Topspin: Solvability of Sliding Number Games
Eric Wilbur · Rose-Hulman Scholar (Rose–Hulman Institute of Technology) · 2001
Abstract: The puzzle Topspin is a sliding number game consisting of an oval track containing a random arrangement of numbered discs, and a small turnstile within the track. A game is of the form [t, n] if it has n total discs, and a turnstile with t discs. Using concepts of group theory, the solvability, or ordering, of the discs is determined or conjectured for all values of t and n. Furthermore, if a game is not solvable, its attainable subgroup is determined or conjectured for all values of t and n. Several notations are used in the proofs of these theorems to help the reader follow visuallyas well as mathematically. Solvabilityis difficult to prove, but in the puzzle [t, n] where t and n are both even, we reveal the complex series of flips and shifts needed to prove the solvabilityof the game. Finally, using the results of the [t, n] games, the solvabilityis determined or conjectured for multiple turnstile games. 1