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.