The Eight Fundamental Rules of Sudoku
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
|
|
|
|
|
|
|
|
The Eight Fundamental Rules of Sudoku |
|
||
|
|
|
|
||
|
|
|
|
|
|
|
|||||
|
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
|
|
|||
|
|||||
|
||||||||||||||||||||||||||
|
|
The Eight Fundamental Rules of Sudoku Since I published the concept of Plum-positions that could replace the 3X3-Boxes as one of the restrictions for standard
Sudoku last year, I have found two more new restrictions that could also replace them. They were named San and Chuan. It was
at this time; Sudoku has changed its face. The definition of a Sudoku should be modified to that as long as there are at least
three restrictions applied to the whole 9X9 grid, it is a Sudoku. For example, if Row restriction changed to San restriction
and Box restriction changed to Chuan restriction, then it is still a Sudoku even there is no limitation on every row that
requires nine digits appear only once. I have, for a long time, recognized that Diagonals could also play in a similar way of standalone property in Sudoku. In
order to have nine diagonals in a 9X9 grid, the diagonal should not be restricted in only one straight line, so I adopted
the concept of pseudo diagonals. A line that can be broken into two pieces and still qualified as a diagonal. However, this
is not a good terminology since I altered the definition of what is defined as a "Diagonal", a line from one corner to an
opposite corner of a rectangle or square. After a disappointed tiny rainstorm in California this past weekend, an imagination come to my mind that why not call them
the "Rain" property? If you look out through the window in a raining day, you will see the rain picture exactly behaved like
this so called pseudo diagonal property. Now I can officially adding two new rules in Sudoku. They are Easterly rain and Westerly
Rain properties. Easterly rain usually come in the Spring when warm and humid wind blow from the Pacific Ocean into China,
and Westerly rain starts in the fall when bitter cold wind blows from Siberia and precipitates the moist local air, thus I
have them named Spring Rain and Fall Rain. These two properties are diagonal to each other just like Rows and Columns. After the two rain properties joint the basic rules in a nine by nine Sudoku, I now think the Sudoku property is complete.
The following graphs each represent one of the eight properties in a Sudoku. Each graph is just one of the nine individual
restriction that should have nine different digits and each digit appears only once. 不久前我把數獨的規則,用圖形做了個整理,以便讀者能夠迅速理解,但做的並不完整.這次我再從新製做了一組圖形.一共包括了八組,既行,列,3X3小九宮,梅花樁陣,三字形陣,川字形陣,還有 不久前我把数独的规则,用图形做了个整理,以便读者能够迅速理解,但做的并不完整.这次我再从新制做了一组图形.一共包括了八组,既行,列,3X3小九宫,梅花桩阵,三字形阵,川字形阵,还有
Row Column Box Plum San Chuan Spring Rain Fall Rain
Any 9X9 grid that has any combination of the above three rules will be considered as a legitimate Sudoku here. This week I present a brand new Rains Sudoku that contains four rules: 1) The Row 2) The Spring Rain 3) The Fall Rain 4) The 3X3 Box Each rule has nine individual constrains of nine-different-digits. I wish readers could enjoy this strange Sudoku. 最後我再附上一個例題.這個例題包含有行,小九宮,春雨陣,和秋雨陣四組九數限制.希望大家喜歡. 最后我再附上一个例题.这个例题包含有行,小九宫,春雨阵,和秋雨阵四组九数限制.希望大家喜欢. Drjsguo 12-14-2007  |
|
|
||||||||||||||||||||||
|
||||||||||||||||||||||||||
|
|
|
|
|
|
|
|
|
|
|
||||||||||||||||
|
|
|
|
|
|
|
|
|
|
|
||||||||||||||||
|
|
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
|
|
|
|
|
|
|
|
|
||||||||||||||||
|
|
|
|
|
|
|
|
|
|
|
||||||||||||||||
|
|
|
|
|
|
|
|
|
|
|
||||||||||||||||
|
||||||||||||||||||||||||||
|
|
|
|
|
||||||||||||||||||||||
|
||||||||||||||||||||||||||
|
||||||||||||||||||||||||||
