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Mathematical Theory in Sudoku Puzzle
Guo Changyu 1 *,Wang Zhiqing 1,Guo Huimin 2
1.School of Mathematical Science,BeiJing Normal University
2.Department of Mathematical Science，Yangtze Normal University
*Correspondence author
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Funding: none
Opened online:12 March 2009
Accepted by: none
Citation: Guo Changyu ,Wang Zhiqing ,Guo Huimin .Mathematical Theory in Sudoku Puzzle[OL]. [12 March 2009] http://en.paper.edu.cn/en_releasepaper/content/30187
 
 
Solving a Sudoku is an NP problem. How to solve a Sudoku puzzle effectively is already a complex problem. To generate a validated Sudoku puzzle of desirable difficulty level is more complex. In this paper, an effective generating algorithm and a simple but efficient difficulty level are proposed. Firstly some common Logical Techniques and Brute Force Search Technique are introduced to solve a Sudoku puzzle. After that, demonstrate an generic generating algorithm, which uses a difficulty level based Analytic Hierarchy Process (AHP). This difficulty level is very reasonable by considering various factors. Some intelligent techniques and sub-processes are used to guarantee this generating algorithm efficient and correct. And the method to generate symmetrical Sudoku Puzzles is put forward just follow it. At last , some useful conclusion is obtained.
Keywords:Sudoku Puzzle;Logical Technique;Brute Force Search Technique;Metric of Difficulty Level;Generating Algorithm
 
 
 

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