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Sudoku/Methods/Advanced/Simultaneous Bivalue Nishio/Unsolveable 28

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Figure 1
  • Raw puzzle.
  • SW Solver: Tough grade, overall score 982.
  • SW Solver was improved to handle this puzzle, using Exocet, a difficult Extreme strategy, put at the beginning of the Extreme list by SW solver. Why? Because Stuart wanted it to be tested extensively.
  • See discussion of difficulty measures on SudokuWiki.
  • See Figure 1. Preliminary study of this puzzle reveals:
  • There are no single-cell pairs, but there are row and column pairs.
  • There are two X-wings in 6, giving four pairs or eight, depending on how we count.
  • There are six other pairs.
  • Pairs are shown as green and red candidates.
At this point it is strongly suspected that recursion will be needed. But we will see.


I used Hodoku, and indeed, recursion was necessary. I used 20 savepoints to crack this, completed 22:09, 16 August 2019 (UTC). It was under about three hours total. I will want to do this again, because the process is error-prone, and most of it is working with defective resolutions, so automatic checking is not possible. I may have been influenced by the display of correct choices, and I want this to be rigorous (and fully verifiable). What was fascinating to see was that as choices were made, analyzing them became easier and easier and SBN became far more valuable. At first it had very little to chew on, so I created many savepoints rapidly.

I did not fully verify the solution (i.e, confirm uniqueness). This would have taken substantially more time. So this is incomplete. Nevertheless, this was a project-class sudoku, the kind they say will take days to solve, or "impossible for humans without guessing."

What was done was not guessing. Pairs were chosen by examining expected consequences. What is difficult with recursion is that one has done a lot of work that gets tossed when the branch is found defective. SBN only became useful after a few choices were established provisionally. This Sudoku was designed to require many proposed candidates in order to make it solvable by basic strategies.