Rules

Basic Rules of Sudoku

1. Grid Structure:

• The standard Sudoku grid consists of 9 rows and 9 columns, forming 81 cells in total.
• These cells are divided into 9 smaller 3x3 subgrids, also known as "regions," "blocks," or "boxes."

2. Objective:

• Fill every cell in the grid so that each row, each column, and each 3x3 subgrid contains the numbers 1 to 9, with no repetition.

3. Starting Clues:

• Every puzzle starts with some numbers already placed in the grid. These are known as "givens" or "clues."
• The difficulty of the puzzle depends on the number and arrangement of these initial clues.

Sudoku Solving Techniques

Mastering Sudoku involves applying a combination of logical techniques. Here are the most important strategies, from basic to advanced:

Basic Techniques

1. Scanning:

• Cross-Hatching: Scan rows and columns to identify where a number can or cannot be placed within a subgrid.
• Counting: Check which numbers are missing from each row, column, or block, and determine possible placements.

2. Pencil Marks (Candidate Lists):

• Write down all possible numbers for empty cells. As you gather more information, eliminate candidates until only one remains.

3. Naked Singles:

• If a cell has only one possible candidate, that number must be placed there.

4. Hidden Singles:

• If a number can only fit into one position within a row, column, or block, place it there.

Intermediate Techniques

1. Naked Pairs/Triples:

• If two or three cells in a unit contain the same two or three candidates, those numbers can be eliminated from other cells in that unit.

2. Hidden Pairs/Triples:

• If two or three numbers can only go in two or three cells within a unit, all other candidates in those cells can be eliminated.

3. Pointing Pairs/Triples:

• If a candidate appears in only one row or column within a block, it can be eliminated from that row or column in other blocks.

4. Box-Line Reduction:

• If candidates in a row or column are restricted to one block, they can be eliminated from the rest of that block.

Advanced Techniques

1. X-Wing:

• If a candidate appears in exactly two cells in two rows, and those cells align in the same columns, the candidate can be eliminated from the other cells in those columns.

2. Swordfish:

• An extension of the X-Wing technique involving three rows and three columns.

3. XY-Wing:

• Involves three cells where a specific arrangement of candidates allows for eliminating a candidate from other cells.

4. Coloring:

• Use colors to track the possibilities of a candidate being true or false, leading to eliminations.

5. Chains (AIC - Alternating Inference Chains):

• Use logical chains to connect candidates and determine eliminations.

6. Unique Rectangle:

• Identifies a configuration where avoiding multiple solutions can lead to eliminations.

7. ALS (Almost Locked Sets):

• Analyze cells where multiple candidates form patterns that can be leveraged for eliminations.

Tips for Effective Solving

• Start with the easiest techniques: Begin by scanning for naked and hidden singles.
• Use pencil marks wisely: Don't overload the grid with candidates. Eliminate options as you gain new insights.
• Work systematically: Focus on one number or one unit (row, column, block) at a time.
• Look for patterns: Identifying common techniques like pairs, pointing pairs, and X-Wings can unlock tough puzzles.
• Stay patient and logical: Avoid guessing. Every step in Sudoku can be deduced logically.

We hope these rules and techniques enhance your Sudoku-solving journey! Keep practicing, and you'll find yourself mastering even the toughest puzzles in no time.