The New Sudoku Players' Forum

[MADDY_KAPUR]

Actually since a few months...I got interested in Sudoku, and I want to solve difficult puzzles, but wanna do them on a basis of difficulty..... I have tries gsf's method and Sudoku Explainer, they are not correct.

[JasonLion-Admin]

There is no good difficulty ranker for Sudoku since there is no good definition of what "difficulty" is. Many of use believe that no such definition is even possible. gsf's method and Sudoku Explainer are both "correct" for their specific definitions of "difficulty", but as you noticed those definitions are not good approximations to human solver difficulty.

[JPF]

The best way to define a rating system for the difficulty of sudoku puzzles close to the difficulty felt by humans is to set-up an ad-hoc committee of human solvers. The committee would solve all the puzzles submitted to them. The average time taken by the committee to solve the puzzle would by definition be the rating of the puzzle, measured in seconds.
To avoid that the growing competence of the members of the committee leads to a bias compared to amateurs, it would be advisable to renew each year a part, say 50%, of the committee...

JPF

[enxio27]

Not "correct", or merely not what you're looking for?? Perhaps you should first list the techniques that are in your own solving repertoire and look for puzzles with only those techniques, possibly with one or two additional techniques to provide more challenge.

I know my own limitations with respect to solving techniques. For many years I have used Ruud van der Werf's (Sudocue) rankings for difficulty of techniques. As I recall, he ranked the techniques specifically for human solvers. If a puzzle requires a technique not in my repertoire, I set the puzzle aside. At this point, I have trouble mustering up the interest to learn additional techniques, so puzzles that require them may or may not ever be attempted by me. I have access to plenty of puzzles that are "enxio27-solvable" but still challenging enough for me to find them enjoyable.

[SpAce]

Hi JPF,

The best way to define a rating system for the difficulty of sudoku puzzles close to the difficulty felt by humans is to set-up an ad-hoc committee of human solvers. The committee would solve all the puzzles submitted to them. The average time taken by the committee to solve the puzzle would by definition be the rating of the puzzle, measured in seconds.

Wouldn't that process give similar ratings to both hard and tedious puzzles? Even if a puzzle took a long time to solve because of many required steps, I wouldn't call it difficult if it could be progressed relatively constantly. A puzzle could also take a long time just because it has a narrow and non-obvious solve path, even if relatively few and easy techniques are actually required. (The latter case is a bit more related to actual difficulty.) Personally I think the most interesting rating is simply based on the hardest step required (like SER but with updated techniques and ratings), though it's obviously not the whole story. No single rating can be perfect even in theory, because there are many forces at play.

To avoid that the growing competence of the members of the committee leads to a bias compared to amateurs, it would be advisable to renew each year a part, say 50%, of the committee...

Why would that bias be bad? Why would anyone (including the amateurs themselves) even care about the opinion of amateurs? I'd rather fill the committee with the best experts in various manual solving methods. I think that would give a much more accurate picture of the real difficulty of a puzzle. If something is difficult for experts, it certainly is (much more) difficult for amateurs too, but not vice versa. The only time that isn't necessarily true is if the puzzle is hard or tedious to solve with methods preferred by experts but succumbs easily to amateur methods (guessing, T&E). Then again, I think most experts would probably find those kinds of solutions pretty quickly too (an example and some comments).

[enxio27]

Even if a puzzle took a long time to solve because of many required steps, I wouldn't call it difficult if it could be progressed relatively constantly. A puzzle could also take a long time just because it has a narrow and non-obvious solve path, even if relatively few and easy techniques are actually required. (The latter case is a bit more related to actual difficulty.) Personally I think the most interesting rating is simply based on the hardest step required (like SER but with updated techniques and ratings), though it's obviously not the whole story.

One of the strengths, IMO, of Ruud's rating system is that it takes into account not only the most difficult technique required, but also how many steps of each technique are required. Unfortunately, as I recall, his rating tool works only on single-grid vanilla puzzles.

[Hajime]

Where can I find info about 'Ruud's rating system'?
I could not find it at Sudocue.net .
My wish is to expand an honest rating system for human solvable puzzles, especially for all kinds of Gattai.

[SudoKai]

Where can I find info about 'Ruud's rating system'?...

Hope the following is what you seek.

Difficulty with Ratings
https://www.sudocue.net/guide.php#Ratings

Difficulty rating (Under: The Status Bar)
This number is calculated by adding the base scores for all solving steps, with some charges and discounts for special situations in the solving path. Details for this rating can be found in the Analysis Dialog. The tooltip will show the rating name that corresponds to this number.
https://www.sudocue.net/sudocueguide.php

Collection file analysis (.scl)
https://www.sudocue.net/fileformats.php

[tarek]

All of these rating systems unfortunately will depend on the resolution rules & the order they are applied. So there will be bias. You also mentioned the number of steps of similar difficulty. These can be accounted for with area under the curve but again it is biased to the order/configuration of the puzzle. The shortest solution path (closely similar to what the players are doing for the daily puzzles is another way of looking on how difficult a sudoku puzzle is but even that is biased towards the single step solution.

There are no winners here ... You just need to choose what suits you

tarek

[Pupp]

I also only recently, a few months ago, started solving sudokus on a serious basis. Before that, last year, I only dabbled in the easy sudokus I could solve without pencilmarks.

I use Soduko Explainer to rate puzzles, other members of the forum like SudoQue, and Minlex seems to be popular. You just need to get comfortable with one app and plug in various difficulty puzzles to get a feel for it's rating system.

Also, I've found that most apps that try to "explain" a step is terrible at doing it in a way that's helpful to me. What I do is look up the technique online for a more helpful tutorial created by a human.

A perfect example is "X-wings". My last puzzle had a couple "X-wings" in it, but I had a hard time finding them. The problem was I couldn't figure out how to exclude certain pencil marks in order to reduce the pattern to an X-wing. Something apps do poorly explaining, unless the entire step was to show how to exclude a pencilmark. Nothing more unhelpful than a program that "explains" a step by highlighting a cell and telling you to "ponder this pencilmark", followed by several other cells where you ponder over a pencilmark, then tells you that some other cell must be a certain number.
-It was a new higher level, so after fumbling around and finally solving the problem poorly, I decided to take a break for a few days in order to clear my head and dig into the subject.

There really isn't any concensus at to what difficulty a "hard" puzzle would rate. On Sudoku 10000, "hard" puzzles start around 3.2 when rated on Sudoku Explainer, but people here have posted "intermediate" puzzles from some nameless magazine that Sudoku Explainer rated about 4.5.
But, multiple sources: apps and website, all seem to agree that "nightmare" level puzzles start about 7.0 or so, and "ludacris" puzzles start around 9 or 10, depending on the app or website.

In any even't, if you can solve puzzles rated over 7.0 on Sudoku Explainer, your an excellent player.

[mith]

For clarification: minlex isn't a rating. It's a way of choosing a "canonical" form of a puzzle (which is useful for determining if two puzzles are isomorphic).

[Pupp]

For clarification: minlex isn't a rating. It's a way of choosing a "canonical" form of a puzzle (which is useful for determining if two puzzles are isomorphic).

Ahh, ok. I have no idea what a "canonical" form of a puzzle is, or what it means for puzzles to be "isomorphic".

[Mathimagics]

Ahh, ok. I have no idea what a "canonical" form of a puzzle is, or what it means for puzzles to be "isomorphic".

Two solution grids are isomorphic (aka "equivalent") if one can be transformed to the other by a set of standard operations (eg reordering the bands).

If two grids are NOT isomorphic, we say they are essentially different, or "ED".

There are 6,670,903,752,021,072,936,960 different solution Sudoku grids, but structurally there are only 5,472,730,538 essentially different grids.

Because there are so many isomorphisms, for analytical purposes we like to deal with a canonical form, this just means a standard representative of all the grids that are isomorphic to any particular one. If you sorted the full set then chose the first grid in the sorted list, that is a good choice - that is called the minlex grid (lexicographically minimal representative).

See: Wiki - Mathematics of Sudoku for a description of all the 3,359,232 x 362,880 ways that grids can be isomorphic.

[Pupp]

Ahh, ok. I have no idea what a "canonical" form of a puzzle is, or what it means for puzzles to be "isomorphic".

Two solution grids are isomorphic (aka "equivalent") if one can be transformed to the other by a set of standard operations (eg reordering the bands).

If two grids are NOT isomorphic, we say they are essentially different, or "ED".

There are 6,670,903,752,021,072,936,960 different solution Sudoku grids, but structurally there are only 5,472,730,538 essentially different grids.

Because there are so many isomorphisms, for analytical purposes we like to deal with a canonical form, this just means a standard representative of all the grids that are isomorphic to any particular one. If you sorted the full set then chose the first grid in the sorted list, that is a good choice - that is called the minlex grid (lexicographically minimal representative).

See: Wiki - Mathematics of Sudoku for a description of all the 3,359,232 x 362,880 ways that grids can be isomorphic.

Thanks.