Abstract
The main purpose of this project is to explore the nine chain ringed game and to solve it through various ways including induction and recursive methods. Associating this game with the binary codes and where the two numbers represent whether the respective ring is on the 1st row-the ring being on the sword or the 2nd row-the ring being off the sword. First, we explored the problem with two mathematical models to find the existing patterns. Then, by the usage of induction, we found the general form of the quickest number of moves needed depending on the number of rings without the repetition of any situation. Hence we called this path a beautiful solution. Similarly, by the usage of induction, we determined the smallest number of steps needed to get from one situation to another situation. Meanwhile, we also formulated nonrepeating sequences to represent which ring will be moved at which step of the beautiful solution’s procedure. Finally, we concluded the project by aggregating the data into a generating function.
Highlights
1.1 Research MotivesNine rings is an ancient Chinese game (Wu, 2003; Zhang, W. & Rasmussen, P. 2010)
We found a nature of the binary function (Press, et al, 1992) in the game as we explored solutions steps, which we combined with a computer software to create a new and easy operation model (Hsu, 1969, 2010; Rosiene, J.A. & Rosiene, C.P., 2014 )
Using Theorem 1, Theorem 2 and inverse deduction method, we explore the number of steps to solve the nine rings: First, let an be the total number of T and L operations needed to change the whole upper state matrix into the first extreme state matrix in the full path state change operation Pn of the 2 n order array graph
Summary
1.1 Research MotivesNine rings is an ancient Chinese game (Wu, 2003; Zhang, W. & Rasmussen, P. 2010). We found a nature of the binary function (Press, et al, 1992) in the game as we explored solutions steps, which we combined with a computer software to create a new and easy operation model We will use the binary to explore the nine rings operation, the connection between nine rings and Gray code (Gardner, 1986; Kuao, 2014; Weisstein, 2011), to create a new method for nine rings operation model (Matrixlab-examples.com, 2009), and to extend it into a three-state game. Through the 2xn order array graph mathematical model, we investigate the perfect solution of the nine rings, and further explore the general solutions for n rings
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
