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.
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.
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.
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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