A puzzle I published

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Re: A puzzle I published

Postby International_DBA » Sat May 25, 2019 6:55 am

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.
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Re: A puzzle I published

Postby SpAce » Sun May 26, 2019 1:54 am

International_DBA wrote: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.
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Re: A puzzle I published

Postby champagne » Sun May 26, 2019 6:37 am

SpAce wrote: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.
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Re: A puzzle I published

Postby SpAce » Mon May 27, 2019 3:43 am

champagne wrote: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.)
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Re: A puzzle I published

Postby champagne » Mon May 27, 2019 6:27 am

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.

SpAce wrote: (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.
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Re: A puzzle I published

Postby SpAce » Mon May 27, 2019 9:03 am

Hi champagne!

champagne wrote: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.

SpAce wrote: (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.
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