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How to make a Sudoku?
Sudoku is a popular number puzzle originally from Japan. It is one of the most popular leisure activities for modern people of all ages. Correctly composed classic Sudoku can have only one solution, and the algorithm itself is not as complicated as it seems at first glance.
1. Composing free Sudoku easy is no less interesting than solving them. Moreover, there can be a lot of options for a classic puzzle. A classic Sudoku is meant as a large 9x9 square, divided into small 3x3 squares.
2. Write down nine lines of nine numbers so that each number appears only once in each row and in each column. The simplest option is to write numbers from 1 to 9 with a shift of three positions as you move down inside the "large" line and one position relative to the first line when moving to the next large line: 123 456 789456 789 123789 123 456234 567 891567 891 234891 234 567345 678 912678 912 345912 345 678.
3. Modify this initial combination in the following ways, combining with your imagination, and you will receive a new puzzle each time. First, rearrange the numbers in the form of "large" columns and rows, ie. elements of this table are 3 digits thick. Thus, Sudoku consists of three large rows and columns.
4. In order to get a new Sudoku online, it is enough to rearrange two large rows and two columns. For example, swap the first and third large lines: 345 678 912678 912 345912 345 678234 567 891567 891 234891 234 567123 456 789456 789 123789 123 456.
5. Swap the first and second large columns: 678 345 912912 678 345345 912 678567 234 891891 567 234234 891 567456 123 789789 456 123123 789 456.
6. Complicate the resulting Sudoku by rearranging the usual rows or columns. This can only be done inside the large columns of the table, because otherwise the Sudoku rule will be violated: in each of the 9 puzzle squares, each number occurs only 1 time.
7. Write in the first large line the second regular in place of the third and vice versa, in the second line replace the first regular with the third, and in the third large line - the first with the second: 678 345 912345 912 678912 678 345234 891 567891 567 234567 234 891789 456 123456 123 789 123 789 456.
8. The original version is no longer recognizable. Now swap the regular columns inside the larger ones in the same way. For example, in the first large column, replace the first column with the second, in the second, replace the first with the third, and in the third column, replace the second column with the third: 768 543 912435 219 678192 876 345324 198 567981 765 234657 432 891879 654 123546 321 789213 987 456.
9. You can do any manipulations, the main thing is to follow the rule: you can only completely rearrange both large and regular table elements. The most convenient way to compose Sudoku is in a computer program, for example, in Miscrosoft Excel. There you can check yourself after all the movements and replacements by calculating the sum of each row, column or small square. It should be 45. For this purpose, the program provides macros and formulas.
10. Now for the fun part: deleting extra digits. Depending on how complex you want to achieve, remove from the resulting table from 30 to 70% of the numbers.
Useful Resources:
What is Sudoku?
How to make a Sudoku?
Is it useful to solve Sudoku?
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