The Objective : The main goal of this project was to identify patterns in solved 9x9 Sudoku puzzles and then to use these patterns to create a new method to solve any standard 9x9 puzzle. This will provide Sudoku solvers a logical way to approach Sudoku puzzles that avoids long, intense calculations and guesswork.

**Methods/Materials**

The materials I used were empty 9x9 Sudoku grids, a large collection of Sudoku puzzles and their solutions (Super Colossal Book of Sudoku by William Shortz), and a pencil or pen.

The first step of my procedure was creating a letter system to map Sudoku puzzles on the 9x9 grid.

The letter systems consisted of the letters A through I, each letter consistently representing a number throughout each Sudoku grid.

I mapped many puzzle solutions and found basic patterns that were evident in the bands and stacks of each puzzle.

I then investigated how these patterns arise and came to the theory that certain transformations occur in a Sudoku puzzle. By examining these transformations on several Sudoku solutions, I discovered many more complex patterns.

I used these patterns to configure a method to solve a Sudoku puzzle. I tested this method on many Sudoku puzzles.

** Results**

I successfully found patterns in solved Sudoku puzzles. I devised a repeating three step method, using band and stack patterns, which can be used to logically solve any 9x9 Sudoku puzzle without guesswork.

** Conclusions/Discussion**

I concluded that there are consistent patterns that arise in any Sudoku puzzle. I fulfilled my goal and created a method to solve Sudoku puzzles that uses these patterns.

This project creates an easily understandable method to solve any 9x9 Sudoku puzzle.

**Science Fair Project done By **Prem M. Talwai

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