Topspin: Oval-Track Puzzle, Taking Apart The Topspin One Tile At A Time

Abstract

A Topspin “Oval Track” puzzle consists of 20 numbered tiles in an oval-shaped track and a flipping window that reverses the 4 tiles in the window. The solvability of the puzzle uses permutations which are combinations where the order matters. A puzzle is considered solvable if each permutation in can be mapped to a spot in the original position through the three different moves the puzzle can make; a left shift, a right shift, and the flip which reverses the order of the 4 tiles in the window. I wanted to find out what math was involved in solving this puzzle. I had certain topics that I wanted to find out more information about, but the major question I had was “what is the fewest number of moves it takes to solve a puzzle”. Other topics I had were what made a puzzle unsolvable and what other types of puzzles use the same kind of math to solve them. To construct this research, I had read different scholarly articles that talked about the Topspin as well as physically looked at the puzzle and see how it works. I had found that there was no way to determine the fewest number of moves it takes to solve a puzzle since it’s impossible to decide what a “more scrambled” puzzle is compared to another. One scrambled puzzle might look completely different from another, and still have the same number of moves to solve it. In addition to this, I was also able to find that the Rubik’s Cube is solved like the Topspin.