Basic Strategy and Rules of Sudoku

April 31, 2007 by aaron

Sudoku is a logical symbol placement puzzle which was originally created in the United States in 1979 under the name of “Number Place”; however, it did not gain popularity until 1986 when it caught on in Japan. After 19 years Sudoku spread from Japan to Great Britain, and from there it continued to spread across the rest of the world and into every home though newspapers and the internet. Because of this I doubt anyone reading this has never seen a Sudoku puzzle, but just in case.

The name Sudoku itself is an abbreviation of a longer Japanese phrase that is literally translated to “single digit.” This refers to the fact that numbers in a Sudoku game can not be duplicated in the same row, column or region.

The premise of Sudoku is fairly simple: each grid is divided into 3 squares by 3 squares (for a total of 3 regions), and then each region is subdivided into 9 squares. An empty Sudoku grid resembles a tic-tac-toe board with each square divided into tic-tac-toe boards. The goal is then to fill in all the cells with the numbers 1-9 without repeating the same number in any 9×1 column, row or 3×3 region. Sounds easy right? Well this is where the difficulty, and fun, comes in: instead of a blank grid some of the numbers are already filled in. Although it would make sense that the more numbers already filled in the easier it would be as you may find this is not true. The main factors in determining the difficulty are the number composition and placements.

Solving a Sudoku requires logic and strategy. Guessing will cause even a simple puzzle to take hours. There are three main techniques used to solve a Sudoku puzzle: Crosshatching, Slicing and Dicing, and Penciling in.

Crosshatching involves finding the squares to hold numbers; that is, find all the squares that cannot hold a number to find the one square that can hold the number. This is done by starting with a single number in a single region and then find all the rows or columns that are part of that region that contain the number. If you can narrow it down to a single square then you can fill in that number and move on, otherwise if you narrow it down to two or three squares you can pencil in the number lightly and move on trying to find another number from the region.

Slicing and Dicing uses the Crosshatch method but unlike the previous Crosshatch method we will search through an entire row of regions and then try to fill the puzzle in by rows or columns rather than be region. Like the crosshatch method you will pick a single number and then try to place it into all three rows or columns using the crosshatch method above to narrow the possibilities down to single or small groups of squares.

Penciling in involves using the crosshatch method to find all the possible numbers that can fit into a square and then lightly penciling them in. After this process is repeated throughout the entire grid, a process of elimination must be used to narrow the options down to a single number for each box. For example, if you find in a single box that it can only hold a 4 and a box in the same region can hold either a 4 or a 9 then you will fill in a 4 into the first box and a 9 in the second. An important thing to remember when Penciling in is to be sure you have the candidate lists for each square completely filled in and that you update them as you go otherwise you risk introducing an error that will throw off the remainder of your puzzle.

Most puzzles will require a combination of the above techniques, and most puzzles can be solved by remembering a few simple rules. 1) If a square has only one Penciled in number then that number is usually correct. 2) If a Penciled in number is the only one in that region, row and column then it goes there no matter how many other Penciled in numbers there are. 3) If a penciled in number only appears in a single row or column in a region then that number will not be in the same row for any other region. 4) If a row, column or region has the same pair of numbers Penciled in then remove both numbers from all other Penciled in squares in the same region, row or column. 5) Similarly when three squares have the same Penciled in numbers or two of the same numbers then remove those numbers from all other Penciled in squares in the same region, row, or column. There are a few more rules but they are rarely used; thus, they are not presented here.

Well that is basically it, two more things to remember. Don’t ever guess until you absolutely have to, although it may seem to work for a while most guesses turn out wrong as you get to the last 3 or 4 numbers. The second thing to remember is that all real Sudoku puzzles are solvable, therefore if at first you don’t succeed try again. Well happy puzzling.

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