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Assassin 74
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gary w
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PostPosted: Tue Oct 30, 2007 11:38 pm    Post subject: brick wall Reply with quote

Hi fellow climbers.

Have "solved" it but only via two hypotheticals.Not very enlightening I know but I really couldn't see any way forward from the point I'ld reached.

The solution..so that you know if you're going wrong is



519762384
763584192
482913576
975241863
346875921
821396745
658127439
194638257
237459618

The placements I referred to earlier Mike were just the result of a LOT of combination work for N258 nothing very fancy.It took a while to eliminate 4 from r1c4 but I was able to show that this implied a 2 in r5c5 and I could show this to be impossible.Useful was the O-I for c6-> r3579c5=r1c4+8.This was instrumental in showing r1c4=7/8/9.Later combo work on r1c456-> r9c5=5 r9c4=4.
Then I really ran into a featureless wall of rock (I like this metaphor!!) and eventually opted for a hypo on the 9s in N 369.



Good luck in your efforts for a "proper" solution.

Best wishes!

Gary


Last edited by gary w on Tue Oct 30, 2007 11:56 pm; edited 1 time in total
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Para
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PostPosted: Tue Oct 30, 2007 11:50 pm    Post subject: Reply with quote

Hi Gary

Nice job. I know a one point where i could lay a hypothetical that should break open (most of) this puzzle, but i'd like to try and find another way through it. And i'm sure if i can't find anything i will try it.

Para
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PostPosted: Thu Nov 01, 2007 1:33 am    Post subject: brick wall Reply with quote

A privilege to go thro' Afmob's and Para's wts.



The combo work on the 15(3) cages in r1 + the 13 and 17 cages in N3 was very impressive stuff.I'ld placed all the digits they did with the exception of the 2 at r1c6 and the 7 at r5c5..and that's when I got stuck.But I don't believe I had as much climbing gear in place as these two expert mountaineers..so let's hope one/both can now make it to the summit.



Great to see two masters at work..even if the summit is still some way off.
This was a terrific puzzle,and even using hypos I felt pretty good on "solving" it.How would you rate it guys??

Regards

Gary
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mhparker
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PostPosted: Thu Nov 01, 2007 8:09 am    Post subject: Re: brick wall Reply with quote

gary w wrote:
Great to see two masters at work..even if the summit is still some way off.

I entirely agree with your sentiments about the first bit, Gary.

However, as far as the second bit is concerned, it looks like you spoke too soon - Para's already done it !!

Para wrote:
[Edit] Another set of moves added. Now 81 digits placed Wink

Congratulations, Para, on a truly impressive piece of work. Applause salut Very Happy Without knowing it, you've given me enough work for the next few days just trying to analyze and categorize all those great moves you made! Wink scratch
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PostPosted: Thu Nov 01, 2007 12:55 pm    Post subject: Reply with quote

Hi folks,

I wrote:
Without knowing it, you've given me enough work for the next few days just trying to analyze and categorize all those great moves you made! Wink scratch

OK, let's get the ball rolling...

Actually, I'm already regretting having given up on this puzzle too early. All that early combination crunching was driving me up the wall (literally!). Little did I know at the time that the second half of the puzzle would have been paradise for me, with all those opportunities for "advanced" techniques (as Andrew always refers to them, with the word advanced in quotes Wink). Ah well, can't win 'em all. But at least sitting back and analysing Para's WT (will look at Afmob's next) allows me to learn some new techniques, rather than simply using what I already know.

As many of you will have already seen, on the Maverick 1 thread, Para asked me how I would categorize his step 46 for the Brick Wall, which turned out to be representable as a Killer XY-Chain, although one of the links was more complicated than usual, because it was based on a digit pair rather than the usual single digit. The chain was very useful, because it resulted in an immediate placement at R6C7.

However, I've since found out that the same result (and more) can be achieved without a chain, as presented below. (BTW, hope you don't mind me doing this, Para!)

Firstly, for reference, here's the grid state after Para's step 45:

Code:
.--------------------------------.--------------------------------.--------------------------------.
| 12356789   12356789   12356789 | 789        346        24       | 12345678   12345678   12345678 |
:----------.---------------------+----------.---------------------+----------.---------------------:
| 2346789  | 12345678   12345678 | 579      | 3678       123468   | 1234578  | 23456789   23456789 |
|          '----------.          |          '----------.          |          '----------.          |
| 2346789    2346789  | 12345678 | 579        13       | 123468   | 12345789   1234789  | 23456789 |
:----------.----------'----------+----------.----------'----------+----------.----------'----------:
| 13456789 | 13456789   13456789 | 278      | 14         145      | 24689    | 12356      12356    |
|          '----------.          |          '----------.          |          '----------.          |
| 13456789   13456789 | 13456789 | 278        78       | 145      | 24689      24689    | 12356    |
:----------.----------'----------+----------.----------'----------+----------.----------'----------:
| 458      | 1245       1245     | 3        | 69         69       | 17       | 14578      14578    |
|          '----------.          |          '----------.          |          '----------.          |
| 5689       5689     | 458      | 1          2        | 7        | 34589      34589    | 39       |
:----------.----------'----------+----------.----------'----------+----------.----------'----------:
| 12       | 45789      45789    | 6        | 389        389      | 12       | 45789      45789    |
|          '----------.          |          '----------.          |          '----------.          |
| 123        123      | 789      | 4          5        | 89       | 126        126      | 789      |
'---------------------'----------'---------------------'----------'---------------------'----------'

From this position, we can basically use exactly the same type of move that Para had already used in his step 44, as follows:

Quote:
46. {35} in C7 only available in R1237C7
46a. -> R123C7 must contain at least 1 of {35}
46b. -> {359} combo blocked for 17(3) at R2C8 = {269/368/458} = {(6/8)..}

47. 17(3) at R2C8 (step 46b) blocks {168} combo for 15(3) at R1C7 = {267/348/357} (no 1)

48. 1 in C9 locked in N6 -> not elsewhere in N6

49. Naked single at R6C7 = 7
...

One reason for mentioning this (apart from the fact that it's a natural follow-up to my other post mentioned above) is that, despite being generally very powerful, SudokuSolver missed the above step 46, as well as missing Para's step 44. Hope you're reading this, Richard! Wink

I'm not sure what one would call the above move. It's a bit like a hidden killer pair, except that the distribution of the two digits can be 2:0 rather than 1:1. JSudoku picks up this type of move using AICs, although that seems like overkill in comparison to the much simpler logic I presented for step 46 above. Anyone else got any ideas on how best to categorize this type of move?
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Last edited by mhparker on Wed Feb 27, 2008 8:09 pm; edited 1 time in total
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gary w
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PostPosted: Thu Nov 01, 2007 2:38 pm    Post subject: brick wall Reply with quote

Fantastic piece of work Para.I missed your move 66..otherwise I might have got there before you. salut Very well done.I'm not sure whether I'll have the mental wherewithal now to tackle no.75. Rolling Eyes And how would you rate the "wall"??

Best regards

Gary
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PostPosted: Thu Nov 01, 2007 5:45 pm    Post subject: Reply with quote

c'est magnifique! well done para i got a long way last weekend but could not bust the top three nonets
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PostPosted: Thu Nov 01, 2007 6:17 pm    Post subject: Reply with quote

Hi

Thanks all. For the rating it is hard. It is the hardest puzzle i solved on my own. It is probably a high 2.0. But honestly as i have never solved a puzzle in the 2.0+ category on my own i find it hard to rate. I'd have to check the A48 Hevvie walk-through maybe to see how the moves compare. It could be a 2.5 rating but i think 2.0 is high enough. It took me 3 days to solve(officially 4 days as i had tried it once when Ruud posted but gave up pretty quickly). But only really started when Afmob posted his partial.

Mike:
That was the thing i had been looking for to make that move, just didn't find the right set of digits. It takes a lot of searching to get those types of hidden pairs(what probably is the right name). I did notice the 3 in R1237C7, which brought me to the chain, but i missed the 5. I think i used a similar move before once, just not the thing you think of quickly. Normally you'd like to have your hidden subsets within cages of single cells as this is usually more productive.
Btw this cage pattern really lends itself for those types of moves because every nonet has 2 cages that are only in that nonet and only in 2 columns. There were probably more, but at one point i was analysing links to see if i can find that break-through chain. I was glad to get back to the more regular techniques at one point though. Maybe that is why i rather stick to the more basic techniques, because i find link analysing far more tedious than combination crunching.
I think most of my chains were there earlier and the WT could be greatly shortened but i am going to keep it like this as it shows a bit more the work put into this puzzle.

greetings

Para
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mhparker
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PostPosted: Fri Nov 02, 2007 11:22 am    Post subject: A74 Brick Wall Reply with quote

Hi folks,

Ratings, ratings, ratings... Always a thorny topic.

Afmob wrote:
What a monster! That was the most difficult Killer Sudoku I've solved so far. But I got no idea about the rating since the hardest I've solved was about 1.75.

Para wrote:
It is the hardest puzzle i solved on my own. It is probably a high 2.0. But honestly as i have never solved a puzzle in the 2.0+ category on my own i find it hard to rate. I'd have to check the A48 Hevvie walk-through maybe to see how the moves compare. It could be a 2.5 rating but i think 2.0 is high enough. It took me 3 days to solve...

Despite not having completed this puzzle myself, I would totally agree with Para about the 2.0 rating. Tough as it was, the A48-Hevvie was significantly tougher. Of course, that last remark should definitely not be interpreted to mean that completing the Hevvie was in any way a better achievement than Para's great work on the Brick Wall. It just means that several T&E and/or "brute force"-like moves were needed to solve the Hevvie, the likes of which Para did not need to resort to on the Wall.

The original idea for the 2.0 rating was that it should represent about the most difficult puzzle possible (at the current state of the art) without having to resort to any hypotheticals, but typically requiring several advanced moved like AICs. I think that description fits Para's solution pretty well.

The A48 Hevvie, on the other hand, was a different story, requiring a big ugly hypothetical from me to even be able to start getting into the puzzle, let alone to solve it. It is also famous for having what is probably the biggest outie move in Killer Sudoku history, namely Richard's original step 102, which considered the possible permutations for no less than 8 outies, taking into account (if I remember rightly) about 3 constraining cells and 2 constraining cages! It took me about 2 hours and a PM to Richard to verify that one move alone, my analysis covering about 2 sides of A4! Richard commented not long ago about one of my moves (in another puzzle) being a "move on steroids". If so, then that step 102 of his could have won the Tour de France! Laughing Indeed, when Ed wrote up the consolidated WT, he dropped that move of Richard's in favor of a huge dual forcing hypothetical chain of Glyn's. The puzzle also contained innie/outie moves from Richard on disjoint (!) nonets, as well as at least one innie/outie difference move using individual (aligned) cells rather than complete cages. Oh, and there was some Nishio in there, too. No wonder Ed came up with the amusing acronym STALE (Still Takes A Lot of Effort Smile) for the consolidated WT! All in all, it was an interesting experience, if not always a "pretty" (and, in fact, usually downright ugly!) one. In contrast, the Brick Wall can be solved quite elegantly, as Para has just proved so well.

We shouldn't forget that a 2.0-rated puzzle also (according to the original definition) would normally be considered to be too difficult to be done as an individual exercise, typically requiring a team effort.

Whilst on this subject, I note that there's been a tendency for people to overrate puzzles recently. The A71 was a good example of this. Sure, it was very tough. But does it really deserve a 1.75 rating? A 1.75 rating was intended to correspond to something like the A60RP-Lite, which Cathy gave up on. Even Para took a couple of days to solve it, and it kept Ed occupied for about a week. By comparison, Cathy solved the A71 within a few hours. And yet they are both ranked identically in Ed's rating list...
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PostPosted: Fri Nov 02, 2007 8:24 pm    Post subject: Re: A74 Brick Wall Reply with quote

mhparker wrote:
I note that there's been a tendency for people to overrate puzzles
I agree to some extent - especially about A71. But if we are going to use A60 RP-Lite as the yardstick for 1.75, then I think the opposite will happen. True, that puzzle technically fits into the criteria for 1.75 since it requires only every-month killer techniques to solve. But every analysis that Richard and I have done on it as we try and get an accurate scoring method, ends up with a score in the 2.25-2.75 range, usually at the upper end of that range.

Also, it took me 3 weeks to get a solution I was totally happy with - and I had much more solving time then. Para's step 25(?) was pretty complex for a 1.75 puzzle.

Because a rating of 1.75 seems to cover such a huge spread of puzzle difficulties, Richard and I are currently trying to get the best scoring correlation with just the .50-1.50 range. Still proving very tricky.

Whatever scoring method we come up with, I think we are wise to keep talking about score for the machine method and ratings left for the humans to ponder Very Happy .

BTW - with the rating sticky, I try not to let the scoring development project influence which rating category a puzzle gets put into. Keep the opinions coming folks!

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PostPosted: Fri Nov 02, 2007 9:51 pm    Post subject: Reply with quote

mhparker wrote:
Ratings, ratings, ratings... Always a thorny topic.

...

The original idea for the 2.0 rating was that it should represent about the most difficult puzzle possible (at the current state of the art) without having to resort to any hypotheticals, but typically requiring several advanced moved like AICs. I think that description fits Para's solution pretty well.

...

We shouldn't forget that a 2.0-rated puzzle also (according to the original definition) would normally be considered to be too difficult to be done as an individual exercise, typically requiring a team effort.

Whilst on this subject, I note that there's been a tendency for people to overrate puzzles recently. The A71 was a good example of this. Sure, it was very tough. But does it really deserve a 1.75 rating? A 1.75 rating was intended to correspond to something like the A60RP-Lite, which Cathy gave up on. ...

Let me reply to this by first quoting what I recently posted on the Maverick 1 thread.

Andrew wrote:
I haven't tried A60RP-Lite or looked at any of the walkthroughs; must find time to do that. However it's clearly hard since that's the one that is always used as the comparison when deciding whether other puzzles should be 1.75.

It's easy to forget that each of these ratings represent a range. Obviously, from what people say about A60RP-Lite, it must be at the very top of the 1.75 rating range.

If we consider A60RP-Lite to be at the top of the 1.75 range, rather than just being a typical 1.75, then surely a lot of this argument goes away. There are currently 15 puzzles rated 1.75 in Ed's rating sticky. A60RP-Lite must surely be one of the hardest of the 15, not just a typical one. I've got no problem with A71 being rated 1.75, with it being at the lower end of that range.

Looking again at that list of 15 puzzles, and also at puzzles in the other rating groups, it appears that within each group they are listed to some extent according to difficulty with the hardest ones first. I must admit that I've only just noticed that. Where several puzzles are of similar difficulty they may then be listed in chronological order. In the 1.75 group, A60RP-Lite and Old School Assassin 72V2 come first with A71 and Maverick 1 last. I might not have put M1 last but I've no doubt that Para had a better solution than I did, based on a comment he made to me off-forum, so Ed got that right.

"We shouldn't forget that a 2.0-rated puzzle also would normally be considered to be too difficult to be done as an individual exercise, typically requiring a team effort."

Since the word normally has been used, it clearly allows for exceptions. I haven't yet looked at the walkthroughs for Brick Wall but it appears that 2.0 is a valid rating for it. Congratulations Para for completing it by yourself!! As you said, it's the hardest one you've done by yourself.

More recently from the Maverick 1 thread

Andrew wrote:
Maverick 1 felt to me at least as hard as any of the other 1.75s that I've done. I spent longer on it than on any of those others. It's definitely my longest walkthrough yet. Therefore I've no hesitation in rating Maverick 1 as 1.75.

Ratings by humans do, of course, depend on the difficulty of finding moves as well the moves themselves and the number of steps to finish a puzzle.

mhparker wrote:
I'm sure you're correct in rating the puzzle as 1.75 is correct as far as the difficulty of your solving path is concerned. However, there's a strong argument that states that the published rating for a puzzle should relate to the difficulty of the optimum path, not the difficulty of the actual path taken by any particular person.

I don't think anyone is disagreeing with Mike's final statement. In practice that means the optimum path of the walkthroughs posted on this forum. When shortcuts are used then clearly decisions have to be made about whether they affect the rating. Ed does an excellent job in his rating sticky, quoting appropriate comments, giving links to posted walkthroughs and outlines and deciding the rating for each puzzle. Applause
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PostPosted: Mon Nov 05, 2007 11:01 pm    Post subject: Reply with quote

Hi Andrew,

Andrew wrote:
Ed does an excellent job in his rating sticky, quoting appropriate comments, giving links to posted walkthroughs and outlines and deciding the rating for each puzzle. Applause

I agree wholeheartedly with your sentiments there, Andrew. Keep up the great work, Ed! Hopefully, the work is still (at least sometimes) enjoyable and not becoming mere drudgery!

Andrew wrote:
If we consider A60RP-Lite to be at the top of the 1.75 range, rather than just being a typical 1.75, then surely a lot of this argument goes away.

From what Ed's saying, the A60RP-Lite will most likely end up with a 2.0+ rating (read: SScore) anyway. And the A74 Brick Wall's SScore will probably be astronomical, due to the fact that SudokuSolver (version 1.4.3) can't solve it! This leaves room for the M1 to be rated at around 1.75, as you suggest, and as Ed has listed it. Incidentally, I was unsure as to whether to rate it as 1.5 or 1.75 when I published it. It was only the comparison with the A60RP-Lite that prompted me to opt for the lower rating.

Hopefully, Ed and Richard will release their long-awaited scoring system soon. Maybe an early Christmas present?

Andrew wrote:
Looking again at that list of 15 puzzles, and also at puzzles in the other rating groups, it appears that within each group they are listed to some extent according to difficulty with the hardest ones first. I must admit that I've only just noticed that.

Well spotted! I hadn't noticed any system here. Would be interesting to find out from Ed if this is indeed the case.
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PostPosted: Tue Nov 06, 2007 1:30 am    Post subject: Reply with quote

Andrew wrote:
Ed does an excellent job in his rating sticky
mhparker wrote:
Hopefully, the work is still (at least sometimes) enjoyable
Thankyou both. I do enjoy it especially when there are lots of opinions given about a puzzle or walk-throughs. I hope to do something similiar for 1-24, 25-49 and forum puzzles to make a complete index. But will need a reliable scoring method to make this really worthwhile.

I don't enjoy it when I forget to click PREVIEW enough Evil or Very Mad .

Andrew wrote:
it appears that within each group they are listed to some extent according to difficulty with the hardest ones first.
Spot-on - a guesstimation anyway. I hope that when we can get a reliable SSscore (BTW- thanks Mike for using the SScore spelling, but it distracts/annoys me every time I read it so have reverted to the extra 's') it can help to get the puzzles into order in each rating category.

BTW - I still have an open mind about basing ratings on (1?) optimized walk-through. For example, to put A72 Old School on the rating sticky as a 1.5 based on Mike's neat puzzle buster seems a bit silly when most puzzlers won't be able to find that trick.

Similiarly, A64V2 would seem very out of place as a 1.25. While Sudoku Solver found a really good short-cut, it was a really complex step to be called a 1.25 puzzle.

On the other hand, A55 was a good example of how Mike's WT really did make it a 1.25 compared to the much more difficult way that the rest of us used - even Cathy took a long time to find the right spot. It was a straight-forward move that was just hard for most of us to find.

BTW - Richard has Sukoku Solver V2 released. The scores given are NOT accurate. Perhaps one day they will.....Ho Ho HO Wink
Ed
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PostPosted: Tue Nov 06, 2007 12:52 pm    Post subject: Reply with quote

Hi Ed,

sudokuEd wrote:
I do enjoy it especially when there are lots of opinions given about a puzzle or walk-throughs.

Me too! Much better than a stony silence or indifference about a particular issue.

sudokuEd wrote:
I don't enjoy it when I forget to click PREVIEW enough Evil or Very Mad .

That's pretty harmless! The worst experience I had was to get my edit windows mixed up. I wanted to post a new puzzle, and so clicked the "Edit" button for one of my previous puzzle posts, in order to use that text as a template. Somewhere or other, I obviously lost track of which window was which and ended up (after clicking the "Submit" button) doing an edit instead of a new post! So now I not only had the new puzzle on an old thread instead of its own (new) one, but had also managed to nuke the original puzzle!! d'oh! Evil or Very Mad Furthermore, the only copy of the original (overwritten) post I had at my disposal was the one in my browser's history (!), which nevertheless allowed me (in true "Apollo 13" rescue mission fashion) to painstakingly work backwards and piece together the original text (including formatting tags) as it must have been just prior to the damage. Needless to say, all this happened just before I was intending to switch off my PC for the night...

sudokuEd wrote:
BTW - I still have an open mind about basing ratings on (1?) optimized walk-through. For example, to put A72 Old School on the rating sticky as a 1.5 based on Mike's neat puzzle buster seems a bit silly when most puzzlers won't be able to find that trick.

Similiarly, A64V2 would seem very out of place as a 1.25. While Sudoku Solver found a really good short-cut, it was a really complex step to be called a 1.25 puzzle.

At the end of the day, after the dust has settled and the shouting is over (who invented these phrases?), an automated solver can only rate a path that it actually takes. Seems obvious. Probably is. But the point is, if one doesn't want the rating to use that "really complex step", the automated solver should not take that step either. Otherwise, some or (in the worst case) all the subsequent steps relate to a path one is not realistically expecting any human being to take, thus partially or wholly invalidating the resulting rating computation.

If it's not possible to get the solver to take an alternative (more "human-like") path, it's arguably better to just bite the bullet and go with the unmanipulated rating, even if it seems significantly too high or too low. At least people will get used to the systematic way the rating is produced, with all its pros and cons, and learn to identify which types of puzzles tend to get overrated, and (correspondingly) which tend to get underrated. This is infinitely better than users not being able to detect any "rhyme or reason" behind the scores, which is a danger when fudge factors are used.

BTW, it would also be nice to get Richard's opinion on this (from a programmer's perspective) from time to time. I've noticed that he hasn't posted on the Assassin forum for nearly 3 months now! I guess that someone (mentioning no names! Wink) is keeping him too busy...

Clearly, no rating system will ever be (anywhere near) perfect, so maybe it would be a good idea to release the system earlier rather than later, so that we can all provide useful feedback for the second version. Trying to guess the feedback in advance and get it absolutely right first time is an almost impossible goal to achieve. For this reason, I expect that there will necessarily be some overlap between the two rating systems, such that our continued (subjective) ratings can continue to be used to enhance the automated scoring system.

Whatever form it ends up taking, I look forward to seeing (and using) the scoring system when it arrives.
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PostPosted: Tue Nov 06, 2007 2:13 pm    Post subject: Reply with quote

Mike, Ed
On the subject of ratings much depends on the perceived complexity of a move (its individual rating) and then the sequence of moves made.

The program which is almost used as the benchmark to rate vanilla Sudoku is Sudoku Explainer. It has predefined complexity ratings for each move, always picks its simplest next move and rates the whole puzzle using the rating of hardest move it uses. Needless to say it doesn't meet with universal approval. Smile

For vanilla Sudoku the most tweakable program is probably Sudocue, techniques can be left out, the order of what it does do can be changed within a hierarchy of techniques, and each technique can be weighted. So after some use each individual could select their own preferences and get a sneak preview of how tough the puzzle would be for them. Even then as the techniques get more complex even subtle changes in the order of moves in the same hierachy have an impact.

Perhaps Richard is already using weighted ratings for each move and experimenting with the order. Hard coding that for the user to tweak would add to the complexity of the program. JSudoku can have techniques switched off but the order of their hierachy is fixed.
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