The connection between Sudoku and Math

Sudoku puzzle game is different from other puzzle games, because Sudoku is has a mathematical structure and also demands a degree of logical thinking in order to figure it out.

The main reason why Sudoku is so difficult to solve is due to so called NP-complete, which is solved on n2 x n2 grids of n x n cells. Since a couple of "givens" are put in the cells on the grids, it will take you some time to clear the Sudoku right.

Sudoku puzzles also has so called game tree that can be pretty large. If a particular game is made with only one possible solution, then solving it can be very hard task to perform. But you can use certain tips to help you figure out your Sudoku much quicker.

The easiest way of discovering the Sudoku puzzle solution is if we call it a graph colouring problem, where the primary goal is to construct a colouring grid in its standard variant of 9 x 9. The entire graph consists out of 81 vertices, with 1 vertex for every single cell that is present on the grid.

We can name each of the vertices with pairs that are ordered and where "x" and "y" are integers, ranging from 1 to 9. Therefore, two individual vertices are names and are also linked by an edge, in case and only in case where the edges correspond.

That means that sooner or later, Sudoku is figured out by imputing an integer, or a number from 1 to 9, to each of the vertices in such way that the vertices, linked by an edge, do not have the same integer imputed to them.

A word about the Latin square

We can also compare the solution of particular Sudoku grid to a Latin square. But you should know however, that there are less solution grids for Sudoku, than there are Latin squares simply because the Sudoku puzzle has another problem: Multiple regions. But despite that, there are endless solution grids for Sudoku puzzle games.

For instance, Bertram Felgenhauer in year 2005 estimated that number to be around 6,670,903,752,021,072,936,960. He gained this number by using logical calculations. 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.