How to Solve Sudoku Mathematically

Use a mathematical solution for your Sudoku puzzles.

Sudoku is actually solvable with a specific mathematical algorithm designed by mathematician, James Crook. The puzzle itself has been a staple in the puzzle sections of some newspapers and magazines the 1980s and has become a very popular type of recreational logic game. Many people have different ways to reach a solution for the puzzles, but the mathematical solution can help to simplify the process. Try using the mathematical solution next time you want to solve a Sudoku puzzle.

Things You'll Need

• Sudoku puzzle
• Extra paper
• Pencil

Instructions

1. Find all of the definite numbers in the puzzle. To do this, look over the puzzle and place numbers into empty squares where the number must be. For example, if you are looking at a set of three nine-by-nine grids in your puzzle and two grids already contain the number three, the final number three must be in the nine-by-nine grid that does not already have a three. And it must be in the only remaining row that does not contain a three. So, the placement of the three is definite and easily found.

2. Mark all of the remaining empty squares with your pencil. Mark the empty squares with all of the numbers that they could possibly contain. Write very small so that you can fit several possibilities in each square.

3. Find sets of numbers that must be used together to complete a row or grid. For example, you have a row that has three empty squares in it, the numbers already in the row are one. five. six. seven. eight and nine. You need numbers two, three and four to complete the puzzle. Check all of the rows, columns and grids to rule out the placement of each number in all but one of the three squares until you have placed all three.

4. Cross out the possibilities in each empty square, as you use those numbers in other squares, so that each number is used only once per row, per column and per nine-by-nine grid.

5. Continue finding sets of numbers and ruling out possibilities until the puzzle is solved.

References

• American Mathmetical Society.: A Pencil-and-Paper Algorithm for Solving Sudoku Puzzles
• Sudoku Essentials: A Snapshot History Of Sudoku Puzzles