The New Sudoku Players' Forum

[denis_berthier]

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First, let me recall my global philosophy about classification or rating: there can't be any unique classification/rating system. Any such system depends on one's goals and even with fixed general goals, there remains many possible systems.

This "relativism" doesn't mean that all such systems are "equal". Some are clearly better than others:
- because they are intrinsic (e.g. invariant under Sudoku isomorphisms);
- and/or because they are founded in logic (instead of on arbitrary choices of rules/procedures);
- and/or because they can classify/rate all the Sudoku puzzles (or still better all the logic puzzles of some general type);
- and/or because they don't involve exotic patterns that apply only in rare cases.

But in any case, this "relativism" implies that one must be aware that adding a new resolution rule or (more generally a new resolution method, e.g. some exotic pattern of some form of T&E) in an existing classification/rating system requires some interpretation of this new rule/method in the original system. This is the only way the impact of the new rule/method can be estimated wrt to the original classification/rating system.
I know, traduttore traditore. But there's no way to avoid this.


Some examples of rating systems are SER, gsf's rating, q1, q2...

But what I'll consider here is my usual very broad universal classification:
- T&E(0) (~ solvable by Singles)
- T&E(1) (~ solvable by braids)
- T&E(2) (~ solvable by B-braids)
...
together with the sub-classifications specific to each T&E-level:
- the Bn hierarchy inside T&E(1)
- the BnB=T&E(Bn, 1) hierarchy inside T&E(2)
- the BnBB=T&E(Bn, 2) hierarchy inside T&E(3)
...

This universal classification doesn't take into account any generic or application-specific pattern that is not directly related to it - not even Subsets.
My view is, with respect to this classification, such patterns are short-circuits that allow to downgrade a puzzle form one level to a lower one (the downgrading depending on the puzzle).
This applies to the simplest patterns (such as Triplets) as well as to the most complex ones (such as sk-loops or Tridagons).

For an example of a Swordfish that brings down a puzzle from T&E(2) to T&E(0), i.e. Singles, see section 8.8.2 of [PBCS].
For an example of an sk-loop that brings down a puzzle from from B3B to gB=B1B, see section 13.6 of [PBCS].
For lots of examples of Tridagons that bring down a puzzle from T&E(3) to much lower levels, see this thread: http://forum.enjoysudoku.com/the-tridagon-rule-t39859.html
For an example of eleven's replacement method (not a resolution rule) that brings down a puzzle from W6 to Z4 (both within T&E(1)) see here: http://forum.enjoysudoku.com/post316286.html?hilit=replacement#p316286


Of course, it works both ways. You can start from any other classification/rating system. If you introduce anything new into it (e.g. some form of T&E), you create (puzzle-dependent) short-circuits between its levels. Example: the standard SER vs a version of SER without uniqueness; for an example by mith, see the end of this post: http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-1243.html

[denis_berthier]

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Someone asked me by email how the T&E-depth of a resolution rule (as defined in this thread) relates to the minimal T&E-depth necessary for proving that a pattern P is contradictory (as I have done in many posts related to anti-tridagons or k-digit patterns).
The answer is trivial:
the T&E-depth of a contradictory pattern P is defined as the T&E-depth of the resolution rule: P => FALSE