Make a Sudoku ― Two Tricks to Fill the Grid

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.

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).
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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.
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How did we achieve the result in Figure 1? Nine steps. Please see Fig 2.
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Fig 2: Nine Steps to fill a Grid.

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