## SK-Loops and MSLS's

Advanced methods and approaches for solving Sudoku puzzles

### Re: SK-Loops and MSLS's

Hi Paolo,

Ajò Dimonios wrote:It seems to me that any resolution technique can be explained by the general logic that is stated in the text by Allan Barker.

Agreed. In my view there are two generic ways with enough power to express every piece of logic in sudoku: set logic and chains (including loops and nets; TDP also goes into this category). That doesn't mean they're both equally suited to every situation. Most simple cases are best expressed as chains because the logic is explicit and easiest to follow that way. On the other hand, things like fishes and big MSLS structures are much simpler to express and understand as set logic. In fact, everything is very simple with set logic as long as there are no triplets, i.e. no overlapping truths or links. If such things are necessary, then things get complicated quickly, and a well-written net diagram (as per totuan's) is probably easier to follow.

The purpose of every single technique of resolution is to solve or attempt to solve a scheme with a clear and simple tool. The more a technique is simple and powerful, the more useful it is to achieve its purpose. What I notice is that in the universe of various resolution methods there is a lot of redundancy and repetition.

That's true, which is exactly why I like to have a clear idea of the relationships between different techniques. Many of them aren't that different when you peek under the hood. Then again, some techniques that use even the same exact pattern might use completely different logic to achieve the same results. Since you only need one of them to get the job done, is there a point in even learning anything else? I think there is. Being able to see the same thing from multiple perspectives is always valuable.

For this reason, anyone who manages to simplify in a few essential methods does a job that everyone likes.

Not necessarily. Nested T&E is a very simple and effective solving method, especially if guessed backdoor solutions are accepted too. Should we only use that?

Obviously there are more forces at play here. Since there's no intrinsic value in a solved sudoku grid, except in competitions, the only value is in the process of solving it. What each solver values in the process is very subjective. The simplest way to do it might also be the most boring, both for the solver and for anyone else who looks at the solution.

Robert's method (TDP) has these characteristics, despite the apparently complex theoretical aspects, the technique is simple and uses only the basic technique.

Yes. Any form of nested T&E has those characteristics without requiring much of a theory at all. Does an expert player find it fun to apply? Does it produce interesting and elegant solution steps, that are concisely expressed yet easy to follow without repeating the process? Those kinds of aspects, and their relative value, are up to everyone's subjective opinion. That's why there's no silver bullet that works for everyone.

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: SK-Loops and MSLS's

Hi Space.

Not necessarily. Nested T&E is a very simple and effective solving method, especially if guessed backdoor solutions are accepted too. Should we only use that?

I don't believe that any backdoor is a valid resolution, not because it is a lucky random solution but because, similarly to all the solutions obtained with so-called "uniqueness methods”, they do not demonstrate the uniqueness of the solution which I believe is a fundamental requirement.

Ciao a Tutti
Paolo
Ajò Dimonios

Posts: 213
Joined: 07 November 2019

### Re: SK-Loops and MSLS's

Ajò Dimonios wrote:I don't believe that any backdoor is a valid resolution,

We should be careful with the word "valid". Since the solution produced is correct, and there's nothing wrong with the logic of guessing, I think it must be considered a valid resolution too. Of course I personally don't accept such solutions but that doesn't make them invalid.

not because it is a lucky random solution but because, similarly to all the solutions obtained with so-called "uniqueness methods”, they do not demonstrate the uniqueness of the solution which I believe is a fundamental requirement.

I believe it's a fundamental requirement too -- for the puzzle provider. For me as a human solver it would be that only if it made solving more fun or produced more interesting and elegant resolutions. It most certainly doesn't. Since I only solve puzzles that I know have a unique solution, there's absolutely no reason for me to avoid uniqueness techniques which are often among the most fun and elegant to use. But to each their own.

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: SK-Loops and MSLS's

I Space

I believe it's a fundamental requirement too -- for the puzzle provider. For me as a human solver it would be that only if it made solving more fun or produced more interesting and elegant resolutions. It most certainly doesn't. Since I only solve puzzles that I know have a unique solution, there's absolutely no reason for me to avoid uniqueness techniques which are often among the most fun and elegant to use. But to each their own.

I think that elegance and style is a very subjective term. In this game I think it is essential to use objective terms. Objectively, if we intend by resolution only obtaining a correct solution I do not find valid reasons between distinguishing between a backdoor and a solution that uses methods that impose uniqueness. I believe this is the reason why many people do not accept this way of proceeding to reach the solution, see the http://hodoku.sourceforge.net/en/tech_ur.php http://sudopedia.enjoysudoku.com/Unique ... versy.html on this topic. However I agree that it is a personal opinion.

Ciao a Tutti
Paolo
Last edited by Ajò Dimonios on Sat Dec 07, 2019 7:58 am, edited 3 times in total.
Ajò Dimonios

Posts: 213
Joined: 07 November 2019

### Re: SK-Loops and MSLS's

Ajò Dimonios wrote:I think that elegance and style is a very subjective term.

Only partly. In most contexts they have measurable qualities most people would agree with. See elegance.

In this game I think it is essential to use objective terms. Objectively, if we intend by resolution only obtaining a correct solution I do not find valid reasons between distinguishing between a backdoor and a solution that uses methods that impose uniqueness.

Are you saying there's objectively no difference in guessing and using uniqueness methods? That would be an interesting opinion.

I believe this is the reason why many people do not accept this way of proceeding to reach the solution, see the "hodoku" comment on this topic.

Who are those "many people"? Followers of Denis Berthier? You don't find many on this forum who share his opinions on that matter. Just look at the Puzzles section and see that most solvers there are quite happy to use uniqueness techniques. Quite often they're among the most elegant solutions, in my subjective opinion.

However I agree that it is a personal opinion.

Oh, I thought you just claimed it was objectively wrong. Seems like a contradiction to me Either way there's no point in beating such a very dead horse. You have every right to think using uniqueness methods is wrong, objectively or subjectively. Makes no difference to me.

SpAce

Posts: 2674
Joined: 22 May 2017

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