The New Sudoku Players' Forum

[International_DBA]

Thanks for that feedback.
I produce these puzzles with a C program which uses a brute force algorithm.
I cannot grade them myself as I am not a strong Sudoku solver yet.
I grade them with Andrew Stuart's grader and solver but sometimes I think it misses the obvious.
One of the members in my Sudoku Puzzles Facebook group said exactly the same thing as you.
She said she was able to solve this puzzle relatively quickly.
I think it could be time to start experimenting with some different graders.

[SpAce]

I grade them with Andrew Stuart's grader and solver but sometimes I think it misses the obvious.
One of the members in my Sudoku Puzzles Facebook group said exactly the same thing as you.
She said she was able to solve this puzzle relatively quickly.
I think it could be time to start experimenting with some different graders.

I think that's a good idea anyway, but it might not help with this particular problem. The three graders I've ever used all gave pretty much the same results (within their own scales):

Sudoku Explainer: 8.9
Hodoku: 11352
SudokuWiki (Stuart's): 1315

All of them indicate a pretty hard difficulty (though they're calculated differently and could mean a bit different kinds of difficulty), and from their points of view it's true because they don't account for the easy guessing possibility found with this puzzle. I don't know if any public graders do, so it's probably something that needs to be checked separately if you want to avoid it. The software and puzzle generation experts on this forum can probably help with that. I'm just a manual solver, so I can only comment from that point of view.

In any case, the one grader that you definitely need is Sudoku Explainer, because it's the most "standard" scale there is (though far from perfect). The only thing that determines its grade is the hardest step needed to solve the puzzle (on a scale up to 11.9). For example, in this case 8.9 indicates that the puzzle contains at least one bottleneck of that level, which should make it pretty hard for most human solvers -- yet almost certainly solvable by any skilled ones. It's right on the edge, though, as the jump from 8.9 to 9.0 is quite steep. Any 9.0+ score indicates bottlenecks that may be very hard for even skilled solvers, unless the puzzle contains certain special patterns. I think 9.0 is also the cutoff where the SudokuWiki solver fails to find a solution; Hodoku's limit is around 9.6 (without any brute force steps).

[For comparison, your previous SE high scores were 8.4 and 8.3. All the others I checked were around 7.1-7.3 which is a very common neighborhood and a kind of a sweet spot for relatively easy but non-trivial puzzles.]

Both Hodoku and SudokuWiki calculate their scores differently from the Sudoku Explainer. They use accumulated scores based on all of the steps needed for a full solution, so they may give a high score for a puzzle that requires lots of not-so-hard steps (which just means it's tedious but not necessarily that hard). So, they rather measure the total amount of work needed to solve the puzzle, not the peak difficulty. From a human solver's point of view both aspects are relevant, but they're not really comparable. (In this case their scores indicate a lot of work -- probably. We wouldn't know that just by looking at the SE score, because it could just as well be a one-trick-pony with a single hard step. Then again, the Hodoku and SudokuWiki scores don't necessarily guarantee that it isn't.)

There's at least one more aspect, besides the mentioned backdoor issue, that affects the perceived difficulty of a puzzle but is not indicated by public graders. It's the narrowness of the solve path. A puzzle which only has one practicable way to solve it is usually more difficult than one with many similarly graded possibilities.

[champagne]

All of them indicate a pretty hard difficulty (though they're calculated differently and could mean a bit different kinds of difficulty), and from their points of view it's true because they don't account for the easy guessing possibility found with this puzzle. I don't know if any public graders do, so it's probably something that needs to be checked separately if you want to avoid it. The software and puzzle generation experts on this forum can probably help with that. I'm just a manual solver, so I can only comment from that point of view.

Hi Space,
By construction, a logic solver does not recognize a positive guess. If a backdoor exists, the rating for this backdoor would be the way to prove negative all other possibilities.
The main (and nearly only ) positive decision in such a solver is "last in row;column;box;cell". Harder steps lead in nearly all cases to eliminations. Counter examples exist as UR type 1 bugs type 1 and some patterns with an exocet, but this does not change the general view.

[SpAce]

By construction, a logic solver does not recognize a positive guess. If a backdoor exists, the rating for this backdoor would be the way to prove negative all other possibilities.
The main (and nearly only ) positive decision in such a solver is "last in row;column;box;cell". Harder steps lead in nearly all cases to eliminations. Counter examples exist as UR type 1 bugs type 1 and some patterns with an exocet, but this does not change the general view.

Hi champagne! I realize all that. My point was just that, when building puzzles for human consumption, all aspects that affect the perceived difficulty should be checked when a certain level of difficulty is implied. By definition, a grader based solely on a logic solver can't estimate the difficulty of finding a solution using guessing (or stumbling on a backdoor by coloring). While that seems irrelevant at first glance because no self-respecting solver accepts guessed solutions, it's not because of psychological aspects.

For example, I never *try* to find backdoors by guessing but I may still find them due to my coloring approach. With easier puzzles or the end games of harder ones it's no big deal (pretty much a given anyway) and doesn't change my approach at all, but it's very disappointing if the puzzle was supposed to be hard and it happens too soon. Of course the puzzle can still be solved normally just to find the logic steps (which is the point anyway), but it's just not as rewarding as when you truly need those steps to unwrap the solution. Here's another example where I lost motivation to solve normally because that happened (although I later completed the solution), even though it took much more to hit the backdoor than with this example.

This aspect of difficulty is totally separate from the logic grade (and shouldn't be mixed with it), but it's still real for human solvers. I'm not sure how it should be measured, though. At the very least, backdoors shouldn't be found within the most obvious coloring cluster like with the puzzle in question:

Code: Select all

.------------------.----------------------.----------------.
| 3      7    18   | 1689   15689  1589   | 568   2     4  |
| 268    9    128  | 168    1568   4      | 7     58    3  |
| 68     4    5    | 2      3      7      | 68    9     1  |
:------------------+----------------------+----------------:
| 4      128  278  | 13678  12568  12358  | 9     1'3"  57 |
| 2579   12   6    | 1379   1259   12359  | 123'  4     8  |
| 25789  3    2789 | 1789   4      12589  | 12    6     57 |
:------------------+----------------------+----------------:
| 2789   28   3    | 4      12789  1289   | 158   158   6  |
| 2789   6    2789 | 5      12789  123"89 | 4     13'8  29 |
| 1      5    4    | 3'89   289    6      | 3"8'  7     29 |
'------------------'----------------------'----------------'

That was my initial seed coloring (because of the multiple bilocation 3s), and when fully developed it produced not only some trap eliminations but also a solution for the '-parity (but no contradiction for the other, unfortunately). Any of those five '-candidates is a basics-backdoor, and finding that fact soon was practically guaranteed from the start (at least with my approach). In other words 3r4c8, 3r8c6, and 3r9c7 are backdoor eliminations. Proving them logically would be hard, but finding them was very easy -- too easy to motivate doing anything else. (Well, technically a full solution for the other parity is a proof too, though not a very satisfying or documentable one.)

[champagne]

Hi Space,
BTW, I have a pending full solution to publish elsewhere, I had to workj a litle more in it, but we have similarities with this discussion.
I just add some comments to your post

As soon as you have assigned enough cells (more than 30 in your PM), the number of bi values grows sharply, so most of such puzzles could be finished in the same way. I had in mind a backdoor appearing at the very beginning, which is relatively common.

(Well, technically a full solution for the other parity is a proof too, though not a very satisfying or documentable one.)

If I catch your point, yes... if the puzzle has only one solution.

[SpAce]

Hi champagne!

As soon as you have assigned enough cells (more than 30 in your PM), the number of bi values grows sharply, so most of such puzzles could be finished in the same way.

Yes, but not necessarily so quickly and certainly. A puzzle state may have lots of bivalue cells (or bilocation conjugates), some of them probably containing backdoors, but if they're isolated it's not obvious which ones to test first. For a computer solver it's easy to test every pairing, but a manual solver needs some way to prioritize. I usually pick the largest conjugate cluster for the first seeding, and then move onto smaller ones if that doesn't work (or is exhausted). In this case the largest cluster, i.e. the obvious choice for my initial seed, yielded the solution. That was the problem -- not that backdoors existed (as they usually do) but that they were located within the largest conjugate cluster and were thus found right away. It's different from a lonely bivalue/bilocation link containing a backdoor because it would take more (bad) luck to hit it quickly. In this case I just couldn't miss it.

I had in mind a backdoor appearing at the very beginning, which is relatively common.

Actually those backdoors are available at the very beginning here too, because the same bilocation cluster of 3s is as well. I just presented the puzzle after basics (9 assignments) because it wouldn't make sense to start coloring before that, but it made no difference really.

(Well, technically a full solution for the other parity is a proof too, though not a very satisfying or documentable one.)

If I catch your point, yes... if the puzzle has only one solution.

Of course. But, if we don't accept that as a premise, then we can't use uniqueness techniques either. That would cripple JExocets too, and in general make solving quite a bit more difficult in many cases.

[International_DBA]

Thanks for all your feedback.
I haven't been back for a while as my program has not come up with anything at your level but I would be interested to hear what you think of this one:

andrews-sudoku.blogspot.com/2019/10/sudoku-puzzle-no-453-extreme.html

[SpAce]

Thanks for all your feedback.
I haven't been back for a while as my program has not come up with anything at your level but I would be interested to hear what you think of this one:
https://andrews-sudoku.blogspot.com/201 ... treme.html

I don't know when or if I'll have time to actually solve it, but the three previously mentioned graders give pretty similar results to the last one:

SE: 8.9
Hodoku: 10100
SudokuWiki: 1184

The jump from SE 8.9 to 9.0+ is pretty high, both for puzzle generation (as far as I know -- I've never done that myself) and for solving. Most of the 9.0+ puzzles aren't much fun to solve manually anyway, so 8.9 can be considered the practical limit for most manual players. Then again, none of these numbers tell the whole story, as we saw last time.

--

Added (31 Oct 2019). I finally found some time to work it out. It's definitely better than the last one, as the backdoors aren't very easy to hit accidentally. That's good! Overall it was still pretty easy for me, but I think it matched the SE rating pretty well, so no disappointment there. I would presume that it's not that easy for most casual players.

I used a single coloring cluster (9s) to get almost to end, and then finished off with a Skyscraper. That was a very quick and straight-forward process, as I didn't worry about documenting the moves this time. Some of the eliminations would have probably been a bit complicated if actually written as chains or nets, though.

Hodoku seems to use 32 non-basic moves (including 4 forcing chains) with default settings, but it can do it with 3 moves (using nets). My approach, if documented, would have probably taken around ten moves. So, definitely not a one-trick-pony.

[International_DBA]

Thanks for all your feedback.
For the first time ever my program has produced a puzzle which came up as unsolvable.
Is there some way to solve it or not?
https://andrews-sudoku.blogspot.com/201 ... ble_2.html

[Mathimagics]

Oh, dear, you've used the U-word to label a published puzzle ...

That can only lead to embarassing blushes, I would think.

My primitive P&P solving established at least that it's a very hard puzzle (I haven't solved it yet, 45m so far) ... on the other hand JSudoku solved it in 4 guesses (including uniqueness proof).

[champagne]

rated 9.0/1.2/1.2 by skfr
not easy, but not so hard ???

[SpAce]

For the first time ever my program has produced a puzzle which came up as unsolvable.
Is there some way to solve it or not?

Code: Select all

...6..5......39..4.2.8.1....3..24..1..4....5.1......9...6...849.9..8.3..3....7...

Interesting. SudokuWiki can't grade (i.e. solve) it, but I think its cutoff is right at SE 9.0 (unless there's a JE, I suppose) so it's no wonder. Hey experts, what is the exact difference between 8.9 and 9.0 anyway? In my little experience with anything > 8.9 there's indeed a very clear jump in difficulty.

On the other hand, Hodoku has no problem, and only needs two forcing chains (out of 34 total non-basic moves). Not even nets, and it gives it about the same rating as the last one (10166) which needed four forcing chains. So, based only on Hodoku's rating, one wouldn't know that it's supposedly harder -- but it probably is because of the higher SE and SudokuWiki failing to solve it.

I haven't looked at the steps so I don't really know what makes it more difficult (SE-wise) than the previous one, but I'm pretty sure there's a reason. I'm hoping to find time to solve it manually and see for myself, but not right now.

[champagne]

Interesting. SudokuWiki can't grade (i.e. solve) it, but I think its cutoff is right at SE 9.0 (unless there's a JE, I suppose) so it's no wonder. Hey experts, what is the exact difference between 8.9 and 9.0 anyway? In my little experience with anything > 8.9 there's indeed a very clear jump in difficulty.

I can answer for both Sudoku Explainer and Skfr.
8.9 and 9.0 use the same solving technique "Dynamic chains".
The main difference is the number of candidates involved in the process.

I had a quick look in skfr to the critical step (where the rating 9.0 is produced). 14 eliminations with the same ratings are done in the same step. The contradiction comes in 2 ways possible here(Nishio, multi chains)

[SpAce]

I can answer for both Sudoku Explainer and Skfr.
8.9 and 9.0 use the same solving technique "Dynamic chains".
The main difference is the number of candidates involved in the process.

Ok, thanks. Does that perhaps mean larger ALSs in chains or something? After solving it manually my way, I looked at Hodoku's steps, and it used pretty large ALSs in some of the steps.

I had a quick look in skfr to the critical step (where the rating 9.0 is produced). 14 eliminations with the same ratings are done in the same step. The contradiction comes in 2 ways possible here(Nishio, multi chains)

I just solved it manually using pretty basic coloring with some smallish ALSs and URs mixed in, and it wasn't very hard at all. I couldn't even tell where the bottleneck was supposed to be. It took some time, though, as I had to use several coloring rounds, but they were all productive. Some were basic traps, some were loops, and some were contradictions. Not really sure how complicated they would have been if documented as chains. The last step was an easy BUG+2. I wouldn't have guessed it was 9.0. Still, definitely harder than any of the previous puzzles in this thread.

I used these as seeds for coloring:

4s, 78r1c9, 56r8c6, 35r7c6, 15r7c5

[m_b_metcalf]

For the first time ever my program has produced a puzzle which came up as unsolvable. Is there some way to solve it or not?

My solver reports a backdoor value 1r2c3.

Regards,

Mike