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Information

Project Types : Descriptive
Grade Division : 10 - 12
Team Size : 5
Subject Area :Mathematics

Software Tools:


LaTeX
TeXworks
LaTeX2HTML version 1.7.1
Mathematica 7.0
Mathematica 8.0
Mathematica 9.01
Adobe Photoshop CS6
Adobe Illustrator CS6
Adobe Dreamweaver CS6
Eclipse Kepler Service Release 2

Hardware Tools:


MacBook Air with Mac OSX 10.8.5
MacBook Air with Mac OSX 10.9.2
iMac with Mac OSX 10.9.2
MacBook Pro with Mac OSX 10.9.2
MacBook Pro with Mac OSX 10.9.0

Source of idea :


In this project we present our research on Mathematical games. We use the word "mathematical games" in a wide sense of the word. We have two topics here.

1. Chocolate games

In this project we present a generalization of the result published in "Journal of Information Processing " (in Japanese, 2012). In this journal the former member of our team proved a theorem for k =3, but in this project we prove the same type of theorem for k=4m+3 for a non-negative integer m.
The method to prove is very different from the method used in the paper, and we hope that this method will be a standard method for proving this kind of games.
Therefore our result is better than the result of a published paper!
These games are variants of well known game of nim. An English mathematician A.C.Robin made a rectangular chocolate game, and we changed the shape of the chocolate, and discovered interesting formulas for the winning and losing states.
We were the first people who studied chocolate problems of the shape that is not a rectangle. We presented some formulas in Canada Wide Virtual Science Fair 2010, 2011, 2012 and 2013
We have published a paper on the chocolate games in "Journal of Mathematics, Statistics and Operations Research, 2012" , a paper on the chocolate games in "Journal of Information Processing "in Japanese (2012) and a paper on Chocolate Games in Mathematica Journal,2013.

2. Numeron

This is a simple version of the game of Mastermind, and this "Numeron" is very popular in Japan. There is a TV program for this game, and many people who studied this game say that a players can reach a correct answer within 6 trial. There are some theories of Numeron on the web, but usually so-called theory is only a sketch of the theory.
The authors have tried to find a complete theory of Numeron on the web by calculating all the possible outcome using computer algebra system Mathematica.


Awards Received:

Our group was awarded 1st prizes in the Canada Wide Virtual Science Fair 2012 and 2013. The previous members of this group were awarded 1st prizes in the Canada Wide Virtual Science Fair 2007, 2008, 2009. 2010, 2011. Some members of our group were finalists of Japan Science & Engineering Challenge 2012 and 2013.
Some members of our group were semi-finalists of Hang Lung Mathematics Awards (2013).
Our research group was selected as an excellent science club, and awarded a grant of 6000 U.S. dollars from Japanese Ministry of Education in 2010, 2011 and 2012.
Our group is going to be awarded the same grant of 6000 U.S. dollars in 2013, 2014 and 2015.
Our teacher Dr.Miyadera received "excellent teacher award" from Japanese Ministry of Education for his activity with this research group, and he was awarded "Wolfram Innovator Award 2012" by the recommendation of the great scientist S.Wolfram himself, and this shows the high standard of our research.


Copyright:

All the computer graphics are made by the authors using Mathematica and Adobe Illustrator. The photos in "Our School Page" were taken by the authors.


Thanks:

We would like to express thanks to our teacher Dr. Ryohei Miyadera for helping and guiding us in our research. We also would like to thank Mr. Masanori Fukui for teaching us computer programming.
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