Classic Sudoku and One Trick to Make It

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