The 3 rule in Sudoku refers to the three fundamental constraints that must be satisfied in every valid Sudoku puzzle. Understanding these rules is essential for anyone learning to solve Sudoku puzzles effectively.
The Three Fundamental Rules
Every Sudoku puzzle follows these three basic rules:
1. Row Rule
Each row must contain all numbers from 1 to 9 exactly once. No number can be repeated in the same row, and no number can be missing.
2. Column Rule
Each column must contain all numbers from 1 to 9 exactly once. Just like rows, no number can be repeated or missing in any column.
3. Box Rule
Each 3x3 box (also called a region or block) must contain all numbers from 1 to 9 exactly once. The puzzle is divided into nine such boxes, and each must follow this rule.
Why These Rules Matter
These three rules form the foundation of all Sudoku solving techniques and strategies. They create the logical constraints that make Sudoku puzzles solvable through deduction rather than guessing.
Logical Deduction
Because of these rules, you can always find the correct number for any cell by eliminating possibilities. If a number already appears in a row, column, or box, it cannot appear again in that same row, column, or box.
No Guessing Required
A properly constructed Sudoku puzzle can always be solved using pure logic. The three rules ensure that there's always a logical next step, eliminating the need for trial and error.
How to Apply the Rules
When solving Sudoku puzzles, constantly check these three constraints:
- Before placing a number, verify it doesn't already exist in the same row
- Check that the number doesn't appear in the same column
- Ensure the number isn't already present in the 3x3 box
Common Mistakes
Beginners often violate these rules by:
- Placing the same number twice in a row or column
- Forgetting to check the 3x3 box constraint
- Not systematically checking all three rules before placing a number
Advanced Applications
As you become more experienced, these rules form the basis for advanced solving techniques like:
- Hidden singles and naked singles
- Pointing pairs and claiming
- X-wing and swordfish techniques