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Home | Fairy Tale | 8 Rules | Fu Xi | Math | San Chuan | Jia Zi | Classroom | Theater | Library | Plum | Henry's Corner | Super Dieluohan | Research Papers | About Dieluohan | Rainbow Web
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數 獨園 |
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articles. In short, they are: Standard: Row, Column, and Box 標準數魔﹕行,列,及九宮陣 Plum: Row, Column, and Plum 梅花樁數魔﹕行,列,及梅花樁陣 San: Row, Column, and San 三字數魔:行,列,及三字陣 Chuan: Row, Column, and Chuan 川字數魔﹕行,列,及川字陣 Finally, I also would like to thank for those frequent visitors (although not many), who like and support
this web site. Drjsguo, Nov 10, 2008 Like Darwin’s Evolution, a Standard Sudoku has been evolved into Plum, San, Chuan, and other Sudokus.
The common ground is that they all have three basic rules. The most common two rules are row and column constrains. I feel
strange not to include Standard Sudoku with nine colors, since all three other Sudokus I have published all have nine colors.
So beginning this week, I will publish the Standard Sudoku with nine colors instead of familiar just yellow and white. Sudokus
thus evolves into "colored domain". With this expression, the patterns speak for themselves. The rules become unified into
only three. They are "No single Row, No single Column, and No single Color can have repeated character". Isn’t that
simple is beautiful? 數魔已進化到九色的領域. 玩本欄數魔的規則,現統一到只有三條: 既 Drjsguo 2/2/2009 
LCM (Least Common Multiple) Sudoku Author: Henry Kwok , Nov 4, 2008 Rules of LCM Sudoku Like the standard sudoku, this sudoku variant has the basic rule: Every row, every column and every 3x3 box in the grids contains the digits 1 through 9. The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the
9x9 grid. At the bottom and right side of the 9x9 grid are numbers ( Altogether 18 Least Common Multiples of 9 columns and 9 rows of unknown digits are given as clues for solving the puzzle. As an example, the LCM of 3, 9, 6, 4, 2 and 1 is 36. In the puzzle, the LCM of the four unknown digits in the second column
beginning from the left of the 9x9 grid is 36, while the LCM of the four unknown digits in the seventh row beginning from
the top of the 9x9 grid is 120. After finding the values of all the unknown digits, the puzzle is solved by the usual sudoku technique and strategy.
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Eighteen Luohans 十八羅漢
Double Tenth Day 雙十節 "One Country, Two Systems" " The Eight Fundamental Rules of Sudoku Story Sudoku Spring Rain, Fall Rain, and Row Sudoku  Following discussions in Chinese Beidu Sudoku Forum (百度贴吧_数独吧), a reader suggested an odd looking matrix and asked
whether it is qualified as the two constraints for Spring Rain and Fall Rain that I have mentioned in my eight essential rules
of a generalized Sudoku. I found it is not only qualified for Spring Rain and Fall Rain constraints, it is also qualified
for a Column constraint, so it is really a legitimate General Sudoku contains a minimum of three of the eight rules. After
developed a puzzle using that matrix as a model, it surprises me that the resulting puzzle only needs five known clues (只給五個數就能解開)
in order to solve it logically. The minimum requirement of seventeen clues for logical solving a traditional Row, Column,
and Box Sudoku, or Sudokus with replacement of Boxes by Plums, Sans, or Chuans is no longer valid in this situation. The condition of Spring Rain and Fall Rain are very different from those of Box, Plum, San, Chuan, Column,
and Row. The former does not easily to be converted mathematically to the later without affecting, or in other word destroying
the other constraints at the same time and vice versa. Besides, there are many more constraints in this puzzle, which are
not obvious and need not to be included or implied as a hint. A combination of this and the difference in types may contribute
to the reason that we are having only five minimum clues here instead of seventeen. Drjsguo 6/7/2008 Riverside, California This is an interesting story for designing the Spring Rain and Fall Rain matrix for last week’s puzzle. I wanted
to make a puzzle of a Spring Rain and Fall Rain matrix with all the diagonals easily shown. It turns out to be not an easy
job. Finally I decided to make it a two-toned chess board matrix and published it. However, the matrix itself is not perfect
and I do not like it since it can not reflect all the typical Rain characters. Later, I tried to make a matrix that includes
two diagonal cross-lines on each cell to divide it into four triangles, with each set of opposite triangles filled with same
colors. However, this design makes no difference than an empty square box for each cell. I know I am back to square one and
need a designer’s help. I put this question on Beidu (百度) Sudoku
Forum for discussion. Quickly I got one suggestion from Skyhuner (藍天). It looks so lovely and enjoyable. I can not resist not publishing it. I think reader will agree. Here
is what he wrote: 这个构思很早之前就有了，但一直没有碰到需要的人或题目，还是大师对限制条件的研究比较深入，才能引出我这个图形。
2008-6-12
Sunlight Observation (觀日一得)  The Earth rotating around its axis daily and in a circular motion around the sun. Therefore we have regular day and night
and yearly cycle. In 1519 Ferdinand Magellan crew set for the first global voyage and completed in 1522 to prove that the
earth is a globe. In 1543 Nicolas Copernicus (Nicolaus Copernicus) published De Revolutionibus Orbium Coelestium
before his death and stated that earth is a globe shaped mass that moves circularly around the sun. The rotating axis of the earth and the axis of the circular rotation around the sun are not parallel. This produces four
seasons on earth. We also know that there are two circular imaginary lines that the sunlight will never cross and defined
the longest and shortest daylight for each hemisphere. They are Tropic of Caner ( I have never paid much attention at the direction of the sunlight. Not many people aware that the sunlight does not always
move from due east to the top of the head (perpendicular) and down due west. The position of the sunlight depends on the season
and where the observer is standing. In another word, it depends on the relative position of the observer, earth, and the sun.
I moved to a house located due north few months ago in Riverside, California. There is a yard all around the house. I told
my wife that the northern part of the front yard closest to the house will never get the sunlight because we are located north
of the Tropic of Cancer, and I was worried that the small plants in front of the house may not grow well. Now the summer set
in and the sunlight gradually moves to the north. Surprisingly I noticed that the sun shines on the northern part of the house
in the morning and also in the evening. It seems that I have gotten the idea all-wrong from my childhood experience and the
plants are all happy after all. Further more I noticed that the sunlight actually moves like an arc from the northeast to
the south and then back to the northwest again. The earth is a globe. At noontime sunlight comes from the south that proves I do live on a place north of the Tropic of
Cancer. The morning and evening sunlight appears on the north side is just an angular phenomenon of light shining on a tilted
spinning globe. The move of the sunlight proves nothing but that the earth is a globe and spinning in a different axis from
the circular annual rotation. As an observer on the spinning earth, naturally sees the sun moving around in a circle. Therefore, we should be seeing
sunlight moving like an arc whether it is a full circle or just half a circle. One can imagine how the sunlight moves at North
Pole ( In accompany to this topic, I have included a Bagua Drjsguo 7/26/2008 Beijing Olympic Game Celebration 慶祝北京奧運會  In order to synchronize with the opening ceremony of the Beijing (北京)
Olympic Game today; I have provided a Dieluohan puzzle, which includes many 9X9 Plum Sudokus. This puzzle is very easy to
solve if you understand the Dieluohan concept of Sudokus (see "Super Dieluohan" above and "Research
Papers" below). Drjsguo 8/8/08 at 8 p.m., California
Dieluohan, the Superimposition of Multiple 9X9 Sudokus 疊羅漢,多重九九魔術方塊的重疊現象 Dieluohan, a New Frontier for Multiple Sudoku Overlaps 疊羅漢,多重重疊魔術方塊的新大陸 Dieluohan Big Bang Theorem 疊羅漢乾坤一爆定律 The Magic Properties
of Holy Turtle Magic Squares 洛書神龜魔方的特性 San, Chuan, and Super Constrained Sudokus 三,川,及超多限制的數魔 Contact Us 通訊
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