## How is the difficulty of a Sudoku puzzle determined?

Everything about Sudoku that doesn't fit in one of the other sections

### How is the difficulty of a Sudoku puzzle determined?

Hi
How is the difficulty of a Sudoku puzzle determined?

With the HoDoKu program it analyzes the puzzle and adds points depending which methods it would use.
For example...
130 points for a Skyscraper, 140 points for an X-Wing and 150 points for a Swordfish.

Is this a pukka method?

Are there other methods, and if so how do I find out about them?

bat999
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Location: UK

### Re: How is the difficulty of a Sudoku puzzle determined?

bat999 wrote:Hi
How is the difficulty of a Sudoku puzzle determined?

With the HoDoKu program it analyzes the puzzle and adds points depending which methods it would use.
For example...
130 points for a Skyscraper, 140 points for an X-Wing and 150 points for a Swordfish.

Is this a pukka method?

Are there other methods, and if so how do I find out about them?

There are many ways, but Sudoku Explainer is usually used in this Forum as a reference.

HTH

Mike Metcalf

m_b_metcalf
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Location: Berlin

### Re: How is the difficulty of a Sudoku puzzle determined?

m_b_metcalf wrote:... but Sudoku Explainer is usually used in this Forum as a reference.
OK thanks

A puzzle that scores 2182 with HoDoKu scores 7.1 with Sudoku Explainer.
I suppose Sudoku Explainer goes about it the same way, deciding how difficult it is by which methods are used.

EDIT

It's in the FAQ for Sudoku Explainer...

"How does the Sudoku Explainer rate the difficulty of a Sudoku?

The difficulty of a Sudoku is rated by the hardest solving technique that is required to solve it. This is not necessary the best rating scheme, and many other solvers might use different rating for some solving techniques (see previous question).

More precisely, the Sudoku Explainer uses the following difficulty ratings of the solving techniques:

1.0: Last value in block, row or column
1.2: Hidden Single in block
1.5: Hidden Single in row or column
1.7: Direct Pointing
1.9: Direct Claiming
2.0: Direct Hidden Pair
2.3: Naked Single
2.5: Direct Hidden Triplet
2.6: Pointing
2.8: Claiming
3.0, 3.2, 3.4: Naked Pair, X-Wing, Hidden Pair
3.6, 3.8, 4.0: Naked Triplet, Swordfish, Hidden Triplet
4.2, 4.4: XY-Wing, XYZ-Wing
4.5 - 5.0: Unique rectangles and loops
5.6 - 6.0: Bivalue Universal Graves
6.2: Aligned Pair Exclusion
6.5 - 7.5: Bidirectioal X-Cycles and Y-Cycles
6.6 - 7.6: Forcing X-Chains
7.0 - 8.0: Forcing Chains, Bidirectional Cycles
7.5 - 8.5: Nishio
8.0 - 9.0: Cell/Region Forcing Chains
8.5 - 9.5: Dynamic Forcing Chains
9.0 - 10.0: Dynamic Forcing Chains (+)
> 9.5: Nested Forcing Chains

It seems that the difficulties 1.2, 1.5, 1.7 and >= 2 correspond to the degrees 1, 2, 3 and 4 of some newspapers. Note that many solvers are rating Naked Singles easier than Hidden Singles (which is reasonable when candidates are always visible). According to some sources, "diabolical" Sudokus are those that are not solvable without trial and error. But there is a great controversy on what "trial and error" means.

The Sudoku generator uses the following levels:

Easy: difficulty 1.0 to 1.2 (can be solved using Hidden Singles in blocks only)
Medium: difficulty 1.5 (requires Hidden Singles in rows or columns)
Hard: difficulty 1.7 to 2.5 (can be solved without writing down candidates)
Fiendish: difficulty 2.6 to 6.0 (can only be solved by writing down candidates, but does not require Forcing Chains)
Diabolical: difficulty 6.2 or more (can only be solved with Forcing Chains)"
bat999
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Location: UK

### Re: How is the difficulty of a Sudoku puzzle determined?

A puzzle that scores 2182 with HoDoKu scores 7.1 with Sudoku Explainer.
...
"How does the Sudoku Explainer rate the difficulty of a Sudoku?
The difficulty of a Sudoku is rated by the hardest solving technique that is required to solve it.

In the HoDoKu manual i could not find, how exactly the score is determined, but it says that it is the sum of the scores of the single steps needed. So a main difference should be, that HoDoKu can rate a puzzle harder, where you need several advanced steps (which means that it takes a manual solver longer to solve it) than if it needs only one step with a "harder" technique.

Concerning Sudoku Explainer it also should be said, that it does not have ALS's as solving technique. Those (at least many of them) can also be spotted by manual solvers relatively easily, but they were hardly known, when Explainer was written. You may have noted that they are commonly used in the "Puzzles" section here. So the Explainer ratings for puzzles solvable with ALS's are overrated.
eleven

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Joined: 10 February 2008

### Re: How is the difficulty of a Sudoku puzzle determined?

eleven wrote:...it is the sum of the scores of the single steps needed

Yes, the "sum of the scores.."
I suppose HoDoKu could rate a puzzle as very difficult even though it only needed easy methods (but lots of them!).
bat999
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Location: UK

### Re: How is the difficulty of a Sudoku puzzle determined?

post60757.html#p60757
and a few other posts after it, go into details on my thoughts for how to rate a puzzle: but for the most part SE as mentioned above is the commonly used base line rating program used by this forum.

its good but as you noted has its faults.

hodoku has some rating advantages as it can change the order of operations of applied techniques and includes techniques not developed when se was published.
Some do, some teach, the rest look it up.

StrmCkr

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Joined: 05 September 2006

### Re: How is the difficulty of a Sudoku puzzle determined?

bat999 wrote:
eleven wrote:...it is the sum of the scores of the single steps needed

Yes, the "sum of the scores.."
I suppose HoDoKu could rate a puzzle as very difficult even though it only needed easy methods (but lots of them!).

It's actually worse than that. HoDoKu solves puzzles by applying various techniques in a specific order. Once it finds an elimination, it starts at the beginning of its "technique list" to look for the next one. Doing it that way may result in applying a number of techniques that are ultimately unnecessary. For example, it might find 3 W-wings before finding an XY-wing that solves the puzzle and was there all along. The puzzle gets a high rating because it "required" 3 W-wings and an XY-wing to solve it. Had the solver been programmed to look for XY-wings before W-wings, the rating would be much lower.

Don't get me wrong. I think HoDoKu is fantastic, but it does have its quirks.
Steve

SteveG48
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### Re: How is the difficulty of a Sudoku puzzle determined?

I am hopeful that Bernhard is still planning to release HoDoKu 2.3. He had a number of plans back in 2012/3. The difficulty rating in HoDoKu was designed to be personalized by each solver. All of the scores attached to each strategy have 'default' values both in 'Score' [a number ranging from 4 to 10000 ] and in 'Level' [Easy, Medium, Hard, Unfair, Extreme]. For my use, I have not changed the defaults much at all. I do now see XY-Chains as part of 'Hard' and I might say that Multi Colors belongs in 'Unfair' but these current thoughts are very personal and I may just change my mind. If Bernhard does return to this project, I would hope that he might consider JExocet patterns and SK Loops in the next release. Also on my suggested list would be Aligned Pair Exclusion, WXYZ Wings and a splitting of Sue De Coq into basic and extended [with different default scores]
ghfick

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