theory

The board can be broken down into 18 lines.
9 top to bottom (y axis) and 9 left to right (x axis).
A sudoku position is valid if the number contained in the
position is the only instance of this number on both it's 
x and y axis. 

This solver will work on the assumption that every starting 
position is valid and then due to the mathematics behind the
game every calculated position is therefore also valid.

The grid of 9x9 is split up into 9 tiles each containing 9
positions.

Those 9 positions can be classed as 1 of 2 types
    1. Valid positions : these positions as stated above
    have already been filled in with a valid number
    2. Possible positions : these positions are blank and
    can be filled by any number not already in the tile

To find/remove invalid possible positions an initial search
can be preformed on every position. If the search finds a
blank position nothing needs to be done, but if the search
finds a cell that has been filled in then we know for the
number found in the cell there are no possible other positions
on the same x/y axis or the title it is contained in and as
such the possible position matrix can be updated.

A possible position can be replaced with a valid position 
when for a given number there is only 1 possible position in
a tile and when the possible position is updated to a valid
position then we can remove any instances of the same numer
in the possible position matrix on the x and y axis. Note:
we do not need to remove and instances in the tile's possible
positions matrix as for the possible position to be converted
to a valid position there can only be one instance of a the
number in the possible position matrix.