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NoticeI am no longer posting new puzzles to this blog. For all of my Sudoku puzzles, old and new, please visit Sudoku in another section of this website. I will still create and offer new puzzles, in batches of a couple of hundred, once a week or so. Sudoku #16Category: Sudoku In #11, #12, and #14, I discussed some advanced Sudoku solving techniques. These three techniques are sufficient for most of the puzzles I've seen. However, one puzzle had me stumped for a while. Obviously, I needed something more. My Sudoku program could solve it, but it had to resort to a trial and error, backtracking algorithm. There just had to be some analytical technique that I was missing. I finally found another technique. However, this is a bit more complicated than the previous techniques. The best way to describe it is to provide a concrete example. The following shows how far I got with that puzzle with just the previous techniques:
To break the impasse, we need to look at two rows and two columns at the same time. In this diagram, look at the four cells where the marked rows and columns intersect. Note that the possibility "6" occurs in all four cells. Note also that in the marked rows, possibility "6" occurs only in the intersecting cells. Thus, the value "6" must appear either in the top right and bottom left cells, or in the top left and bottom right cells. Either way, "6" cannot appear in any other cell in the two marked columns, and can therefore be eliminated from those other cells. In this case, the three underlined sixes can be eliminated. Theoretically, I suppose you could extend this technique to three rows intersecting with three columns. But I doubt you'll ever have to resort to that. Now that my Sudoku program knows about this technique, does that mean I will now post even more challenging puzzles? To answer this question, you'll just have to wait and see. For today, though, another relatively easy puzzle, with a blank middle group. Hans
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