How to solve Sudoku puzzles.

Sudoku Puzzle Grid

Sudoku puzzle.	Sudoku puzzle solved.

Sudoku Puzzles are constucted on a 9x9 grid. The grid is further seperated into nine 3x3 regions. The puzzle is complete when each row, column, and region contains the numbers one through nine.

The Sudoku puzzle grid has 81 cells. A cell that contains a number that cannot be changed is often referred to as a hint cell or static cell. There can be any number of hint cells, but the minimum required will allow for only a single solution to the Sudoku puzzle.

To solve the Sudoku puzzle, you must fill in all the non-hint cells so that all the columns, rows, and regions contain all the numbers 1 through 9.

Column - Row - Region Scan

The best approach to solving Sudoku puzzles is the scanning method. The scanning method attempts to exclude candidate numbers from a target cell by accounting for all the numbers in use in the target cell's column, row, and region.

In the examples above, the cell with the blue background is in the first row, eigth column, and third region. To scan possible values for this cell:

• Scan the target cell's column for numbers already in use
  • Top to bottom - 5, 2, 9, and 8
• Scan the target cell's row for numbers already in use
  • Left to right - 6, 7, 8, 2, 3, and 4
• Scan the target cell's region for numbers already in use
  • Across and down - 3, 4, 8, 5, 6, 2, and 7
• Determine which of the numbers 1 through 9 have not yet been used
  • In use: 2, 3, 4, 5, 6, 7, 8, and 9
  • Available: 1

The scan for our target cell indicates that only the number one can be entered into that cell. In fact, because there are only hint cells in its column, row, and region we can confidently say that the number one is the correct number for that cell in the solution.

Wikipedia is excellent source of information on Sudoku.
http://en.wikipedia.org/wiki/Sudoku