I have only recently learned of sudoku, and it looks like I will soon be addicted if I am not already. Like everyone else I have poked around to see if I could find quicker or novel ways to solve them. Many of the things I have found out are, alas, completely useless in that regard. Here are some of them:
(1) It is obvious that if you were to assign values to the positions of each row and column--1 to 9 from top to bottom and left to right, or whatever--then the sum of the position values of any given number in a completed sudoku adds up to 45, since 1+2+3+4+5+6+7+8+9=45 and each number appears in every row and column only once. This is also true, however, when you assign position values 1 to 9 within the 3x3 boxes of the sudoku--even though a given number might appear at the same position in 2 or 3 different boxes (3 is the limit I think). For instance, number X might appear in the 9th cell of the upper-left hand box and also appear in the 9th cell of the center box, but this high total (18 for only two boxes) will be elsewhere balanced off and 45 will be the total of the position values of X. Cool!
(2) If you assign values to the positions of the entire sudoku (1 to 81), then the total of the position values of any given number is 369, which is a fine, fine number. Cool!
(3) Take a sudoku puzzle. Select any 3x3 box (or column or row) that has some numbers in it. In a blank sudoku write the numbers 1 to 9 in order (they don't have to be in order but it makes it easier as they are meant to be position values) in the 3x3 box that corresponds to the one you have chosen in the puzzle. As you figure out numbers in the puzzle, in the corresponding cells of the blank sudoku write the number of the position that that number you have figured out occupies in the chosen 3x3 box of the puzzle. (For instance, suppose you have chosen the top left box. You then figure out that r7c6 is a 9. In the top left box there is a 9 at position 4. Write 4 at r7c6.) This process creates in the blank sudoku another valid sudoku. Upon reflection it is clear that this must be so--and it is so obvious as not to be helpful. I thought at first that the two "sister sudokus" might help each other to maturity in a sort of logical feedback and transfer snowball maelstrom, but they don't as, of course, each one contains the exact same information. Of course, sometimes you don't see something in one of the sudokus that strikes you immediately in the other, and this can be helpful, but it is too rare an occurrence (for me) to bother with it. It is certainly not any faster than the standard approaches.
(4) I am very unsure about this one, but my probably very unorthodox (and probably very misguided) statistical approach revealed that there are 46,000+ ways of validly placing a given number onto the sudoku grid. Is that right? Seems like a lot.
Anyone else got any of these sort of dead-end ideas?