AI-Sudoku-Solver

A Comprehensive Beginner's Guide Of Suduku

Whether you're a complete beginner or wanting to up your game, this guide is for you.

Understanding Sudoku: What is Sudoku?

Sudoku is a globally popular puzzle game. The objective is to fill a 9x9 grid so that each column, each row, and each of the nine 3x3 boxes (also called blocks or regions) contain all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which typically has a unique solution.

The Rules of Sudoku

The rules for Sudoku are simple according to Sudoku.com:

  • A 9×9 square must be filled in with numbers from 1-9
  • No repeated numbers in each row, column or 3x3 grid
  • Each 3x3 grid is marked by bold lines, and no number in these small boxes can be repeated
  • The puzzle starts with several numbers already filled in, and your job is to fill in the rest

Basic Sudoku Strategies

1. Learn the Sudoku Grid.

Understanding the structure of the Sudoku grid is a crucial first step. It is divided into three types of grids: rows, columns, and boxes, and each of these must contain 9 numerically-identified cells. Consider each 3x3 cell as a box, each horizontal line of cells as a row, and each vertical line of cells as a column. On this game board, each "box", "row", and "column" must contain all numbers from 1 to 9 without any repetition.

2. Don't Simply Guess Solutions.

Guessing should be considered as a last resort for solving Sudoku, rather than a first choice. This is because Sudoku is a game of logic, and guessing does not help you cultivate problem-solving skills. Whether you're dealing with beginner or advanced Sudoku, there's usually one or more methods that can help you definitively determine which number can be filled into which cell.

In the following example of a Sudoku game, we can try applying this strategy:

-------------------------
| 5 3 . | . . 7 | . . . |
| 6 . . | 1 9 5 | . . . |
| . 9 8 | . . . | . 6 . |
-------------------------
| 8 . . | . 6 . | . . 3 |
| 4 . . | 8 . 3 | . . 1 |
| 7 . . | . 2 . | . . 6 |
-------------------------
| . 6 . | . . . | 2 8 . |
| . . . | 4 1 9 | . . 5 |
| . . . | . . 8 | . 7 9 |
-------------------------

To avoid guessing, we can adopt the following strategies to solve this Sudoku:

  • Cell's Candidates Method: First, traverse each unfilled cell and find out all possible candidate values for this cell. For example, the upper right cell in the upper left area, its candidate numbers are 1, 2, 4. We can use this information to see if we can confirm the value of this cell in other locations.
  • Elimination Method: If a number has already appeared in the current row, column, or 3x3 area, then this number cannot be placed again in the other cells of that area. We can use this method to eliminate impossible candidates.

Using these techniques, we can start filling in the numbers one by one, without any guessing at all. This is the charm of Sudoku, finding the correct answer for each cell through pure logic reasoning.

3. Find Easy Opportunities First.

The "Find Easy Opportunities First" strategy is a basic method of solving Sudoku puzzles, which involves filling in those numbers that can be determined without guessing first. Those numbers that have already appeared in the same row, same column, or the same 9-square grid do not need to reappear. We first find those numbers that have only one possible position, thereby obtaining clues to solve the Sudoku puzzle.

Now, let's explain in detail the "Find Easy Opportunities First" strategy based on the above Sudoku game example:

-------------------------
| 5 3 . | . . 7 | . . . |
| 6 . . | 1 9 5 | . . . |
| . 9 8 | . . . | . 6 . |
-------------------------
| 8 . . | . 6 . | . . 3 |
| 4 . . | 8 . 3 | . . 1 |
| 7 . . | . 2 . | . . 6 |
-------------------------
| . 6 . | . . . | 2 8 . |
| . . . | 4 1 9 | . . 5 |
| . . . | . . 8 | . 7 9 |
------------------------
  1. Observe the numbers that have a unique possible location. For example, in the third square (the middle 9-square grid), the number 2 can only be placed in the fifth row and sixth column.
  2. Use the filled-in numbers to deduce. After filling in 2, the sixth square (the 9-square grid in the top right corner) has only the first row and the ninth column left where 2 cannot be placed, so fill in the number 2 here as well.
  3. Continue to look for confirmable numbers. It can be observed that at this time, the fifth row can only fill in the number 7 in the fourth column.

In summary, this strategy is to find out the numbers that are easy to fill in, start from these numbers, and gradually narrow the possible number range of other vacancies, making the problem of solving Sudoku simpler. Of course, for complex Sudoku games, we can also assist with some other strategies, such as the Pencil i and X-Wing strategies.

Advanced Sudoku Techniques

Once you have a good grasp of the basic strategies, you can start learning advanced techniques, like the 6 advanced ones explained in SudokuOnline.io. This often involves looking at larger portions of the grid at once to calculate possibilities.

Useful Resources for Sudoku Players

There are numerous free resources available online to play Sudoku and learn strategies. Some of these include Sudoku.com, Kristanix, and MasteringSudoku.

Conclusion

By understanding the rules and embracing the process of logical deduction, Sudoku can be a fun and addicting game that players of all ages can enjoy. With this guide, you are now prepared to start playing Sudoku and improving your game.