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玩数独,设计数独​

Play Sudoku, Design Sudoku

Make a Sudoku ― Two Tricks to Fill the Grid

1/6/2018

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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! 

​One of the steps of making a Sudoku is to fill every square of an empty grid. Please see Fig 1.


Fig 1: Task to fill every empty square.

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Did it take you long to achieve this task?

If you can quickly fill every empty square satisfying that every row, column, and box has nine different numbers 1 to 9, please drop me an email telling me how you did it at create.classic.sudoku@gmail.com; if not, would you like to know a shortcut to achieve it?

The shortcut uses two techniques: Group Filling and Circular Shift.
Group filling – instead of fill one square a time, you fill the one row (or column or box). You fill the row (or column or box) with nine different numbers 1 to 9.
Circular shift – every time you fill the row (or column or box) by a circular shift of the sequence in the previous row (or column or box).
​
With group filling, you fill the grid much faster. With the circular shift, you tactfully avoid conflict of the same number in a row or column or box.
​
How did we achieve the result in Figure 1? Nine steps. Please see Fig 2.

​

Fig 2: Nine Steps to fill a Grid.

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Step 1:  Fill nine different numbers into the first row. Let us fill the first row with the sequence 692453781.

Step 2:  Perform a circular shift the sequence in the first row by THREE slots. We can fill it with 453781692. We do a permutation of 781 in the second box to 817. And a permutation of 692 to 269 in the third box.  In summary, we fill the second row with 453817269.

Step 3: Perform a circular shift the sequence in the second row by THREE slots. We can fill it with 817269453. We do a permutation of 817 in the first box to 781.  In summary, we fill the third row with 781269453.

Step 4: Perform a circular shift of the sequence in the third row by SIX slots, which is 453781269. But 453 in the first box has a conflict, so we do a permutation to 534. We do a permutation of 269 in the sixth box to 692. In summary, we fill the fourth row with 53478692.

Step 5:  Perform a circular shift of the sequence in the fourth row by THREE slots, which is 7816923534. But 453 in the first box has a conflict, so we do a permutation to 345. We do a permutation of 269 in the sixth box to 692. In summary, we fill the fifth row with 178692345.

Step 6: Perform a circular shift of the sequence in the fifth row by THREE slots, which is 69234 5178. But 692 in the fourth box has a conflict, so we do a permutation to 269. We do a permutation of 345 in the fifth box to 534, and a permutation of 178 in the sixth box to 817. In summary, we fill the sixth row with 269534817.

Step 7: Perform a circular shift of the sequence in the sixth row by THREE slots, which is 534817269. But 5 3 4 in the seventh box has a conflict, so we do a permutation to 345. We do a permutation of 9 6 2 in the eighth box to 926, and a permutation of 269 to 926. In summary, we fill the seventh row with 345178926.

Step 8: Perform a circular shift of the sequence in the seventh row by THREE slots, which is 178926345. But 178 in the first box has a conflict, so we do a permutation to 817. We do a permutation of 345 in the ninth box to 534. In summary, we fill the eighth row with 817926534.

Step 9: Perform a circular shift of the sequence in the eighth row by THREE slots, which is 926 534817. But 534 in the eighth box has a conflict, so we do a permutation to 345. We do a permutation of 817 in the ninth box to 178. In summary, we fill the ninth row with 926345178.

Want to know more about making a Sudoku? Please refer my book CREATE CLASSIC SUDOKU selling on Amazon.com. Here is 

Today’s Medium Sudoku

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