Resumen de Depth and Symmetry in Conway�s M13 Puzzle

Jacob A. Siehler

• 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.