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# Difference between revisions of "Sudoku/Methods/Advanced/Simultaneous Bivalue Nishio/Nokia"

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## The puzzle

No Solution found
Insufficient logical strategies are known to properly grade this puzzle (Bowman's excluded). ie, it is really difficult. Or it has multiple solutions (check with [Solution Count]).

Bowman's Bingo strategy found nothing.

Solution Count:

Number of solutions: 1 (recursed 128577 times)

Group/ALS Analysis:

• 2 Bivalue Cells
• 5 Multibox Row bilocation links
• 5 Multibox Column bilocation links

20 total possible SBN seeds

Solution by SBN was expected.

Abd Ul-Rahman Lomax https://www.sudokuwiki.org/sudoku.htm... puzzle cannot be graded because inadequate logical strategies exist in solver. It has one solution, Solution Count shows. I took the puzzle into Hodoku and it rates the puzzle as Extreme. It does show a solution path. I will use this as a demonstration of Simultaneous Bivalue Nisho, which I expect can crack this puzzle. (This is full coloring on pairs of any kind).

results: this puzzle was more difficult than world-famous "unsolveables." Why? Well, with the unsolveables, I know what I'm getting into, and it looks hopeless, so I use Ariadne's thread from the beginning (Bivalue Ariadne's Thread). That is easy, if requiring patience. This puzzle, from the Hodoku display, had possible logic. What it took was many uses of Simultaneous Bivalue Nishio, some abandoned, most, at first, producing a single elimination. I did one Nishio on a digit that would have required Trivalue, which I don't do because it is too complicated. I did keep notes and this could be confirmed, if someone is interested. The notes were enough to see what I did, but some details were not recorded. 8 productive SBN pairs were analyzed, plus a single digit Nishio, and a 2-string kite at one point.

## The request

Libor Matousek Abd Ul-Rahman hi I'd be interested in your notes showing a logical solution to this puzzle (even though I expect they will be complicated and not sure I'll be able to follow them :) )

This page was created as a full response to Matousek. SBN, which is the primary tool used to crack this puzzle, is easy to understand if one looks at it step by step. The expectation of "complicated" is part of what inhibits learning.\
This strategy, as well, will not be usable on most phone solvers, and certainly not on a relatively dumb phone, without coloring tools. It can be done in ink and pencil on paper, and it can be done on smartphone solvers like those on [[1]]. Understanding this explanation should be easy if it is taken step-by-step. On a dumb solver, one may verify a contradiction by "guessing" it. Guessing is not necessary when coloring can be used, as it can in ink/pencil on paper (and I often do it purely in ink, but with a puzzle like this, that would have produced an incorrigible mess. With pencil coloring -- distinctive marking of the candidates -- no problem, because a coloring can then be erased if needed. The erasure will leave the candidate marks! Those are X'd out, neatly, when a candidate is logically eliminated.
I recommend that interested solvers download, install, and use Hodoku. Coloring is trivial in Hodoku, and can be erased with a single click.

## Solution Notes

seed pairs

• r59c4, 5. 1 elimination
• r4c57, 2. elimination(s)
• r5c45, 1 r5c5<>8
• Nishio r2c7<>5
• r2c7={23} cont =>3
• r7c2&2r9c3,2 =>r7c2<>9, r2c2=6. cont r7c2=2
• 2-string kite in 2.
• r5c2={79} => mutual r3c9=9, seed => 9
• r59c4, 5. cont = r5c4=5.
• r29c8, 5. mutual r6c7=5, r2c8=2 completes.
• uniqueness not proven.

## Detailed solution process

For this summary, the solution was recreated following the above notes. It is always possible that an elimination was a logical error that was nevertheless moving to the solution. So this re-creation may be more careful and may be checked using BAT. Generally, chaining operations are not reported in detail; in this case, only a "difficult" chain extension will be reported. (i.e., one that might relatively easily be overlooked.) SBN reduces puzzles to simpler puzzles and to practice it well may require learning to see chains amidst noise. The logic is that of easy sudoku solving, though. Advanced logic could be used within a chain, but it is more difficult to spot. SBN is presented as a method to use when one's logical tool kit doesn't work. It can crack puzzles even if some basic strategies (like triples) are missed. The detailed examination often finds missed strategies.

Some possible seed pairs were examined without any mutual results. They are ignored here, but anyone attempting to use SBN without a map like this will find that many or most seed pairs do produce results. In this case, the bivalue cells were "punk," i.e, produced nothing. That is unusual but given how few there were, not surprising.

### r59c4, 5

easy elimination: green chain, r5c4=5?. red chain r9c4=5?. red: => r8c8=5 so r8c4 sees both a green and a red 5, so must be eliminated. This could also be seen by a Nishio on r8c4=5?. Chains do not extend beyond that, coloring abandoned.

### r4c57, 2

green:r4c5=2? red: r4c7=2? => r4c3=7, r9c6=7, r3c5=7. 2 in r3c5 is eliminated in the red chain and sees the green 2 in r4c5, so is a mutual elimination. No more chain extension seen

### r5c45, 1

originally found only this: r5c5<>8; however this time I was able to extend the r5c4=1? coloring almost to completion, found a contradiction. So r5c5=1. However, I will not implement this, only the elimination found before (which was the first I found this time), in order to confirm the original report. It is possible there were errors in it. I kept an image of this coloring.