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 [1/0] and [0/1] 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.

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