IDEAS home Printed from https://ideas.repec.org/a/ibn/jmrjnl/v9y2017i6p24.html
   My bibliography  Save this article

Gray Code in the Solution of the Nine Rings Chinese Game

Author

Listed:
  • Erick Ceasar Huang
  • Sharon Sherry Huang
  • Cheng-Hua Tsai

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.

Suggested Citation

  • Erick Ceasar Huang & Sharon Sherry Huang & Cheng-Hua Tsai, 2017. "Gray Code in the Solution of the Nine Rings Chinese Game," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(6), pages 24-54, December.
    • Handle: RePEc:ibn:jmrjnl:v:9:y:2017:i:6:p:24
    as

    Download full text from publisher

    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/view/70489/38856
    Download Restriction: no
    File URL: http://www.ccsenet.org/journal/index.php/jmr/article/view/70489
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    nine rings; Gray Code; binary code; matrix; recursion; function; sequence;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ibn:jmrjnl:v:9:y:2017:i:6:p:24. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Canadian Center of Science and Education (email available below). General contact details of provider: https://edirc.repec.org/data/cepflch.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.