Instructions for sudoku

I recently started playing this asian game that spread across the whole world in the last years and I understood why: it's catchy and simple to learn, the rules are very easy to follow and it's a logical and attention game. I've played it on paper, but there are electronic versions too, there are many sites on the net that offer boards for all skills, from beginner to expert, bref, it's quite available to try. The instructions for playing Sudoku are : "Fill in the grid so that every row, every column, and every 3x3 box contains the digits 1 through 9. " The grid is 9x9, so all digits appear only one time on every row, column and in every box of 3x3 (the grid is partitioned into 9 such boxes). Starting from this rule, one can build an exclusion logic algorithm, based on the digits offered in the initial grid and fill it entirely. Look at the following grid, for example: if we check the 3 top boxes, we see that the top center and the top right ones already have a 6, so the free cells from the first row : cannot contain the 6 they lack in the 2 boxes I've mentioned. The only cell that is in this top row and can hold a 6 that follows the rules is this one, marked in red:
Not every cell can be deducted this straight forward, sometimes a choice must be made, when all the simpler cells are completed. Let's say 2 digits are the candidates for one particular cell, we choose one of them and remember it, then continue deducting just as shown above. If we reach a contradiction, and we are absolute positive no mistake has been made, then the choice we made was wrong and the other digit is the one corresponding to the cell we considered. Well, enough is enough, just wanted to share some tips in playing Sudoku, maybe it'll fill somebody else's hours in a plane or a train too :)