# Sudoku Rules

The Sudoku grid consists of 81 cells, arranged in a 9×9 format. Each cell can either be empty or filled with a number from 1 to 9. The grid is divided into nine 3×3 subgrids, each containing nine cells. The rows are labeled from A to I, and the columns are numbered from 1 to 9.

## Rules of Sudoku

To play Sudoku, you need to follow a set of rules:

**Each Row Contains Unique Numbers**: In every row, there should be no repetition of numbers from 1 to 9. Each number must appear only once in each row.**Each Column Contains Unique Numbers**: Similar to the rows, each column must contain a unique set of numbers from 1 to 9. No repetition of numbers is allowed within a column.**Each Subgrid Contains Unique Numbers**: Within each 3×3 subgrid, there should be no repetition of numbers from 1 to 9. Each number must appear only once in each subgrid.**Numbers Fill Empty Cells**: Fill the empty cells with numbers from 1 to 9, following the row, column, and subgrid rules. The initial puzzle will have some pre-filled numbers to provide hints for solving.

## How to Play Sudoku

Playing Sudoku is a straightforward process once you understand the rules. Here’s a step-by-step guide on how to play Sudoku:

**Examine the Initial Puzzle**: Start by examining the given numbers in the grid. These pre-filled numbers provide hints for solving the puzzle.**Identify the Empty Cells**: Locate the empty cells in the grid. These are the cells you need to fill with numbers.**Start with the Number 1**: Begin by looking for cells where the number 1 can be placed based on the row, column, and subgrid rules. Fill in the number 1 in any appropriate empty cell.**Continue with Numbers 2 to 9**: Move on to the number 2 and repeat the process. Look for cells where the number 2 can be placed without violating the rules. Fill in the number 2 in a suitable empty cell.**Logic and Deduction**: As you progress, use logic and deduction to determine the placement of each number. Analyze the existing numbers in rows, columns, and subgrids to deduce the correct placement of the remaining numbers.**Trial and Error (if necessary)**: If you reach a point where no logical deduction can be made, resort to trial and error. Make an educated guess for an empty cell and continue solving. If contradictions arise, backtrack and try a different number in that cell.**Complete the Grid**: Continue filling in numbers based on logical deductions and trial and error until the entire grid is complete.

## The Logic Behind Sudoku

Sudoku is a game of logic and deduction. While it may appear complex at first, each number placement follows a logical pattern. The key to solving Sudoku lies in analyzing the existing numbers and applying the rules to determine the possibilities for each empty cell. By employing logical reasoning, you can systematically fill in the grid and arrive at the correct solution.

## Strategies for Solving Sudoku

To solve Sudoku puzzles more efficiently, consider the following strategies:

1. **Scan the Grid**: Start by scanning the grid and identifying any numbers that can be easily placed based on the row, column, and subgrid rules.

2. **Elimination Technique**: Use the elimination technique to narrow down the possibilities for each empty cell. Analyze the existing numbers in the row, column, and subgrid to eliminate numbers that violate the rules.

3. **Candidate Lists**: Maintain candidate lists for each empty cell. Keep track of the potential numbers that can be placed in each cell based on the row, column, and subgrid constraints.

4. **Hidden Singles**: Look for hidden singles, which are numbers that can only fit in one particular cell within a row, column, or subgrid. Identifying hidden singles can provide clues for filling in other numbers.

5. **Crosshatching**: Crosshatching involves scanning rows and columns to identify potential candidates and eliminate possibilities. This technique helps narrow down the options for each empty cell.

6. **Advanced Techniques**: Once you’ve mastered the basic strategies, you can explore advanced techniques such as X-Wing, Swordfish, and XY-Wing. These methods involve identifying patterns and making deductions based on them.

### Common Mistakes to Avoid

When playing Sudoku, be mindful of the following common mistakes:

**Repetition of Numbers**: Ensure that each row, column, and subgrid contains unique numbers from 1 to 9. Double-check your placements to avoid repetition.**Incomplete Scanning**: Thoroughly scan the grid, rows, columns, and subgrids to identify potential placements and deductions. Incomplete scanning can lead to errors.**Inconsistent Logic**: Maintain consistency in your logical deductions. Inconsistent logic can lead to contradictions and incorrect solutions.**Guesswork Without Deduction**: Avoid making random guesses without proper deduction. Guessing without logical reasoning can lead to incorrect placements and complicate the puzzle.**Lack of Patience**: Sudoku requires patience. Rushing through the puzzle can lead to oversight and mistakes. Take your time and approach each step systematically.