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# Sudoku/Methods/Advanced/Simultaneous Bivalue Nishio/Sudoku Addicts Workbook/147

## Introduction[edit]

From Sudoku Addict's Workbook, Paul Stephens (2008).

- raw sudoku, link to SW Solver.
- Diabolical grade, overall score 298.
- Stephens estimated solution times: Improver: N/A, Expert: 310 minutes, Genius: 103 minutes.

## Solving[edit]

- puzzle cleaned up with simple resolutions. This is the puzzle as shown on the right as Figure 1.
- Seed cell chosen in light orange. Green choice solves the puzzle, no difficulties.

## Proving Uniqueness[edit]

- Normally at this point it's fairly easy to prove uniqueness. But this puzzle was tough, at least basic strategies didn't work, and the solvers don't care about making progress with Bad Sudoku. Still I can try something.

### Using a Savepoint[edit]

On the left, figure 2, is what I had. So I created a savepoint with the name "r2c1=7", and then made it so. Hodoku squawks, making the number red and also all consequential eliminations the same.

- Choosing a new seed at r3c1=4, the green chain comes to a contradiction (the blue coloring is 6s in box 6, all eliminated in the green chain) therefore the seed=8 (i.e., within that chain, which we already suspect is invalid, and know it if we trust the solver.) Implementing that, the sudoku then came to another contradiction (not shown), proving that the solution found above is unique.
- This was fast and efficient. It only got a little complicated in proving uniqueness, and many will not bother to do that.

## Conclusions[edit]

Using a savepoint somewhat simplified the rest of the study. With difficult sudoku, a secondary bifurcation seed may be needed. Whatever common resolutions or eliminations are found with the first seed remain valid, so another seed has a leg up, so to speak. If a poor choice of seed is made, using Hodoku, it's trivial to abandon it while keeping all the common findings.

Savepoints can be used to implement Ariadne's Thread, making the solution of extremely difficult sudoku possible, but such are far from the ordinary puzzles that most solvers work with. Advanced solvers (like the SW Wiki solving assistant, or Hodoku's equivalent) may give up on these.

(But the brute force solvers don't. They use Ariadne's Thread, so we can claim that it is likely that **this approach will solve all sudoku without "guessing".** Rather, the method identifies bivalued seeds likely to be productive, and then tests both legs.)

As with all solving strategies, not every examination of the puzzle bears fruit. So which ones do we use first? How do we choose what to look at? "Guess" means a random choice, but an informed choice is not random, and if both legs of an exclusive choice are examined, this is pure logic, operating on chosen data from a large set.

Dismissing this method as "trial and error" completely missed the point, and that has been missed by nearly all experts.