Studi di Astronomia, Palermo (1764). http: //www.ourway.net/orsapa1/catalogo/m13.htm.
M. Schönert and others, GAP — Groups, Algorithms and Programming, v3.4.3, Lehrstuhl D für Mathematik, RWTH Aachen (1995). http: //www — math.math.rwth — aachen.de/gap/.
R.R. Wilson, ATLAS of Finite Group representations Birmingham (1997). http: //for.mat.bham.ac.uk/atlas/.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Egner, S., Beth, T. How to Play M 13?. Designs, Codes and Cryptography 16, 243–247 (1999). https://doi.org/10.1023/A:1008331827156
Issue Date:
DOI: https://doi.org/10.1023/A:1008331827156