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How to play Sudoku

Sudoku is a fun Japanese puzzle based on numbers and grids, but don't let that scare you! No special math skills are needed, only a little bit of logic and some good old concentration. After we've taken you through solving your first Sudoku, you'll be as hooked as we are!

Let's first take a look at a typical sudoku puzzle first:


As you can see from this example, a sudoku puzzle is split up in 3 different sections. First you have the columns. There are 9 of them, and one of them is highlighted as an example:


Secondly, a sudoku puzzle is split up into 9 rows:


And last (but certainly not least) are the regions. A region is a 3x3 area made up from the cells within a Sudoku. A sudoku has 9 regions, of which one is highlighted here:


So how do all these rows, columns and regions add up to fun? It all starts with a simple rule (take care to read this bit carefully):

Every column, row and region must all contain the numbers 1,2,3,4,5,6,7,8 and 9 in no particular order, but never duplicated!




Let's go straight to an example to demonstrate this. As you can see from below, the highlighted row, column and region are completed. Notice how each row, column and region all contain 1 to 9 with no duplicates.


Can you see how each completed row, column and region fit into one another when the correct numbers are found! This is the joy of playing sudoku, finding those numbers and filling the entire puzzle in so that every row, column and region contain 1 to 9 with each number slotting into one another perfectly.

So how do you find those numbers? There are many ways, ranging from easy to do with the eye to blisteringly difficult! Luckily we're going to touch on the basic ones, which despite the name will allow you to finish almost all puzzles you come across.

Method 1) scanning


By far the easiest method of finding a correct number is a method called "scanning". To start scanning, you must first find an empty cell within the puzzle and while reading its row, column and region, determine if there is only one possible number to fill in. When only one exists, it is entered into the puzzle and the next empty cell is found, upon which the whole process begins again.

This method is perhaps best shown with an example. Let us first pick an empty cell:


From this cell, we first scan its row, which contains 2,3,4,7 and 9. Secondly we scan the column, which contains 2,5,6,7 and 8. Lastly we scan the region, which contains 2,4,5,6,7 and 9. The following example demonstrates this:


Let's add all those numbers up and see what we have: 2,3,4,5,6,7,8 and 9. Can you see the missing number? That's right, there is no number 1. That means this cell is meant to be number 1.

If we continue using this method, we will hopefully keep filling in cells until there are no empty cells left!

Method 2) pencil marks


So what happens when you can't find a cell with only 1 clear number left? There are many methods, but by far the easiest is the use of pencil marking! Pencil marks are small notes of number "possibilities" per cell and are only normally written when there are only a few possibilities.

Pencil marks are very useful to visually be able to aid scanning techniques. The best way to show this is with an example. The following puzzle has been partially filled in and we've come to the conclusion that we're a bit stuck trying to fill in the following region:


Using pencil marks we can aid our scanning techniques by doing the following:

  • 1) Find each unsolved cell
  • 2) Fill in the possibilities for the unsolved cells

If these steps are carried out, we are left with the following (note that the pencil marks are always written slightly smaller around the cell):


How does this help? Well, we are now capable of removing the possibilities with simple scanning techniques to help us. Lets first start by trying to eliminate the possibility 3:


By finding a 3 in this row, we know that it is not possible to have another cell in this row containing the number 3, so we can now eliminate the possibilities of 3:


If you now look carefully, there is only 1 possibility left for a 3, so we can simply solve that cell:


We're now much closer to finishing our region. Unfortunately, we're left with a difficult decision, 1 or 7? Thankfully, the pencil marks will help us out again, lets look at another example:


You can see that this field must be a 1 (the highlighted row and column both contain a 1 so therefore the field marked by the arrow must be a 1). Because of this, and reminded by the pencil marks, we can now remove the 1 from the pencil mark in the same column:


With this left, we've basically solved this region. The last 7 pencil mark gets replaced by a solved 7 and we know a 1 is all that is left to fill in. Just for the record, here it is:


Tips `n tricks


There are hundreds of other techniques for analyzing Sudokus, and if you check out the references section below you will see links to some of them, but we're going to leave you with some simple tips to get you through some of those more difficult puzzles:

Row / Column / Region Completion

While scanning can be effective, it often pulls your eyes away from singular rows or columns. Let's take a look at a partially solved puzzle and keep our eyes on the singular rows and columns:


As can be seen, the middle row is missing a few options. Instead of individually going through each empty cell and trying to find its solution, let's look at the row as a whole:


The row contains the following numbers: 1, 2, 3, 4, 6 and 9. This means we are missing 5, 7 and 8. How does this help us? Well, if you inspect the regions that comprise the row, you can see that the first region can only contain an 8; the second region can only contain a 7 and lastly the third region can only contain a 5! We've solved the whole row completely based on the row itself.

This tip is perfectly applicable to columns and to rows.


Pencil mark inference

Pencil marks are good for lots of different techniques. By fair the easiest to catch with the naked eye is called (in sudoku addict circles) the "Naked Pair" technique. The naked pair is clearly visible when using pencil marks and can be spotted by looking for pencil marks in two cells (in the same row, column or region) that contain 2 identical possibilities. As always, let's start with an example:


As can be seen from the pencil marks, there are two cells with the possibilities 1 and 7. This is your naked pair! Because of this, we know that either one of these cells must contain a 1 or a 7 and therefore we can remove any 1 or 7 as possibilities in any other cell in the region, leaving us with this:


As you can see we have taken ourselves a step further to solving the problem!


Finished puzzle


For the inquisitive, here is the completed puzzle used in the above examples:


If you want to continue playing sudoku, we recommend starting with an Easy puzzle, and this can be played right here!


Further Links


There are lots of useful references for playing sudoku online, here is a small selection of some of the best:


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