The oval track puzzle (also known as Top Spin) is a game consisting of 20 numbered tiles in an oval shaped track. Also, there is a fixed window (the swapping window) of 4 tiles that reverses the order of the tiles within the window, leaving the other 16 tiles fixed. The object of the puzzle is to reorder the tiles into counting order using the mechanisms of the puzzle. Our paper presents conditions for both solvability and non-solvability for the general oval track puzzle with n total tiles and k tiles in the swapping window. This paper answers questions left over from the work done by Eric Wilbur in his paper entitled Topspin: Solvability of Sliding Number Game from Volume 2, Issue 2 of the RHIT Mathematics Journal. Using his notation and terminology as a reference, we reproved some cases as well as proved open problems from his paper.

Author Bio

Sam Kaufmann is a sophomore at Carnegie Mellon University㤼㸲s School of Computer Science. He is currently pursuing a B.S. in Computer Science, and is also completing a double major in discrete mathematics and logic. In the spring of 2009, along with Andreas Kavountzis, he underwent research in the field of applied group theory. Under the guidance of professor Richard Statman, he and his partner used group theory to solve the oval track puzzle in the general case. He is currently looking forward to working at Kennedy Space Center this summer as part of an internship for NASA.

Andreas Kavountzis is a fourth year undergraduate at Carnegie Mellon University. He is pursuing a B.S. in Pure Mathematics. In 2009, Andreas did research in the field of applied group theory, solving the oval track puzzle in the general case. When not busy with the Carnegie Mellon Tartans Ice Hockey Team, Andreas can be found reading mathematics literature and doing research on sustainability, in hopes of designing and building a self-sustaining home. In his off time he enjoys skiing, rock climbing, backpacking and chainsaw work.