Depth and Symmetry in Conway�s M13 Puzzle

• Autores: Jacob A. Siehler
• Localización: Mathematics magazine, ISSN 0025-570X, Vol. 84, Nº. 4, 2011, págs. 243-256
• Idioma: inglés
• DOI: 10.4169/math.mag.84.4.243
• Texto completo no disponible (Saber más ...)
• Resumen

  • We analyze a sliding tile puzzle (due to J. H. Conway) which gives a presentation of the Mathieu group M12, one of the sporadic simple groups. We use the symmetries of a finite projective plane to classify automorphisms of M12 which preserve the depth of puzzle positions, and give an algorithm for solving the puzzle by hand.