Sudoku tutorial

What is Sudoku? Sudoku (or Su Doku) is a japanese puzzle based on the digits from 1 to 9. You have to find the correct positions for these digits in the field to complete the puzzle. The difficulty depends on the numbers given at the very beginning. Easy? No way if you do not have an idea how to begin. And be aware that a good Sudoku puzzle has only one possible solution and can be solved without trying!

### Why Sudoku? ###

I like Sudoku. With Sudoku you have to turn your concentration completely off from anything else. Sudoku makes me use my brain, which I frankly don’t use a lot these times. It is a complex game with a few easy rules that in my opinion makes it the best puzzle these days.

### Rules ###

Sudoku consists of a 9×9 grid with nine 3×3 boxes in it. Each column, row or 3×3 box has to filled with the digits from 1 to 9. Every digit must exist exactly once in each column, row and 3×3 box. You start with the numbers given.

### Tips ###

If you begin solving Sudoku puzzles you may take a pencil and write down the possible digits for each field. This is very time consuming and may lead to confusion when there are a lot of choices left. Better try to think of this: if a digit already exists in a certain row then it can’t appear again in this row. Then find another row within this 3×3 box the first row appears to be in and look for the same digit. If there exists such a second row, then the third row of this 3×3 box has to hold this digit too. And this can only be in the 3×3 box, where this digit doesn’t already exist. I’ll give you an example.

### Sudoku example ###

This is the base grid. The grid consists of 9 columns, 9 rows and 9 3×3 boxes. Each box has a number in it such that it can be referenced for further explanation. This sample grid is filled with 29 given digits. The amount of given digits does not neccessarily tell us the difficulty since a good combination of fewer number may or may not be easier to solve than a hard combination of more numbers.

I’ll use the colour red to highlight rows or columns that already have a certain digit in them. A highlighted blue row or column indicates a new digit will be placed in this zone. This digit itself is blue and has a blue marking around. Newly inserted digits will be coloured black in the next step to minimise confusion.

### Step 1 ###

Look at the image at step 1 (Image 3). As you can see there are two rows highlighted in red that indicate the two rows containing a digit (in our example it is the 3). The 3×3 boxes that are of our interest are 7, 8 and 9. In box 9 the digit 3 is missing, and it may not be inserted in a highlighted field (since that row already has 3 in it). This way the only field left in box 9 is the one centered at the bottom.

### Step 2 ###

This step basically does the same as the first step (see Image 4). Instead of 3 the interesting digit will be 7. And this time we will use columns instead of rows (which of course doesn’t matter). The 3×3 boxes 3, 6 and 9 are highlighted, but only the middle one (box 6) fails to have 7 in it. The only field in box 6 left obviously is the one at the top left.

### Step 3 ###

This is a tricky step. You see a lot of rows and columns selected. First look at box 7: it contains 7 at the very left, this columns is highlighted. Now take a look at box 6: the containing 7 lives at the top of this box, this row is highlighted. This leaves us the following choice in box 4: either put 7 at the very center field of this box or at the bottom center field. Either way, you do *not* write any digit in this box. The only thing you have to know is that this center column has a 7 in it (box 4) and the other boxes (1 and 7) must not have a 7 at the centered column. That is the reason this column is also highlighted. And because there’s a 7 in box 2 at the top row and a 7 in box 3 at the bottom row the only field left for 7 in box 1 is: You got it! The middle right field.

This way you can fill up a lot of empty places with digits. You might fill up everything with this technique, but you may as well get stuck at a point with too much choices to handle. Then I go back to the good old write-the-choices-in-a-space-and-go-on. Sometimes I discover something I haven’t seen before. Just do not use trial and error techniques.

### Where to next ###

Sites that give you good Sudoku. Whenever I find a site with good Sudoku puzzles I’ll add it to this list.

* [derStandard.at](http://derstandard.at/sudoku)
* [The Times Online](http://www.timesonline.co.uk/section/0,,18209,00.html)
* [Too good for Fiendish?](http://www.timesonline.co.uk/article/0,,7-1757275_1,00.html)
* [Sudoku.com](http://www.sudoku.com) (has a tutorial too)

### Acknowledgements ###

The images where made by myself with [The GIMP](http://www.gimp.org). I used the given digits from a Sudoku puzzle from [derStandard.at](http://derstandard.at/?id=2175346).