Making Sudokus: Yes, you can!
Why don’t we see if we can bring the D.I.Y. spirit to Sudokus? How difficult do you think it is to make Sudokus? The answer: not very. Let me refer you to a classic in this field,” A Sudoku Puzzle-Setter’s Guide to Create Classic Sudoku”, by Yalin Zheng. Yalin picked Sudokus to be the focus of part of her doctoral work in computer science at the University of Nebraska. She makes a very important point in her preface, which I paraphrase here: “Technology is not essential for making classic Sudokus”.
There are four steps to making a Sudoku puzzle. They are: 1) create a filled Sudoku, the Starter Sudoku, 2) shuffle the row blocks and column blocks and individual rows and columns of the Starter Sudoku to create a new filled Sudoku, 3) remove numbers from the filled Sudoku to form a Sudoku puzzle, and 4) check that the Sudoku puzzle can be solved and has a unique solution. We can do step 4 the long and manual way, but you can just as easily plug the numbers in an online Sudoku solver and get that done. Also, we will skip Step 1 for the next book in the series, so as not to overwhelm you with information.
Step 1: This step is not essential, since we can just use any filled Sudoku (e.g., the already filled Sudoku in the next figure). After you get better at steps 2 – 4, you will want to learn step 1, so you can disassemble a Sudoku into its most basic pieces and put it back together.
Step 2: As explained above, we don’t need to do step 1. We can shuffle (or rearrange) the row blocks of a filled Sudoku (obtained from the solution-page of a Sudoku book, for example) to make another filled Sudoku. We can arrange the row blocks 1, 2 and 3 in 6 different ways, as shown in the Figure. After we have arranged the row blocks in any of the 6 ways we want, we can shuffle the column blocks in any of six ways: [ ABC; ACB; BAC; BCA; CAB; CBA], as shown in the last Figure. Wait! there’s more. We can shuffle each of the three rows inside a row block in 6 ways, just like we shuffled the row blocks. Similarly, we can shuffle each of the columns inside a column block in 6 ways, just like we shuffled the column blocks. The number of ways we can shuffle this initial filled starter Sudoku is extremely large. We get to choose how we shuffle or rearrange the starter Sudoku shown in the Figure. Well, that completes step 2. Please note that all the steps mentioned in this step are optional. We can choose to do none, a few, or many of the steps mentioned here. The rationale for going through step 2 is that we can take an existing filled Sudoku (e.g., from any of the solution pages in a Sudoku puzzle book), and rearrange that to get an entirely new filled Sudoku. The number of different filled Sudokus we can generate from an existing one is so large that we will have more than enough filled Sudokus for the rest of our lives.
Step 3: This step is quite simple. We will remove the numbers from cells RnCm and R[10-n] C[10-m]. For example, if n=2 and m=3, we will remove R2C3 and R8C7 at the same time. If we choose n=5 and m=5, we remove only one cell, the cell R5C5. We choose the values of n and m, and we go ahead and remove those two numbers. We can repeat this step with different combinations of n and m.
Step 4: After each application of step 3, we will do step 4 and check to see that we can solve the Sudoku. Please note that the Sudoku will NOT have a unique solution if we have removed more than 63 numbers from the filled Sudoku. In fact, there are cases when we can NOT get a unique solution even if we remove just 4 numbers from a filled Sudoku. If you join our mailing list at www.gamebrainon.com, we will send you examples of Sudokus with only 4 missing cells that do not have unique solutions. One way to do step 4 fast is to use an online Sudoku solver. There are many free online Sudoku solvers (we will have one soon at www.gamebrainon.com), and you can just plug in the numbers and check if the Sudoku puzzle we made is solvable. We stop removing numbers if: a) the Sudoku we have is as hard as we want it to be, or b) we are not getting a unique solution when we plug the numbers in the online Sudoku solver. That’s it, then. Here is the Sudoku puzzle and the finished Sudoku. All done in a matter of minutes.