There are around 6 different strategies required to solve squares in a sudoku puzzle. You shouldn't ever have to guess
at a square - if you find yourself guessing you have either made a mistake or there is information in the grid or a
strategy that you are not aware of. (The other possibility is that the grid has more than one solution and is therefore
not considered to be a true sudoku!)
Depending on where you look the different solving strategies have all been given different names by different people
but by far the most widely used strategy and one that you will need for all sudokus is Scanning and Eliminating
Scanning and Eliminating
The technique of scanning and eliminating is the simpest of all sudoku solving techniques.
It involves using the numbers one digit at a time and the knowledge that each row,
column and block MUST include ALL the digits from 1 to 9.
Take this example of an easy solution. First of all we need to look at all the "1"s.
If there is a "1" in a row then there cannot be another "1" in that same row. The same is of course true for
columns and blocks and other numbers.
Fig 1. New Sudoku puzzle
So we scan the rows and columns ruling out the possibilities of squares containing a particular number.
In Figure 2. We can see that the "1" in the bottom left block and the "1" in the middle middle block rule out
the possibility of there being a number "1" in all but one square of the left middle block.
Fig 2. Scanning using the "1"s
Since each block MUST contain all digits from 1 to 9 and this is the only square in the left middle block
that can contain a "1" then it must contain a "1" so we write it into the grid.
Using this new information we can make further progress with the puzzle that wasn't possible before.
Fig 3. It must be a "1"
Using the new number "1" we discovered in the left middle block with the "1"s in the bottom left block and
the top middle block we can see that there is only one square that can possibly hold a "1" in the top left block.
Fig 4. Scanning using the new "1"
As before we enter the number "1" into the square and continue on with the puzzle.
When we are unable to make progress with the number "1"s we move onto the number "2"s and so on possibly looping through
the set of digits several times before either solving the puzzle or getting to the stage where other strategies are needed!
Fig 5. Next solved "1" entered
As mentioned there are several other strategies for solving sudokus and you will need to work these out for yourself but
remember: the key is ruling out the possibilities!
How to Solve a Sudoku!
