Sixty 9-digit Rules Jia Zi

After published San and Chuan Sudoku last week, I managed to make a very complicated highly restrained Sudoku. It is a wonderful feeling of discovering this sixty 9-digit restrained Sudoku. This Sudoku contains the following restrictions:

1. Every row must uses 9 different digits.

2. Every column must uses 9 different digits.

3. Every 3X3 box must uses 9 different digits.

4. Every Plum position must uses 9 different digits.

5. Every San position must uses 9 different digits.

6. Every Chuan position must uses 9 different digits.

7. Every diagonal starting from the upper corners of a 3X3 box must uses 9 different digits.

The restriction rules from 1 to 6, each has nine different arrangements. The diagonal has six arrangements. Total is sixty, thus I give it the name Jia Zi (甲子數魔), which means sixty years in Chinese. I was thinking to name it Fu Xi (伏羲) Sudoku or Magic (神奇) Sudoku for such a complicated sixty degreed 9-digits rules. But I think Jia Zi is more appropriate, because I do not know if this highly restrained record of "sixty" has already been broken or will be broken in the future.

Beside the familiar two primary nine-digit straight-line diagonals, there are four additional secondary nine-digit diagonals, which are not easily recognized. These secondary diagonal lines are discontinued at one of the two vertical edges of Sudoku, but continued at the other end of the vertical edge. If we use Dieluohan (疊羅漢) expansion technique it is easy to see them as genuine nine-digit straight diagonal lines.

My first logic puzzle of this kind contains nine known digits. I was surprised it did not go down further. However, consider it only has sixty restrictions; the Sudoku still got plenty of freedoms to fill the numbers. I have already found numerous combinations of Jia Zi Sudokus.

繼上個星期發表三川數魔以來,很興奮又發現了一個具有六十個九數限制的數魔.

這個數魔具有下列七個特點:

一. 每一行必須用全部九個數.

二. 每一列必須用全部九個數.

三. 每一個三乘三九宮必須有全部九個數.

四. 每一組梅花樁位置必須有全部九個數.

五. 每一組三字的位置必須有全部九個數.

六. 每一組川字的位置必須有全部九個數.

七. 每一條由最上層三乘三九宮上起畫的九數對角線必須有全部九個數.

頭六個限制都各有九種.第七個限制只有六種.其中除我們常見的九數大對角線外,還有四個.這四個是不連續的大對角線.如果您用疊羅漢定律將它向四方擴大,就能看到它們的直線性.

因為一共有六十條九數限制,故我把它起名叫”甲子數魔”.

本週的邏輯題一共只給九個已知數.原本希望可以給得更少.其實八十一格中只有六十個限制,理當還有無限變化的.

继上个星期发表三川数魔以来,很兴奋又发现了一个具有六十个九数限制的数魔.

这个数魔具有下列七个特点:

一. 每一行必须用全部九个数.

二. 每一列必须用全部九个数.

三. 每一个三乘三九宫必须有全部九个数.

四. 每一组梅花桩位置必须有全部九个数.

五. 每一组三字的位置必须有全部九个数.

六. 每一组川字的位置必须有全部九个数.

七. 每一条由最上层三乘三九宫上起画的九数对角线必须有全部九个数.

头六个限制都各有九种.第七个限制只有六种.其中除我们常见的九数大对角线外,还有四个.这四个是不连续的大对角线.如果您用叠罗汉定律将它向四方扩大,就能看到它们的直线性.

因为一共有六十条九数限制,故我把它起名叫”甲子数魔”.

本周的逻辑题一共只给九个已知数.原本希望可以给得更少.其实八十一格中只有六十个限制,理当还有无限变化的.

Drjsguo 5-20-2007

Please refer to other web pages of “The Sudoku Club” about Plum position, San position, Chuan position, and Dieluohan theory.

有關梅花樁位置,三字的位置,川字的位置,及疊羅漢定律請參考本”數獨園”網站相關的資料.

有关梅花桩位置,三字的位置,川字的位置,及叠罗汉定律请参考本”数独园”网站相关的资料.

This week a logic Jia Zi Sudoku puzzle with eight given digits was presented. In accompany to this difficult puzzle, a very interesting logic puzzle with equal difficulty is presented for reader to solve.

This is one of my favorite logic puzzles. I encountered this puzzle when I was serving in the Chinese Marine Corps (中國海軍陸戰隊, zhong guo hai jun lu zhan dui) between 1968 and 1969 on an island offshore of Taiwan. A second lieutenant (少尉 shao wei) asked me this Twelve balls puzzle (十二球問題, shi er qiu wen ti) during an outing on the way back to our base in an evening. When I showed him my answer two hours later, he was surprised that my answer was different from his. Later I found out this puzzle actually having numerous solutions.

This Twelve balls puzzle is excellent for logic exercise. It is not as easy as you may think. A correct answer is not very simple but a little complicated. A successful solution should cover all possible cases.

Here is the puzzle:

Twelve green-balls all look alike. They all have same weight, except one is slightly different with no information on its weight. Given a simple double-pan balance (秤, cheng) with no weights, can you find the odd ball with only three weighing (秤三次, cheng san ci) and be able to tell whether it is lighter or heavier?

十二個一模一樣的綠色球.只有一個重量稍微不同.現給您一個簡單且沒有砝碼的雙盤天平秤.您能只秤三次就將它找出,並知道是輕些還是重些嗎?(本題答案需包含所有的可能性.解有許多個.難度倒是和本週只給八個已知數的"甲子數魔"邏輯題相當.)

十二个一模一样的绿色球.只有一个重量稍微不同.现给您一个简单且没有砝码的双盘天平秤.您能只秤三次就将它找出,并知道是轻些还是重些吗?(本题答案需包含所有的可能性.解有许多个.难度倒是和本周只给八个已知数的"甲子数魔"逻辑题相当.)

Drjsguo 5-25-2007

This is another one of my favorite puzzles. A coworker sent me this quiz via an e-mail few years ago. At first I wasn’t paying much attention so I ignored it. Shortly, that e-mail had generated many responds for more clarification and discussion floating around the cyberspace. I then realized this puzzle is not an ordinary one.

When I started working on it, amazingly the puzzle turned alive. Imagine all digits jump around if you change them fast enough for searching the correct answer. It is a fantastic feeling. It is recommended that you solve it on a computer to experience the digits jumping. This puzzle has two solutions.

Fill in the blanks:

"In this sentence the number of occurrences of 0 is __, of 1 is __, of 2 is__, of 3 is __, of 4 is __, of 5 is __, of 6 is __, of 7 is __, of 8 is __, of 9 is __."

Each blank is to be filled with a numeral of one or more digits.

在底下的空格裡請填入個位數或多位數數字:

“在這句話裡頭一共有__ 個 0, __ 個 1, __ 個 2, __ 個 3, __ 個 4, __ 個 5, __ 個 6, __ 個 7, __ 個 8, __ 個 9.”

本題應有兩個答案.

在底下的空格里请填入个位数或多位数数字:

“在这句话里头一共有__ 个 0, __ 个 1, __ 个 2, __ 个 3, __ 个 4, __ 个 5, __ 个 6, __ 个 7, __ 个 8, __ 个 9.”

本题应有两个答案.

Drjsguo 6-1-07


				*Sixty 9-digit Rules Jia Zi*



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		Jia Zi Sudoku 甲子數魔 After published San and Chuan Sudoku last week, I managed to make a very complicated highly restrained Sudoku. It is a wonderful feeling of discovering this sixty 9-digit restrained Sudoku. This Sudoku contains the following restrictions: 1. Every row must uses 9 different digits. 2. Every column must uses 9 different digits. 3. Every 3X3 box must uses 9 different digits. 4. Every Plum position must uses 9 different digits. 5. Every San position must uses 9 different digits. 6. Every Chuan position must uses 9 different digits. 7. Every diagonal starting from the upper corners of a 3X3 box must uses 9 different digits. The restriction rules from 1 to 6, each has nine different arrangements. The diagonal has six arrangements. Total is sixty, thus I give it the name Jia Zi (甲子數魔), which means sixty years in Chinese. I was thinking to name it Fu Xi (伏羲) Sudoku or Magic (神奇) Sudoku for such a complicated sixty degreed 9-digits rules. But I think Jia Zi is more appropriate, because I do not know if this highly restrained record of "sixty" has already been broken or will be broken in the future. Beside the familiar two primary nine-digit straight-line diagonals, there are four additional secondary nine-digit diagonals, which are not easily recognized. These secondary diagonal lines are discontinued at one of the two vertical edges of Sudoku, but continued at the other end of the vertical edge. If we use Dieluohan (疊羅漢) expansion technique it is easy to see them as genuine nine-digit straight diagonal lines. My first logic puzzle of this kind contains nine known digits. I was surprised it did not go down further. However, consider it only has sixty restrictions; the Sudoku still got plenty of freedoms to fill the numbers. I have already found numerous combinations of Jia Zi Sudokus. 繼上個星期發表三川數魔以來,很興奮又發現了一個具有六十個九數限制的數魔. 這個數魔具有下列七個特點: 一. 每一行必須用全部九個數. 二. 每一列必須用全部九個數. 三. 每一個三乘三九宮必須有全部九個數. 四. 每一組梅花樁位置必須有全部九個數. 五. 每一組三字的位置必須有全部九個數. 六. 每一組川字的位置必須有全部九個數. 七. 每一條由最上層三乘三九宮上起畫的九數對角線必須有全部九個數. 頭六個限制都各有九種.第七個限制只有六種.其中除我們常見的九數大對角線外,還有四個.這四個是不連續的大對角線.如果您用疊羅漢定律將它向四方擴大,就能看到它們的直線性. 因為一共有六十條九數限制,故我把它起名叫”甲子數魔”. 本週的邏輯題一共只給九個已知數.原本希望可以給得更少.其實八十一格中只有六十個限制,理當還有無限變化的. 继上个星期发表三川数魔以来,很兴奋又发现了一个具有六十个九数限制的数魔. 这个数魔具有下列七个特点: 一. 每一行必须用全部九个数. 二. 每一列必须用全部九个数. 三. 每一个三乘三九宫必须有全部九个数. 四. 每一组梅花桩位置必须有全部九个数. 五. 每一组三字的位置必须有全部九个数. 六. 每一组川字的位置必须有全部九个数. 七. 每一条由最上层三乘三九宫上起画的九数对角线必须有全部九个数. 头六个限制都各有九种.第七个限制只有六种.其中除我们常见的九数大对角线外,还有四个.这四个是不连续的大对角线.如果您用叠罗汉定律将它向四方扩大,就能看到它们的直线性. 因为一共有六十条九数限制,故我把它起名叫”甲子数魔”. 本周的逻辑题一共只给九个已知数.原本希望可以给得更少.其实八十一格中只有六十个限制,理当还有无限变化的. Drjsguo 5-20-2007 Please refer to other web pages of “The Sudoku Club” about Plum position, San position, Chuan position, and Dieluohan theory. 有關梅花樁位置,三字的位置,川字的位置,及疊羅漢定律請參考本”數獨園”網站相關的資料. 有关梅花桩位置,三字的位置,川字的位置,及叠罗汉定律请参考本”数独园”网站相关的资料. Twelve Balls Puzzle 十二球問題 This week a logic Jia Zi Sudoku puzzle with eight given digits was presented. In accompany to this difficult puzzle, a very interesting logic puzzle with equal difficulty is presented for reader to solve. This is one of my favorite logic puzzles. I encountered this puzzle when I was serving in the Chinese Marine Corps (中國海軍陸戰隊, zhong guo hai jun lu zhan dui) between 1968 and 1969 on an island offshore of Taiwan. A second lieutenant (少尉 shao wei) asked me this Twelve balls puzzle (十二球問題, shi er qiu wen ti) during an outing on the way back to our base in an evening. When I showed him my answer two hours later, he was surprised that my answer was different from his. Later I found out this puzzle actually having numerous solutions. This Twelve balls puzzle is excellent for logic exercise. It is not as easy as you may think. A correct answer is not very simple but a little complicated. A successful solution should cover all possible cases. Here is the puzzle: Twelve green-balls all look alike. They all have same weight, except one is slightly different with no information on its weight. Given a simple double-pan balance (秤, cheng) with no weights, can you find the odd ball with only three weighing (秤三次, cheng san ci) and be able to tell whether it is lighter or heavier? 十二個一模一樣的綠色球.只有一個重量稍微不同.現給您一個簡單且沒有砝碼的雙盤天平秤.您能只秤三次就將它找出,並知道是輕些還是重些嗎?(本題答案需包含所有的可能性.解有許多個.難度倒是和本週只給八個已知數的"甲子數魔"邏輯題相當.) 十二个一模一样的绿色球.只有一个重量稍微不同.现给您一个简单且没有砝码的双盘天平秤.您能只秤三次就将它找出,并知道是轻些还是重些吗?(本题答案需包含所有的可能性.解有许多个.难度倒是和本周只给八个已知数的"甲子数魔"逻辑题相当.) Drjsguo 5-25-2007 Counting Puzzle 填數遊戲 This is another one of my favorite puzzles. A coworker sent me this quiz via an e-mail few years ago. At first I wasn’t paying much attention so I ignored it. Shortly, that e-mail had generated many responds for more clarification and discussion floating around the cyberspace. I then realized this puzzle is not an ordinary one. When I started working on it, amazingly the puzzle turned alive. Imagine all digits jump around if you change them fast enough for searching the correct answer. It is a fantastic feeling. It is recommended that you solve it on a computer to experience the digits jumping. This puzzle has two solutions. Fill in the blanks: "In this sentence the number of occurrences of 0 is __, of 1 is __, of 2 is__, of 3 is __, of 4 is __, of 5 is __, of 6 is __, of 7 is __, of 8 is __, of 9 is __." Each blank is to be filled with a numeral of one or more digits. 在底下的空格裡請填入個位數或多位數數字: “在這句話裡頭一共有__ 個 0, __ 個 1, __ 個 2, __ 個 3, __ 個 4, __ 個 5, __ 個 6, __ 個 7, __ 個 8, __ 個 9.” 本題應有兩個答案. 在底下的空格里请填入个位数或多位数数字: “在这句话里头一共有__ 个 0, __ 个 1, __ 个 2, __ 个 3, __ 个 4, __ 个 5, __ 个 6, __ 个 7, __ 个 8, __ 个 9.” 本题应有两个答案. Drjsguo 6-1-07