The rules for playing the game are very simple:

• Sudoku is played over a 9×9 grid, divided into 3×3 subgrids.
• The play begins with some given numerals from 1-9 that are preplaced in a few of the grid cells.
• Only the digits 1 through 9 are used.
• A number can only appear once in each row.
• A number can only appear once in each column.
• A number can only appear once in each 3×3 subgrid.

Sudoku has what is known as a “game tree”. The game tree of this puzzle game is quite large and, when there is only one solution to be found, makes solving it fast an unfeasible plan. There are, however, tips that you can use to solve Sudoku as fast as possible.

Perhaps an easy way of describing the solution of a Sudoku puzzle is to call it a “graph coloring problem”. The basic goal of the puzzle is to build, in its standard form of 9 x 9, a coloring grid. The entirety of the graph is composed of 81 vertices, with one vertex for every cell on the grid. Each of the vertices can be named with pairs that are ordered and where “x” and “y” are integers anywhere from one to nine. This means that two separate vertices are names and are connected by an edge if, and only if the edges match. The Sukoku puzzle is eventually solved by assigning an integer, from one to nine, to each of the vertices in a way where the vertices connected by an edge don’t have the same integer assigned to them.

A Latin Square

The solution of the Sudoku grid is much like a Latin square. There are, however, less solution grids for Sudoku, than there are Latin squares. This is because Sudoku has the additional problem of multiple regions. Still, there are virtually endless solution grids for the Sudoku puzzle. As much mentioned in another article, in 2005, Bertram Felgenhauer calculated the number to be about 6,670,903,752,021,072,936,960. He arrived at this number using logical computations. The analysis of the number of solution grids was further simplified by Frazer Jarvis and Ed Russell. It has not yet been calculated how many solution grids there are for the 16 x 16 Sudoku puzzle.

There are some 9 x9 grids that can be recreated into other grids. This can be done by (1) rotating or reflecting the grid, (2) permuting some columns and rows, and (3) changing around the numbers. In 2005 Frazer Jarvis and Ed Russell calculated the number of different Sudoku grids that could be created and came up with a total of 5,472,730,538.

Unique Grids

In order to keep the Sudoku grid unique it’s important not to provide too many “givens”. The maximum number of “givens” that can be included in a puzzle before the grid solution is considered too unique is four less of a full grid. When there are two instances of two numbers which are each missing, and the cells which they are supposed to fill are each the corners of an orthogonal rectangle, there will only be two ways in which the numbers may be added together.

The opposite of this is just as true. The least number of “givens” that can be used before a solution is unique, or rather is a puzzle that can’t be solved, is 17. Some Japanese puzzle experts believe that this number is 18. Regardless how the least number of “givens” are rotated, the Sudoku puzzle will be unsolvable unless there are enough “givens” to make it symmetric.

Mathematically, the Sudoku puzzle is a work of art that has only one solution. This means that you may almost complete the puzzle only to find that it is one cell that turns out to be wrong. You will have no choice but to start over so that you can accurately place the numbers in the regions.

It has not been recorded who designed the Americanized puzzle but some believe it was Walter Mackey, who was one of Dell’s constructors of puzzles.  Others believe it was a 74-year-old retired architect and freelance puzzle creator from Indiana named Howard Garns. The reasoning for believing that it was Garns was because he was always on the list of contributors in issues of Dell Pencil Puzzles and Word Games that included “Number Place”, but his name was always absent from issues that did not.

Sudoku finally reached Japan when the Japanese found a “Number Place’ in a Dell magazine and translated it as something quite different: su meaning number and doku meaning single unit. It immediately caught on in Japan, which is only natural, when you consider that Crosswords don’t work very well in the Japanese language, and so number puzzles are much more prevalent than word puzzles in that language.

The Japanese version was introduced by Nikoli in 1984.  The puzzle appeared in the Monthly Nikolist in April as “Suuji wa dokushin ni kagiru”.  This can be translated to “the numbers must be there in only on instance”.  In 1986 Nikoli introduced two different versions of Sudoku as the popularity of the puzzle increased.  No more than 30 “givens” were allowed that the grid became symmetrical.  Sudoku is now published in many mainstream Japanese periodicals, including the Asahi Shimbun.  The trademark name of Sudoku is still held by Nikoli while other publications in Japan use other names.

Sudoku quickly spread to the computer.  In 1989 DigitHunt  was created for the Commodore 64 by a company called Loadstar/Softdisk Publishing.  This home computer version of Sudoku allowed people of all ages to enjoy the game in a computerized style.

Sudoku is now published in a variety of places including the New York Post and USA Today.  The puzzle is also reprinted by Kappa in GAMES magazine.  Many times you will find Sudoku included in puzzle anthologies which include The Giant 1001 Puzzle Book.  In these books Sudoku is usually titled something like “Nine Numbers”.  Surprisingly Dell, who invented the Americanized version of the puzzle, has failed to cash in on this big puzzle rage.

The Sudoku puzzle continued to grow in popularity and reached craze status in Japan in 2004 and the craze spread to the United States and the UK through pages of national newspapers. With this increased popularity came more analysis and deeper scrutiny of Sudoku. It was an accepted belief that practically speaking, there are virtually endless solution grids for the 9×9 Sudoku puzzle.  In 2005, Bertram Felgenhauer calculated the number to be about 6,670,903,752,021,072,936,960.  He arrived at this number using logical computations.  The analysis of the number of solution grids was further simplified by Frazer Jarvis and Ed Russell.  It has not yet been calculated how many solution grids there are for the 16 x 16 Sudoku puzzle.

Today, The Daily Telegraph uses the name “Sudoku” and you may see the puzzle called “su doku” in other places.  However, there is no doubt that Sudoku has reached such popularity that its name has been adopted into modern parlance, much like the word “crossword”.

•  Scanning

Scanning can be performed from the very beginning and throughout the solution process. Scanning basically has two techniques; Cross-hatching and Counting.

Cross-hatching can identify which line in a particular region may contain a particular number.

For example, if there is a 2 in the first row, first column and a 2 in the 3rd row, last column as illustrated below, and you are trying to figure out where a 2 would go in the  4th, 5th or 6th columns, you can immediately see that it can only go in row 2, since row 1 and row 3 already have a 2 in them, and you are only allowed to use a number once in each row.

2xx | xxx | xxx
xxx | ??? | xxx    (the 2 must go in this row)
xxx | xxx | xx2

Counting is a technique of actually actually counting through the numbers 1-9 along a single column or row to discover which number or numbers are missing. It can also be done within a single 3×3 sub-grid.

•  Marking Up – the candidate numbers are simply written in subscript in the cell. The disadvantage of this is that some first puzzles are printed in magazines and newspapers which are usually too small to accommodate many preferred numbers.  You can also use a pattern of dots within the cell, wherein the position of the dot corresponds a number from 1-9. Dot notation can be an advantage to a Sudoku that is printed on paper. In playing Sudoku that is printed, using a sharp pencil with an eraser is highly recommended.

•  By Analysis – you can approach the game by either “candidate elimination”or “what if”. In candidate elimination, numerals from one or more cells are eliminated and leaving just one choice. After each answer is placed, another scan can be done. You can check to see the effect of the contingencies. In the “what if” approach, a cell can be placed with two candidate numbers then a guess should be made.

As you gain more experience in solving Sudoku puzzles, you will settle on some favorite techniques. Your skill in using these techniques will increase so that before long, you will find yourself able to solve a puzzle much faster than when you first got started.

In order to solve a Sudoku puzzle, you must first understand the overall goal. The goal of the puzzle is to place numerical digits from 1 to 9 in each cell of a 9×9 grid which is further divided up into 9 3×3 sub-grids or regions. To help you get started playing the game, you are given a small number of pre-placed numbers in a few of the cells, which are called “givens”. The goal of the puzzle is to use the numbers 1-9 to fill in the rest of the empty cells. The challenge is that each number must be used only once in each row, column and 3×3 subgrid.

Basic rules

Rules in playing the game are very simple:

•  Sudoku is played over a 9×9 grid, divided into 3×3 subgrids.
•  The play begins with some given numerals from 1-9 that are pre-placed in a few of the grid cells.
•  Only the digits 1 through 9 are used.
•  A number can only appear once in each row.
•  A number can only appear once in each column.
•  A number can only appear once in each 3×3 subgrid.

Now you finally know the basic rules in playing the game, but you’re really just starting the process of finding solutions to how finish the game. There are several solution methods that can help you and these will be covered in other articles.  In the meanwhile, you can take pleasure in the fact that by playing the “fastest growing puzzle in the world”,  you can have fun while sharpening your thinking and analytical skills.

One of the most popular puzzles is Sudoku. It is an addictive number puzzle game that is taking the United States and the whole world by storm. It has become one of the most famous puzzle games ever created.

It is played using a 9 x 9 grid that is divided into nine equal squares. The objective of the puzzle is to place the numbers from 1 to 9 correctly in the grid. Each number must appear only once in every row, column and in 3 x 3 squares.

A Sudoku puzzle game usually begins with a set of numbers already given in the puzzle. Depending on the given numbers and the placement of the numbers, this determines the skill level of this puzzle. The puzzle normally differs from the simple or easy down to the difficult level of play. Sudoku puzzles are solved using logical skills.

If you haven’t tried playing a Sudoku puzzle yet, it is suggested that you begin with the easiest one available. If you want to purchase a puzzle book, the different levels are labeled – whether it is easy, moderately hard or very difficult.

If you want to look for the game in a newspaper, you will usually find the easiest Sudoku puzzle at the start of the week (Monday). By starting with the easy Sudoku, it will help you improve the strategies and techniques you have. In addition, it is not as frustrating as the difficult Sudoku.

How to play the Easy Sudoku

For beginners, there are steps which can be helpful in solving the easy Sudoku. Be sure to follow each step carefully and correctly to have a better chance of solving the puzzle.

1.  You should think carefully and cleverly. Once you already know that you cannot have two same numbers in each row, column or 3 x 3 boxes, it will be a good help or hint which you can use to get another number in the series. Remember the more difficult the Sudoku is, the less chance you have to get off to an easy start.

2.  In solving an easy Sudoku, the first thing you must keep in mind is to look for the possibilities. Possibilities are the numbers that are possibly just around. Beginning at 1, make an imaginary line on the boxes in the 1’s row and column. When you see that only one box is left in the nine-square block, you will know that it is a possibility.

3.  Carefully work on the numbers from 1 to 9. Since you have already placed some of the numbers, this will help you to get other numbers which have more possibilities.

4.  If you are trapped, go back, but be sure to look at the other numbers. When trapped, you can be fairly sure that you have missed something in the puzzle. That thing is normally where you need to be active again. If, during that process, you still cannot find the “missing number”, begin by labeling each block with everything that has a chance to be in the box.

5.  It would be advisable that you begin a game in the newspaper. Most of the newspapers in the country already have Sudoku puzzle games. Most of the easy puzzle games are published on Monday and Tuesday. The more difficult puzzles are published Wednesday through Friday.

The basic technique most players use in playing the Easy Sudoku is by going through every number and by trying to place as many numbers as the puzzle permits. You have to observe the numbers on the rows and columns to make sure that there are no same numbers present on the same row, column or 3×3 grid.

If you are working your way on the numbers 1 to 9, remember to think about going through the same process again. Then, look at the squares to know the numbers you can use to prevent other numbers from being used.

Try to train your mind to consider the numbers in all 3 x 3 boxes, columns or rows. In this way, you can easily spot the missing numbers which you need in each 3 x 3 set of boxes, column or row.

Last of all, if it is your first time to play the game, be patient. It may be an easy Sudoku but it is not as simple as you may think. It still requires great logical skill and careful thinking in order to win and complete the puzzle.