I was recently forced to spend some deal of time sitting down at the DMV. so, to occupy said deal of time, i brought along a Sudoku book. Being of academic inclination I believe most members of the forum know the basics of Sudoku, however for those who do not know:

A sudoku problem is a 9x9 grid of squares - thus totaling 81 tiles - which when complete have the numbers 1-9 repeating exactly once in every row, column, and major box. a major box is one of nine boxes consisting of a smaller 3x3 grid inside of the 9x9 grid. A sudoku problem is only considered properly posed if it can be solved without any guessing, and if none of the hints - tiles already filled in - are redundant. This means that if the tile were erased, you could not use logical methods to derive the correct value for the tile using only the hints.

the objective is of course to fill in all the tiles such that each row, column, and box has the numbers 1-9 exactly once each. This requirement of a solved sudoku problem leads to a number of logical devices that can be used to solve it. Here I wish to present a novel logical device which can be implemented by humans (as opposed to the many devices computers can use) to rapidly solve the puzzles.

The device I present requires an initial input of time, however after this time input it greatly decreases the amount of time that must be spent to complete each next tile.

one starts by examining the top-most, left-most square. If the square is a hint, proceed onto the next square, otherwise identify the values of all the hints and previously filled squares which share either a major box, row, or column with the square in question. mark the box with all the values that are not identified in this manner, these are the possibible values of the box.

one then repeats this process for the next square to the right, and continues in this manner down the rows untill all the squares are either marked or are a hint.

during this process the better part of the squares will have multiple possible values, however some squares invariably are identified as having only one possible value as a result only of the hints.

begin with one of these known squares. upon filling in its value, you can eliminate that value as a possibility from the squares that share a row, column, or major box with it. This often reveals other known squares, and if it does not then there are other known squares for which to repeat this process and eliminate more possibilities. It is key that upon filling in a known square you immediately remove it as a possibility from that boxes which it affects, as if you do not you will end up with a lack of important information about the potential values of boxes.

I have found that in all well posed sudoku puzzles, it is possible to rapidly complete the grid(within minutes for a well practiced person) once the initial possibility plotting is done.

if anyone believes my method is faulty, a better method exists, i have not explained it sufficiently, or that improvements can be made i welcome your criticisms.