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# Sudoku/Reviews/Systematic Sudoku/Sudokuwiki Ends Nakex 63 On Its Own

This was based on Mixed Solutions on Nakamoto Extreme 63.

Puzzle in SW Solver Extreme Grade (550).

## Abd's solution

- After basics, 2-String Kite: 3 in r2c4,r4c1 (connected by r4c5,r6c4) => r2c1<>3

and then another basic. SBN in Gordonian order

- r1c3={49}. Mutual eliminations: r89c8<>5, r9c3<>7. Impasse.
- r2c4={35}. Mutual elim. r4c1<>9. Impasse.
- r3c2={38}. Impasse. (3 chain extends, 8 totally punk).
- r4c1={35}. 5 chain contradicts (after much extension), so r4c1=3. Easy to the end.

## Review of Welch comments

*This post picks up on the Sudokuwiki/Sysudoku resolution of Nakamoto Extreme 63 where it was overtaken by pattern analysis and coloring, and finishes it in two ways, one humanly practical and one not.*

The SW Solver solution path is mostly "humanly practical," but much is not explained. One step is, I'd say, not practical. Solving assistants like SW Solver all present the "next step" in solution. They do not explain how to find the step.

The "next" step is the one which is simplest for the computer to find, using "logical strategies" that are assigned a difficulty rating.

A vague myth has developed that there is "the next step." In fact, there are generally many "next steps." If a human does not follow a systematic approach, it may not be "humanly practical" to find what SW Solver will suggest, for advanced "strategies." But if the human has such an approach, it may be entirely practical and, in fact, I do this about every day.

*Sudokuwiki doesn’t maintain coloring clusters between moves, or use pattern analysis to expand them. After the 785-wing in the solution of the previous post, Sudokuwiki continued with a two solution paths [sic] too instructive to pass up.*

It is correct that SW Solver (which is not "Sudokuwiki") only uses coloring to explain the "next move" that the Solver has found.

*The first continues with an Andrew Stuart cell forcing chain. The idea is to remove a candidate that forces all candidates in some cell to be false. It takes a modern computer very little time to determine what a single candidate forces out, but how many such examinations fail between cell forcing chain successes? Way too many for human tolerance.*

He made that up. I am sure he has not tested this claim. I have. Cell forcing is most efficiently done with a Nishio on a pair of mutually exclusive possibilities. A puzzle of this class will have many such. Welch has defined this narrowly, as only "cell forcing chain," when there are multiple possibilities from study of a paired choice. So, for example, what if the chain completes the puzzle, not finding any contradiction? Is that a "failure"?. In fact, if we assume uniqueness, that is a total success, all that is missing is proof of uniqueness.

The other possibility is that two chains are considered together, so not only could one of them come to a contradiction, but both chains could require an elimination or resolution. Mutual eliminations are especially common, and accumulate so that even if paired chain analysis still comes to impasse, it is not a failure of any kind unless it produces no results. Which is true for most analytical efforts, they produce no results, until they do.

The present puzzle is quite difficult. I picked seed pairs with no regard to their apparent "value." It can expected in a puzzle like this, that there will be more "punk" seeds, meaning that it generates no results, a logically required result of any kind being defined as a "success." Still of the four choices, only one was abandoned without mutual results. That is normal in my experience, that half of the choices or more result in success. This percentage can be raised by more careful choice of seed; I do that in ink on paper solving. But using Hodoku it is so easy to color chains that the easiest way to evaluate a pair may be to start coloring based on it.

*But here’s one. 3r1c9 forces 7r8c2 off via 3-chain and 7-chain. The ALS forces 1r8c1 on, 15r8c1 off. Is that a peacock or a swan?*

It appears that nobody is checking his work. When it is so complex, that could be common. He means "3r9c1." What I would write as r9c1=3.

What does "15r8c1" mean?

This is what I see as real: nobody uses the SW Solver "strategies" as they are. What people working on puzzles of this class do is to color chains. They don't drop the coloring when it is still incomplete, unless they find it at an impasse. So their solving path will be different from what SW Solver does. It was designed to take a current position and find a "next step," and it only reports more than one result when those are implicit in the "next step."

The SW Solver site does include explanatory articles, of varying pedagogical efficiency.

I find it extraordinarily difficult to follow Welch's arguments. There are many obstacles. He has developed his own language, and his notation system is incompatible with what SW solver, Hodoku, and nearly everyone else uses. He may claim that his system is "better," but if we include the human factor of efficient communication, perhaps not so. I have yet to see how he uses positional information. His sequential notation, where candidates have different positions in different cells, is guaranteed to slow down pattern recognition.

SW solver does not make it clear how to find the patterns it shows. It just reveals the patterns. This leads to Welch's complaint: this isn't human-usable. But it is, if one knows how to find the patterns!

In actual practice, with chain logic, one simply implements mutual eliminations and resolutions as found and keeps on extending a coloring. A contradiction in one chain is a kind of mutual resolution. I.e., the contradicted chain confirms its opposite.

One of the SW Solver patterns is this, and it was this chain Welch was writing about:

- Step 21 - Cell Forcing Chain docs
- Type 2: All three candidates in H2 lead to 3 being OFF in J1, so it can be removed.
- +1[H2]-1[H1]+3{H1|D1}-3[J1]
- +5[H2]-5[H6]+1[H6]-1[H1]+3{H1|D1}-3[J1]
- +7[H2]-7[G3]+7[F3]-3[F3]+3[J3]-3[J1]

I would never even look at this for an ordinary Sudoku, unless I ran out of pair forcing chains (SBN seeds), except once I did when another sophisticated user pointed to it as an example of Trivalue Simultaneous Nishio.

This would be an example of how the SW Strategies are not "human-oriented." However, any human can verify that strategy, looking at one of the chains at a time.

It is far more difficult to track the results of three choices, looking for triple agreements, than it is to do this with two choices. It could be done, but is there any need for it? --Abd (talk) 19:09, 30 March 2020 (UTC)