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# Difference between revisions of "Sudoku/Methods/Advanced/Simultaneous Bivalue Nishio/Sudoku Addicts Workbook/148"

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## Introduction

• Raw puzzle.
• SW Solver: Diabolical grade, overall score 706.
• Stephens' estimated times: Improver: N/A, Expert: 342 mins, Genius: 114 mins.

## Solution

Figure 1

First pass, seed pair is r6c37{1}, Figure 1 on the left. This was not a good pair, but it had many Red resolutions.. It looked like a contradiction, but I did not trust my work, so I did it again, this time defining the seed pair as r6c3{15}. (That is not exactly the same, because the two cells in the first trial are not strongly linked in 5, and what shows from an invalid choice may differ with sequence. But I'm not entirely clear on this.)

Figure 2

In any case, Figure 2 on the right, this led to a contradiction in Red, there is no 9 in column 2, the ones that show in Box 4 are eliminated by the {79} pair in column 3. Therefore r6c3=1. This led to some quick resolutions and then I bifurcated again on r3c9{24}.

Figure 3
Figure 3 on the left shows the state of the puzzle when red completed. Green had been taken out to an easy extent.

Figure 4

### Confirming uniqueness

I continued to examine this and found more mutual eliminations and resolutions until green was close to completion, and finally confirmed the red leg. See Figure 4 on the left. The confirmed 1 in r5c9 will require 2 in r8c9, which then requires the red seed.

This is a full proof of the unique solution.

Figure 5

### Another seed

One more pass at this. In the book, I had marked bifurcation on r2c5, but had not actually done it, I don't know why. So here it is. That was actually a great choice, it led directly and quickly to mutual confirmation of r2c5=3, as shown on the right in Figure 5. Red paired or tripled "chain candidates" are shown in pink, and they eliminate {58} in r7c6, which then is confirmed as 6 in both chains, thus confirming that the seed is 3.

There might still be another bifurcation required to complete this, but as long as a bifurcation finds some result (i.e., a mutual confirmation or elimination) it makes the next steps more productive. In the book, in ink, I don't know how it would have worked out. Maybe I'll try it with pencil, which will allow me to erase the "coloring" for the next pass. I also sometimes can "recycle" the marks. But for serious project sudoku, pencil on top of ink candidate marks might be fantastic.

## Comments

Choosing the idea bifurcation seed is not essential. There may be many choices, and, using a computer-assisted solver like Hodoku, it may be more efficient just to start looking at anything promising. This is a very difficult sudoku; more ordinary sudoku mostly need just one pass to solution and full uniqueness proof.

Prepping the sudoku, I used only basic strategy (as used on SudokuWiki Solver with all tough or more advanced strategies turned off).