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Dieluohan Papers 疊羅漢論文


























1.  Dieluohan, The Superimposition of Multiple 9X9 Sudokus, J. S. Guo, 10/9/2006
 

Abstract

Degrees of multiple superimpositions of many 9X9 Sudokus forming a tight ring structure is discussed. The degree of overall superimposition is the maximum number of the Sudokus that are superimposed on any one of the 3X3 square blocks in the ring. A new 9X9 Sudoku named Rainbow web Sudoku is introduced.

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2.  Dieluohan, a New Frontier for Multiple Sudoku Overlaps, J. S. Guo, 11/12/2006

Abstract

The three classic Sudoku rules are modified slightly in this paper for Dieluohan study. By eliminating the numbering limitation rule on each 3X3 grid, and replacing it with a numbering limitation on each cell position for all its’ 3X3 grids, we are able to construct a highly overlapped multiple layer Sudoku with 81 layers of superimposition. In this paper, Dieluohan degree and the Dieluohan pattern have been defined. There is no size limit for building very large Dieluohan due to its replicate nature.

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3. Dieluohan Big Bang Theorem, J. S. Guo, 11/24/2006.

Abstract

Dieluohan can replicate in all directions indefinitely like a Big Bang. This is a universal phenomenon.

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Magic Square Papers 洛書神龜魔方論文

 

1.  The Magic Properties of Holy Turtle Magic Squares, J. S. Guo, 6/24/2007

 

Abstract

 

Holy Turtle Magic Square is defined according to the first known Magic Square.  Holy Turtle Magic Squares contain an additional magic property: “any two numbers with center symmetry are complimentary to each other; their sum is equal to two times the center digit.”

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2.  San, Chuan, and Super Constrained Sudokus, J. S. Guo, 6/24/2007

 

Abstract

 

Properties of San and Chuan in a Sudoku are explained.  The discovery of Jia Zi Sudoku and Fu Xi Sudoku are two milestones for super constrained Sudokus.  Jia Zi Sudoku contains a full range of Box, Plum, San, and Chuan properties.  Fu Xi Sudoku is derived from 9X9 Magic Square that is from the Holy Turtle Magic Square class.  Fu Xi Sudoku contains only San and Chuan properties, but has far more 9-digit constraints.

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