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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.