9. Solving a Sudoku as nine interlocking number grids ('Unsolveable' #29 by Andrew Stuart)

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  • čas přidán 16. 10. 2023
  • This Sudoku is in the same range of difficulty ("extreme" or higher) as the ones by Arto Inkala shown in videos 6, 7, and 8. In fact, my experience with this one was much like my experience with "Everest." A while ago I worked out a solution to it and left myself notes about the approach I had taken. But when I returned to this Sudoku, it was so difficult that I couldn't solve it again, even following those notes!
    So then I tried the same method that had worked the second time around for Everest: I tried to see if I could get individual numbers to reproduce themselves to the greatest extent possible. I started with the numbers that were already best represented.
    There are five 3s in the original puzzle. However, it was not possible to place a 3 anywhere in such a way as to place 3s in unique cells in all the other blocks. After the initial (brief) cross-hatching, there were also five 2s and five 4s. The 2s, at first, presented the same difficulty as the 3s. But there were two ways to place a 4 in a cell in such a way as to place 4s in unique cells in all the other blocks. One of those ways permitted doing the same with the 2s. And once the 4s and 2s were in every block, it became possible to place a 1 where it would reproduce 1s in unique cells in every block. And after that, as the video shows, all the other numbers filled in, one at a time, starting with those 3s.
    This method is still brand new to me and I have many questions about it. For example, it does not seem that the solution to a puzzle must necessarily lie along a path that involves being able to place one or two or three numbers in every block right at the start. However, attempting to do that does call on logic within the constraints of the Sudoku design. So I am eager to explore this method more.
    I am grateful to Andrew Stuart for permission to reproduce this puzzle. His site www.sudokuwiki.org has great Sudokus to try, along with many other kinds of puzzles, and interesting discussions of puzzle theory. (The term "unsolvable" in the title of this puzzle means that it could not be solved by the site's solving algorithm. The site presents a puzzle like this one every week to promote discussion of Sudoku solving.)

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