郑亚玲 博士

       无论您是在旅行还是正在医院康复，数独都是一款完美的老少皆宜的益智游戏！它有助于培养您的逻辑推理能力，耐心，专注解决问题的能力，和自信心。有朋友告诉我，制作数独太复杂了是不可能的。但其实只要你制作数独的一个基本理念―“和玩数独完全相反的方向”，制作数独  其实很简单。怎么个简单法呢？请看下面的一个小例子你就知道了。

       对于不熟悉数独游戏的朋友，什么是数独呢？数独是一种逻辑性的数字填充游戏，玩家须以数字填进每一格，而每行、每列和每个宫（即3x3的大格）有齐1至9所有数字。游戏设计者会提供一部分的数字，使谜题只有一个答案。

        一个经典数独要求这个数独有并且只有一个答案。并且，位于第x 行和第y列的方格（我们称为RxCy）和位于第10-x 行和第10-y列的方格要么同时被填充要么同时没有被填充。(1 ≤ x, y ≤ 9) 例如 R8C1和R2C9要么同时被填充要么同时没有被填充。

​       P1 是一个经典数独。解一下数独，是不是只有一个解(答案)？是不是位于位于第x 行和第y列的方格和位于第10-x 行和第10-y列的方格要么同时被填充要么同时没有被填充 (1≤ x, y≤ 9) ？     

经典数独P1​​

​思考一下:  如果我们去掉R8C1和R2C9的数字, 新的数独P2还是一个经典数独吗？答案是肯定的。为什么呢？

首先，我们去掉这两个方格的数字后，这个数独依然满足这个对称的要求：位于第x 行和第y列的方格和位于第10-x 行和第10-y列的方格要么同时被填充要么同时没有被填充 (1 ≤ x, y ≤ 9 ).
其次，如果我们去掉 R8C1 和R2C9的数字，这个新的数独还是只有一个解（答案）。

数独P2​

       R8C1 必须是 9。因为在第一列 ：数字9 不能在R1C1因为第一行已经有数字9；数字9不能在第二行因为第二行已经有数字9；数字9不能在第五行因为它所在的3x3宫格已经有数字9。根据排除法，第一列的空格中，只有R8C1可以是数字9。

       R2C9 必须是数字2。因为在第二行：数字2不能在R2C1或者R2C3因为第一宫已经有数字2了；数字2不能在R2C4因为第4列已经有数字2了。根据排除法，在第二行的空格中，只有R2C9可以是数字2。
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        根据推理，我们可以将数字9和数字2填到R8C1和R2C9。这个填写数字后的数独，正好是经典数独P1。因为P1有且只有一个解，所以我们可以说数独 P2有且只有一个解。

        思考：对于数独P2, 如果去掉 R4C6 和R6C4 的数字，新的数独P3还是一个经典数独吗？
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​        所有createclassicsudoku.com 的数独都是根据这个理念―“和玩数独完全相反的方向”设计的。来试一下今日数独？

今日数独 （难度：中等）

Dr. Yaling Zheng

Whether you are traveling, taking a break, or recovering in hospitals, designing a number puzzle game would be a perfect brain workout for you!  I have met friends who think making a Sudoku puzzle is almost an impossible mission.  However, if you know the basic principle to make a Sudoku puzzle – REVERSE WAY OF SOLVING A SUDOKU PUZZLE, making a Sudoku will become easy for you!  In this article, I will talk about one trick to make a classic Sudoku. 

Let us first take a look at the definition of a Sudoku. Sudoku is a puzzle in which missing numbers are to be filled into a 9 by 9 grid of squares which are subdivided into 3 by 3 boxes so that every row, every column, and every box contains the numbers 1 through 9. 

A "Classic" Sudoku is a symmetrical Sudoku that has one and ONLY one solution.  A symmetrical Sudoku is a Sudoku in which any two symmetrical squares (around the center square) are either both filled with numbers or both empty.  In the following we use RxCy to represent the square at the xth row and the yth column. R8C1 and R2C9 are symmetrical squares around the center square R5C5.   Here is an example of classic Sudoku. We call it Sudoku Puzzle P1.  

Sudoku Puzzle P1

​This Sudoku is a symmetrical Sudoku and it has one and only one solution (you can check that out by solving it).
Question:  If we remove numbers from R8C1 and R2C9, is it still a classic Sudoku? 
The answer is “Yes”. Why?
First, if we remove numbers from R8C1 and R2C9, it is still a symmetrical Sudoku.
Secondly, if we remove numbers from R8C1 and R2C9, the new Sudoku still has one and only one solution.  Why?

Sudoku puzzle P2​

R8C1 can be immediately inferred to be number 9 because in the first column
(1) Number 9 cannot be in the first row because the first row contains number 9 already;
(2) Number 9 cannot be in the second row because the second row contains number 9 already;
(3) Number 9 cannot be in fifth row because the fourth box contains number 9 already;
(4) number 9 can only be in the eighth row because it cannot be in the other empty squares in the first column.

R2C9 can be immediately inferred to be number 2 because in the second row
(1) Number 2 cannot be in the first or third column because the first box contains number 2 already;
(2) Number 2 cannot be in the fourth column because the fourth column contains number 2 already;
(3) number 2 can only be in the ninth column because it cannot be in the other empty squares in the second row.  

If we fill numbers 9 and 2 into R8C1 and R2C9 separately in Puzzle P2, it becomes puzzle P1.  Since puzzle P1 has one and only one solution, we can declare that puzzle P2 has one and only one solution too.

Think:  Remove numbers in R4C6 and R6C4 in puzzle P2, name the new puzzle P3. Is the puzzle P3 a classic Sudoku?

​All Sudoku puzzles made in www.createclassicsudoku.com are made using this basic principle – REVERSE WAY of solving a Sudoku puzzle.  How about try solving today’s medium Sudoku? 

Today’s Medium Sudoku