SudokuSolver Forum

! = 0.10 change from previous Score
pg# on this thread - PART B
(E) = Easy (H) = Hard

======================================================================
|A ##       Rate  Score|A ##       Rate  Score|A ##       Rate  Score|
|----------------------+----------------------+----------------------|
|A.51              0.95|A.53v2           !1.05|                      |
|A.52              0.95|A.53v2.5   E1.25  1.10|                      |
|A.52v2     1.50  !1.80|A.53v3      1.75 !2.80|                      |
|A.53             !0.90|A.53V0.1   H1.75 !2.65|                      |
|====================================================================|
                          (+ratings posts)
                              page #1


======================================================================
|A ##       Rate  Score|A ##       Rate  Score|A ##       Rate  Score|
|----------------------+----------------------+----------------------|
|A.54              1.00|A.56              0.80|A.57v2X   1.50   !2.05|
|A.54v2           !1.15|A.56v2    1.50   !1.80|A.58             !1.25|
|A.55             !1.50|A.57      1.00    1.05|                      |
|A.55v2   2.0!(t&E)5.80|A.57v1.5  E1.5   !1.40|                      |
|====================================================================|
                              page #2


======================================================================
|A ##       Rate  Score|A ##       Rate  Score|A ##       Rate  Score|
|----------------------+----------------------+----------------------|
|A.58v1.5  1.25   !1.20|A.60RP-L E1.75   !2.55|A.61             !1.40|
|A.59      1.25    1.35|A.50v2   3.0(t&E)!5.00|A.61X     1.50   !1.50|
|A.59v1.5  1.75   !2.15|SKX4v2    4.0      DNF|A.62      0.75    0.85|
|A.60      1.50   !1.75|A.61XV3            DNF|A.62v2    2.00   !5.10|
|A.60RP   !2.5(t&e)5.50|A.68v3    3 !(t&E)7.30|                      |
|====================================================================|
                        (+"Unsolvables" posts)
                              page #3


======================================================================
|A ##       Rate  Score|A ##       Rate  Score|A ##       Rate  Score|
|----------------------+----------------------+----------------------|
|A.63      1.00    1.05|A.64v2    1.75    2.15|A.66      1.00   !1.25|
|A.63v1.5  1.25    1.00|A.65      1.25    1.05|                      |
|A.63v2   H1.50   !1.35|A.65v2   H1.50   !3.50|                      |
|A.64      1.25   !1.25|A.65v3    1.50   !1.95|                      |
|====================================================================|
                              page #4


======================================================================
|A ##       Rate  Score|A ##       Rate  Score|A ##       Rate  Score|
|----------------------+----------------------+----------------------|
|A.66v1.5  1.75   !1.45|TransX    H1.5   !2.80|A.68v3    3 !(t&E)7.30|
|A.67      1.00   !1.20|TransX-L  1.25    1.00|A.68v1.5  1.25   !1.25|
|Vortex    1.75    1.70|A.68      1.25    1.05|A.69      1.25    1.15|
|Vort-Lite 1.25    0.95|A.68v2    1.75   !1.45|A.69v1.5 E1.50   !1.90|
|====================================================================|
                              page #5


======================================================================
|A ##       Rate  Score|A ##       Rate  Score|A ##       Rate  Score|
|----------------------+----------------------+----------------------|
|A.70      1.00   !1.00|A.71v2   E1.50   !1.45|A.72v2     1.50  !5.40|
|A.70v2           !1.80|A.71v1.5 H1.25    1.25|A.73       1.00  !1.00|
|A.70v3    1.25    1.15|CS        1.25    1.35|                      |
|A.71     H1.50   !1.65|A.72      1.00    1.20|                      |
|====================================================================|
                              page #6


======================================================================
|A ##       Rate  Score|A ##       Rate  Score|A ##       Rate  Score|
|----------------------+----------------------+----------------------|
|A.73v1.5 H1.50   !1.75|A.74BWall 2.00   !3.30|                      |
|Mav.01   H1.50   !1.90|A.75      1.25   !1.20|                      |
|A.74      1.00   !1.00|                      |                      |
|A.74v2    1.25   !1.05|                      |                      |
|====================================================================|
                              page #7

Ruud

In the forum on http://www.sudoku.org.uk you have posted a message rating some of their killers and including ratings for some recent Assassins.

It would be interesting if you could post a similar rating here for all the Assassins, except any currently active, and possibly some of the posted variants and other puzzles posted on this forum.

We could then see how these ratings compare with our own personal experiences of which were the hardest puzzles. It would also show whether Assassins have generally been getting harder, which I think they probably have.

Your rating counted the number of advanced steps and also the level of the most advanced step required. If you produce a list here, it would be interesting to know which advanced steps count for each of the levels.

I would also suggest that, if the list is posted, it should be as a one message topic with a sticky. Therefore if Ruud contacts me before posting a list, I'll delete this message. Any discussion of the list would probably be best done on a separate topic.

Andrew,

I see Ruud hasn't answered your post (yet), but I'm already wondering whether it's feasible to rate all assassins, as you suggest, because a program can surely only accurately rate puzzles it can solve, and several of the newer assassins are AFAIK not solvable by SumoCue.

Maybe Ruud can give some more input on this.

I will assemble and post a list of ratings for the Assassins so far, but don't be surprised when many of them are "off the scale". When SumoCue cannot complete an Assassin, I often copy the semi-finished puzzle between several programs to find additional steps, which are not reflected in the rating.

Keep these walkthroughs coming! They are my primary source for selecting additional techniques to implement in SumoCue.

cheers,
Ruud

Getting closer to a numerical, software generated version of this Andrew...but want to get some feedback on a smaller selection first - all from the A50+ Ratings Sticky.

Richard released (on Sunday) SudokuSolver V2.1.2 [edit to correct V number], available in the software forum, which includes what I call an SSscore. This software generated score tries to predict what human rating we, on the Assassin forum, end up giving to a killer after we solve it. Here is a summary of the SSscores for all the puzzles that are currently on the Ratings Sticky.

I have also included a suggested new rating for 14 of the puzzles that are on the Sticky. This is to bring those 14 puzzles closer into line with the SSscore AND still reflect the general difficulty that we human solvers commented on. If there was general consensus about the rating for a puzzle then it should not be one of the 14. But if there were a range of human ratings given, or none, then I propose moving these 14 to a rating category that better fits the SSscore.

I also hope to re-organize the Sticky to give a more accurate sense of hardest to easiest in each rating category. The 1.75 rating category, for example, appears to include a huge range of difficulty level (based on the SSscores).

Another reason for the change of rating category is that it raises the correlation between the predicted SSscore and the ratings from 85% to 89% for (.125) rating accuracy. This correlation is from a group of 130 killers including (most) Assassin, Assassin forum and a few other representative puzzles from DJApe, Michael Mepham's Diabolical killer's and a Times Deadly. All of these 130 get an SSscore below 2.0.

HOWEVER - I have had to guesstimate the rating for each of these puzzles not on the Sticky in order for Richard to develop/find a scoring routine which could predict these ratings. If it appears that the SSscore is reasonably accurate, then I will post the complete list, and hope to use it to increase the Rating sticky to include Assassins 1-24 and 25-49.

Just to restate - I would really like some specific feedback, especially objections/concerns about moving these 14 puzzles (3rd 'column' & in bold - thanks Mike). And of course, specific feedback about if you feel we are on the right track would be really appreciated.

Can someone put this list into nice wide columns for me please, or send me a PM with how to do it? Thanks.

Was Cheerful
Ed

.......Sticky Rating-- SSscore-- New Rating?
A01- 0.75 0.50....................0.50
A01 (V2)- 1.25 1.25

A48 Hevvie- 2.50 2.63

A50- 1.75 2.13
A50 (V0.2)- 0.75 0.63
A50 (V2)- 3.00 3.00

A51- 1.25 1.38

A52- 1.25 1.25
A52 (V2)- 2.00 2.00

A53- 1.00 1.00
A53 (V01)- 2.00 2.38
A53 (V2)- 1.25 1.00..............1.00
A53 (V25)- 1.25 1.25
A53 (V3)- 1.75 1.75

A54- 1.25 1.13
A54 (V2)- 1.75 1.50..............1.50

A55- 1.25 1.25
A55 (V2)- 2.00 2.13

A56- 1.25 1.00...................1.00
A56 (V2)- 1.75 2.13

A57- 1.00 0.88
A57 (v15)- 1.00 1.25..............1.25
A57 V2- 1.75 1.63

A58- 1.00 1.13
A58 (V15)- 1.50 1.13.............1.25

A59- 1.25 0.88
A59 (V15)- 1.50 1.63

A60- 1.50 1.50
A60 RP- 3.00 3.13
A60 RP-Lite- 1.75 2.50

Special X
Killer 4 (V2)- 4.0 no score

A61- 1.25 0.88................1.00
A61X- 1.50 1.50
A61X V3- 4.0 no score

A62- 0.75 1.0
A62 (V2)- 2.00 2.25

A63- 0.75 1.0
A63 (V15)- 1.00 1.38
A63 V2- 1.50 1.25..............1.25

A64- 1.25 1.13
A64 (V2)- 1.75 2.25

A65- 1.25 1.25
A65 (V2)- 1.75 1.75
A65 (V3)- 1.75 1.75

A66- 1.00 1.25
A66 (V1.5)- 1.50 1.88.................1.75

A67- 0.75 1.00

Vortex X- 1.75 1.25................1.50
Vortex X Lite- 1.25 0.88

Trans X- 1.75 2.13
Trans X Lite- 1.25 1.37

A68- 1.00 1.25....................1.25
A68 (V1.5)- 1.25 1.50..............1.50
A68 (V2)- 1.75 1.75
A68 (V3)- 3.00 2.88

A69- 1.25 1.38
A69 (V1.5)- 1.50 1.63

A70- 0.75 1.13
A70 (V2)- 1.75 1.38
A70 (V3)- 1.25 1.38

A71- 1.75 1.13.......................1.50
A71 (V1.5)- 1.25 1.75..................1.50
A71 Full
Border- 1.50 1.25

CS- 1.25 1.13

A72 - 1.00 1.38
A72 Old School- 1.75 2.63

A73 - 1.00 1.00

Maverick (1)- 1.75 1.25

A74- 1.00 1.25
A74
Brick Wall- 2.00 4.50
A74 (V2)- 1.25 1.25

A75- 1.25 1.50

A76- 1.00 1.13
A76X- 1.25 1.38

Diagonal
Surprise- 1.25 1.0

DJape
Easy (6/11)- 0.50 0.50

DJape
Brain (8/10/06)- 0.75 0.75

DJape
IQ (17/11)- 0.88 1.0

DJape
Insane (6/11/06)- 1.25 1.38

MM Online
Diab (19-11-07)- 0.63 0.63

Times
Deadly (673)- 0.63 0.63

Hi Ed,

Thanks for the status update. I get the feeling that this thread is going to get quite a few new posts in the near future...

Hmm, don't know what Andrew's going to say about SudokuSolver giving the A74 the same rating (read: SScore) as the M1! It proved impossible to convince Andrew about downgrading the M1 from 1.75 to 1.5, let alone making a 1.25 out of it, as is the case here!

That said, I notice that this puzzle is apparently not one of the 14. BTW, these 14 are the ones with three columns of numbers, right? Maybe it would be a good idea to highlight these (e.g., color or bold type) so that they are visible at a glance?

On the postive side, many ratings seem to be quite convincing, like the 1.38 for the A76X, which is mid-way between my estimation (1.5) and Para's and Afmob's verdicts (1.25). The Diagonal Surprise at 1.0 is probably also realistic. I think Andrew and I only rated it higher because (in contrast to machines) humans tend to have more of a problem with diagonal cages (although they are child's play in comparison to Para's toroidal jigsaws... ).

Keep up the good work!

I had to check back to on A74 and I see that I commented "This one flowed easily for quite a time, then got a bit stubborn so I'll rate it at 1.0". Clearly I had considered rating it lower. That would seem to suggest that the SS score of 1.25 for it is dubious.

I seem to remember something about SS finding a shortcut for M1 although I can't remember the details. That would explain it's absurdly low rating. Ratings shouldn't be based on shortcuts if there are normal solutions available which don't need hypotheticals or T&E. Mike has, in the past, stated that the rating should be based on the best human solution, which I take to be the best posted one. Clearly best doesn't includes solutions using shortcuts unless they are essential which, in the case of M1, they weren't. When I posted my walkthrough
For that reason I feel it should remain at 1.25.


Are you sure you've given the SS scores for these three in the right order?

It was generally agreed that A71 was the hardest ever original Assassin and that both variants were easier than the original. I see that I commented for V1.5 "I'll rate it at least a 1.25. Maybe it should be rated higher because it was a fairly narrow solving path and a lot of work after the breakthrough." Maybe therefore the 1.25 rating for V1.5 is low but it wasn't a 1.75.

The only other ones I will comment on are that the SS scores for Vortex X and Vortex X Lite look far too low. Maybe more cases of SS using shortcuts? I just don't believe those two scores.

I've commented before about each rating number representing a range of difficulty. However I'm not sure if I've commented that when humans rate puzzles they probably also take account of whether they found steps quickly or took a long time to find them; this may be done consciously or without realised that it has been done. It's not just the difficulty of steps but also the ease or difficulty of finding them.

It is always going to be problematical using a program to produce reliable preditions of how a human is going to rate a puzzle.

I agree with you Andrew that a human solver adds other factors into the perceived complexity of a puzzle - I can sometimes stare at a puzzle for hours before spotting an "obvious" move and so may consider it more difficult than it deserves. Equally, if I spot a key move early on - regardless of how "complex" it may be then the puzzle "feels" easier.

In the rewrite of some of the routines in SudokuSolver to try to get a better correlation to human percieved complexity, I've simplified a number of routines to ty to make them more "human" and along the way introduced a couple of new tricks that the forum has pointed out to me. The former now means that there should be more understandable moves earlier on and only getting to really convoluted combinations when the simple moves fail to turn up eliminations.

The other result is that there are a lot fewer T&E steps turning up in SS solver logs now - of the 135+ puzzles Ed and I have worked on, the only ones now requiring T&E are A39V2, A41V2, A55V2, A72V2, A74BW and A60RP.

But despite all that, there are still some real surprise in there. As you picked out - A71 is a great example. However many times I tried to persuade the program that the original A71 was harder than the variants, it stubbornly resfused to agree with me and consistently solves A71 much quicker, with fewer steps than either of the variants. I'm still sifting through some of the solver logs to see if there are any hidden complex moves that are not getting correctly factored - but there's nothing jumping out at me.

When all is said and done, the solver just mechanically applies a set of rules over the problem and Ed and I have calculated the best weighting to apply to each rule to get a close correlation to the perceived scores. Whilst we can use this to pose some questions, and maybe highlight some puzzles with "back-doors" that lead to quicker solutions - it's never going to replace the human factor. And much as I'm quite proud of the programming in SudokuSolver, I don't think I'm ever going to be able to give it enough intelligence to really rate puzzles like a human would.

Rgds
Richard

Hi guys,

I've now gone through Ed's posting in more detail, and tried to identify the ratings (sorry, SScores...) in most need of attention. There were 20 I could see where the SScores deviated substantially enough from the perceived ratings in order to potentially receive special attention. Here are my initial comments on these.

Of course, this is all only my personal view. But it shows that IMO only 9 puzzles in the list require "urgent" (detailed) attention, which is a very encouraging result! No rating scheme can ever be perfect, but the results obtained up to now are already better than I originally expected them to be. Thanks, Ed and Richard!

Whether all the deviations highlighted in red above need to be fixed prior to release is open to question. But at least it would be nice to have an explanation for the difference in each case.

BTW, last but not least, I've just noticed that no less than 11 of the above 20 puzzles are from me or Para. Seems like we're especially good at keeping SudokuSolver on its toes...

Good to see your post Richard. It seems quite a long time since we've heard from you.

It's interesting to read your views on the ratings. You and Ed are doing a great job. Without your continued improvements to SS there wouldn't be any ratings apart from the human estimates. Many thanks to both of you! =D> Thanks also to Mike for formulating the original rating definitions.

I've been a bit busy keeping on top of modifications to the solver - one of these days, Ed and I will get back to solving, if I can remember how .

Ed has done a tremendous job pushing on with the ratings work and prompting a lot of the changes to the program.

We are a lot closer on a lot of the ratings than I thought we'd ever get and, who knows, we may yet get a breakthrough on the problematic puzzles. More work analysing the solver logs compared to the forum walkthroughs and looking for any additional routines or simplifications and we may yet get there.

Rgds
Richard

I've went through the solver log of A71 and i think i can see what the problem is.
Firstly there's a really narrow solving path, even for Sudoku Solver. Secondly there are amazingly many contradictions between C7 and N6 and Sudoku Solver does this unbelievably effective. It took me loads of steps and time to accurately analyze these contradictions but Sudoku Solver does them really effectively and with some of its "basic techniques". After this it goes about in a really effective way through the puzzle. It just seems that this puzzle exactly fits Sudoku Solvers way of solving a puzzle. It will probably always stay a fluke.


Para

One thing that I don't think has yet been discussed is how we interpret each range.

For example Para and I gave different ratings for A77. Here are a few quotes, with Para's permission to quote from our PMs.
Actually I'm not sure about that last sentence now. On further thought people can have a different personal view of a puzzle's rating and still assign it the same rating value. For example a hard 1.25 might be 1.35 to me, because I consider 1.25 to cover the range 1.13 to 1.37 (make that 1.15 to 1.35 in practice) while someone who considers the rating value 1.25 to cover 1.25 to 1.49 might rate the same puzzle as 1.45. Both of us would rate this puzzle as a hard 1.25.

I must admit I was surprised when Ed first told me he took each rating range as extending from the rating value right up to the next rating value, for example that a rating value of 1.25 represented 1.25 to 1.49. It had started from a discussion about what an estimate of 1.0 to 1.25 meant. Ed said it must mean 1.0 because 1.0 to 1.24 was in that range while I said it meant that it could equally well mean either 1.0 or 1.25. I'd assumed, from when the ratings appeared, that each rating represented a range around the rating value so that one formed an opinion on the rating of a puzzle and then rounded to the nearest rating value. One thing is clear. When quoting a rating for a puzzle it's best just to give one value rather than a range; at least that removes one possible source of misunderstanding.

When I asked Para's permission to quote from our PMs he replied Well no need to quote from Para's A78V2 walkthrough message since it's been done there.

The important thing is that Para is confirming that A60RP-lite is at the top end of the 1.75 rating range, rather than just being a typical 1.75. That's also confirmed in Ed's excellent rating sticky where it is listed as the first in the 1.75 rating group, indicating that it's the hardest in that group.

It's interesting to see in the original definitions for the rating valuesAn interesting "maybe"!

I better get a flurry on . Congratulations Mike (IA). Thoroughly deserved. I also have doubts about your last statement Andrew. Our ratings are an approximation. On most puzzles, there is a reasonable consensus about the difficulty level. I think this is in large part due to Mike's original suggestion of just 6 different levels of difficulty for the 'normal' assassin puzzler (0.5 - 1.75). The validity of our 'gut feel' rating is shown by the fact that Richard and I have been able to get higher and higher correlation between the SSscore and forum ratings - at least up to low 1.75. After that, each 0.01 of Para's ratings is about a 10 added to the SSscore. More on that another time. Ruud must type fast, or has SudokuSolver V1. Part of Richard's upgrade to V2, which he has been too modest to mention, is that it solves (scores) up to 450 times quicker (A52: from 78 seconds to 0.17 sec)! An incredible achievement by Richard!

BTW - for those that use SudokuSolver, under "options" menu, down the bottom of the window is a "Step Delay" option. It has 6 different speeds, with the default setting on medium. I've put into my Christmas wish-list for Richard to change the default to "none". Occasionally I like the medium pace - something hypnotic, soothing and comforting about seeing SS show off those pretty colours while it powers along. I think I'm right that SudokuSolver V2.1.2, the current released version, scores it as 1.63. You have to make sure you go to the options and click on the "Scoring" routine before "scoring". Incidentally, the current scoring version 2 Richard and I are working on scores it higher than this at 1.87. This again shows why we need to keep some distinction between the human 'ratings' and the mechanical version. If the humans are agreed that this puzzle doesn't have that extra 'trick' essential to a 1.75 rating puzzle, then the SSscore is a good indicator of.....something else yet-to-be-discussed-at-some-length.

I haven't commented on the excellent feedback from Mike, Andrew and Para about the SSscores V1. Richard is doing another lot of changes to SS - but even before these we are getting higher correlations. So, will be back another time with updates.

Cheers
Ed

Just a comment on one pointIs that a new requirement? As far as I'm concerned a 1.75 rating requires either an extra 'trick' or a lot of very difficult work. Am I wrong to include the second part of that? When I solved a puzzle that took me far longer than any other that I'd managed to solve I rated it as a 1.75 and felt justified in doing so.

The trick not really a requirement, it's just something i notice in my walk-throughs of puzzles that are rated 1.75 by me. They always have something extra. It doesn't need to be a "trick" (like my Transformer puzzle trick really), it could be some really heavy combination analysis, really hard use of 45-tests or a very difficult single elimination that is needed to solve the puzzle. But they tend to have that something "extra". Of course it doesn't depend on that step alone. But it shows something for the difficulty that i need to resort to certain steps/moves. But as i say it is not a requirement, just something i notice in my walk-throughs.

greetings

Para

Good to see that reply. I was thinking in particular of really heavy combination analysis or really hard use of 45-tests when I made that comment.

Ed is planning to extend his Rating Sticky to cover Assassins 1 to 49 including, I assume, variants of these puzzles and other earlier forum puzzles.

He has told me that he would welcome estimated ratings for these puzzles, either in this thread or by PM to him, which could be quoted in the Rating Sticky.

As a start, I've just posted a walkthrough and rating for A17V2. This is a puzzle that Ed encouraged me recently to try again.

May I suggest that people who were forum regulars have a look at the posted walkthroughs for the earlier puzzles; you may still have memories of which ones were easy or hard.

I would also encourage newer forum members, plus those who read the forum and/or solve puzzles but haven't yet posted a walkthrough, to have a go at these earlier puzzles and post your opinions.

Earlier in the thread, it has been suggested that A1 should probably be downrated from 0.75 to 0.5. When I first started solving Assassins A13 had just appeared but I decided to start at A1. It only took me a few days to complete the first 12 Assassins, without using elimination solving, so it's reasonable to assume that most of them are likely to be 0.5 rather than 0.75. Then they started getting harder from A13 onward.

Please support Ed and Richard in their rating efforts! If you are not sure of the definitions for the various rating levels, they are given in the first message of the Rating Sticky. Remember that each rating level covers a range of difficulty levels; the ones quoted in the definitions are usually toward the hardest end of each level.

As I commented in the Assassin 5 thread, on Mike's definitions we can't rate Assassins lower than 0.75, which was what Caida rated Assassin 5.

Assuming we stick with that definition(*), I would say that most or all of A1 to A17 would be rated 0.75. Even though I still used insertion solving for A18, and possibly a few more beyond that, A18 was distinctly harder than the earlier ones so from memory I'll rate that at 1.0.

(*) At this stage I think the rating definitions are probably best left as they are. There may be some puzzles that need their ratings adjusting, I'll leave that to Ed and Richard, but we shouldn't be changing the definitions now except possibly to indicate whether the "benchmark" puzzles are at the top, centre or bottom of each rating range.

Maybe it's a bit of a generalisation but I would suggest that any Assassin or forum puzzle that needs elimination solving should be rated at least 1.0.

The next big jump in difficulty was Assassin 24. I think Ed said that SS came in with a relatively low rating for that one but I would imagine most human solvers would rate it a bit higher than SS did; I certainly would.

True - though it is working much better for SudokuSolver to score Assassin 1 at closer to .50 (see my previous update post).

Unfortunately, I can't give any definite scores yet. Richard and I are still doing the final, final, final tweaking of what scoring we think works best. It will blow you away when you see all the changes to SudokuSolver that Richard has made (Almost Locked Cages/Hidden Killer Mutuals/Cage Overlap etc, etc). A very nice Chrissie present =P~ . As a result, the scoring for many of the former "problem" puzzles is looking much better.

Lets continue this discussion about what each category means when we all have the next lot of SSscores to analyze - and have the solver to play with. Ho Ho HO!!

Cheers
Ed

It might be better to keep Assassin 1 rated as an easy 0.75 unless there's evidence that it was significantly easier than A2 to A12. If you downgrade A1 to 0.5 then you might have to also downgrade what is currently defined as 0.5. In view of Ed's comment maybe 0.75, or possibly the lower end of 0.75, might need to be redefined as one of the other very early Assassins if it is thought that A1 was significantly easier.Fair enough. Hope you didn't mind this small contribution limited to one specific part of the rating range.

After some heavy modifications to SumoCue, I have compiled a table with the ratings for all (currently 82) original Assassins, with the new SumoCue rating, the (average) human player rating and the rating by Richard's Sudoku Solver.

Since player ratings started with A50, there are only a few post-rated early Assassins. It would be nice if we had at least a player rating for A26, A33, A46 and A48.

There are 6 Assassins which cannot yet be solved by the improved version of SumoCue (this used to be more than 20). Assassin 69 is strange: it has a low player rating, while SMQ cannot solve it and SSRB rates it 2.0.



Like Sudoku Explainer, I'm using a rating system based on the most difficult technique required. A Killer solvable with singles only will have a score around 1.0. The average Assassin has a score around 4.0. This gives me a little room below the Assassin level to differentiate between easy and very easy killers.

If the technique has measurable elements, different scores are assigned to each measurement.

Currently, the measurable elements are:
1. Cage size
2. Cage sum distance from minimum/maximum
3. Number of rows/columns/nonets in a 45-test
4. Total border length in a 45-test
5. Total number of innies-outies in a 45-test
6. Naked/hidden subset size (2,3,4)

The SumoCue scores are preliminary and may change if the program is subject to further improvements.

Ruud

Thanks for the offer, Ruud!

As you can all see, I've just provided a WT and rating for the A33. Maybe one or more fellow forum members can join me in tackling the others that Ruud mentioned above? I hope so.

P.S.:BTW, what's that?!

Finally - update time!

SudokuSolver (v3) Score (SS(v3)score) tries to:
1) make sure the most notorious puzzles (A1, 50, 60, 60RP-Lite, 71 and all the recent ones) score very close to the Rating AND
2) that no easier puzzles (0.75 & 1.0 & low 1.25) score higher than their rating.

Method
To put it very crudely: uses a sum of the number of steps taken by a fixed routine order with individual weightings for each routine.

Generally, the SS(v3)score achieves its purchase through being equally inefficient at solving a puzzle. However, sometimes it finds an efficient way through a puzzle, so the score given will be (much) lower than humans' experience.

A rule-of-thumb is that any SS(v3)score above 0.97 (see Maverick 3) is going to be a hard killer. I'm finding this out this week while trying to make a uA94. The puzzle gets an SS(v3)score of 1.05 - but it's got me beat!! Hope I can finish it to become uA95!!

As always, your feedback is most appreciated. If you feel these scores are close enough, I'll use them to reorganise the Rating Sticky where the human feedback as quoted on the Sticky allows.

NOTE 1: lowest rotated score used for each puzzle (to minimize the effect of puzzle orientation on SS's solving routine). The original orientation's score may differ.

NOTE 2: variations for A50-59 not included since these don't correlate well and were from before we started consciously thinking about ratings.

NOTE 3: Puzzles that are 1-rating out are noted in the +/- 0.25 column [edit: look for the ones with "OUT" or "JUST in"]. Your reactions to any that are "OUT" or "JUST in" will be really interesting. Those reactions might make there way onto the rating sticky .

NOTE 4: We may need to have a discussion about adapting Mike's original rating definitions now that we have some firm numbers to work with.


SS(v3)scores for Rating Sticky Killers

Thanks, Ed!Yippee! :bounce: What's happened to that last column? Several puzzles are marked as "yes", even though they are way over 0.25 out, whilst others are within +/- 0.25, but are marked as "nearly" or even "no"!

Look forward to going through the list in more detail later.

Hope it's clearer now. I couldn't put smiley emoticons on all the "in" puzzles - but they are with-in 1 rating of the sticky.

Look for the ones that say "OUT" - they are more than 1 rating +/- from the Sticky. "JUST in" are borderline - so think about them as well.

At least I got (pretty) straight columns this time - thanks for the tip Nasenbaer .

Any more tips for presentation let me know by PM and I'll do my best!!

Thanks Mike.
Ed

I'm not so sure it would be such a good idea to include the SS scores in the rating sticky since:

1) They depend on the version of SS, so an update to SS means an updates to the scores and the sticky.
2) There are too many cases where the rating is "out".
3) You don't need to look for SS Scores here since you use SudokuSolver on your own where as the human ratings cannot be replaced (yet) by a software (2) and can only be found in the sticky.

I think especially hard Assassins (1.75+) are often "out" since it's tough to judge how difficult a chain/heavy combo analysis is and whether they are T&E or not. Using Mike's approach only chains which are AIC would be acceptable (so rating <= 2.0 if they are not too long) otherwise they are T&E and so the rating must be 2.5+.
And since most puzzles aren't of such difficulty we have only few examples and wts for such monsters, which is quite understandable if you have ever tackled one of those Killers. So the main focus for adapting SS Scores should be Assassins of rating <(=?) 1.75.

Great work Ed and Richard! =D>

Some very good points by Afmob. I agree that SS scores shouldn't go in the rating sticky because they depend on the version of SS. BTW the original rating sticky for A50 to A74 said that a few puzzles couldn't be solved by SS, stating how many steps were done. I wonder if those entries are still valid. I'm not suggesting that statements of how many steps were done should be removed, just updated if appropriate since we know that SS has been significantly improved since that sticky was first posted.

However there is still a valid place for SS scores in messages like Ed's one in this thread, where they are given in the context of a particular version of SS.

Is it really true that the only acceptable chains are AIC and that any others are T&E? Mike has made the point in previous discussions that AIC don't alter the grid state whereas some other steps that start with a "what if" assumption do change the state as they progress through a chain. That is clearly a valid distinction. All chains, whether AIC, contradiction chains, forcing chains or pure T&E must start with a "what if" assumption.

Then there is methodical combination/permutation analysis. Sometimes in my walkthroughs I present this as a series of sub-steps so it may at first sight appear to look like T&E. Others will just give a long string of combinations and permutations which don't give that same impression. How it contributes to the rating will clearly depend on the level of the analysis. In most cases a puzzle needing methodical combination/permutation analysis will be at least a Hard 1.25 and more likely a 1.5; some will rate higher than that if really heavy analysis or repeated analysis is required.

Ed asked us to comment on ones that are Just In or are Out. Of course that depends on one's interpretation of the range covered by each rating level. I must admit I was surprised when, in discussion with Ed, I learned that he considers the rating 1.25 to cover scores from 1.25 to 1.49; I subsequently learned that Para has the same interpretation. I had interpreted 1.25 to cover roughly 1.15 to 1.35 and still take that view. On that basis some of the ones that Ed scores In are, in my view out, and vice versa. The difference of interpretation only matters when comparing human ratings with SS scores which clearly must follow Ed's interpretation. Among humans the difference doesn't matter. If I rate a puzzle as High 1.25 meaning 1.35 and Ed gives the same rating meaning 1.45, we both know what we mean by a Hard 1.25; one that isn't quite hard enough for a 1.5 rating.

Even on Ed's interpretation there are several that are Just In, ranging from 0.21 to 0.24 above the Sticky rating but there is one that is 0.25 above so is listed as OUT.

Maybe it would be more realistic, IMHO, to consider that SS scores ought only to be quoted to the nearest 0.05, particularly since Ed mentions that puzzle rotation is used with sometimes different scores for the various orientations. I realise there would be a downside to this since any that are currently Just In at 0.23 and 0.24 would become OUT at 0.25.

There were a few cases where I was amazed at the differences.

A71 (Full Border) was one that Mike and I did as a "tag", mostly Mike with a few steps from me in the middle. While it was a relatively easy puzzle for a "tag" solution, I'm completely surprised that SS rated it as low as 1.11.

Mav 4 is scored at 2.57 by SS. Having solved that puzzle, although I haven't yet gone through posted walkthroughs or posted my one, I don't see how it can be that high. It took a bit of methodical combination/permutation analysis but not particularly heavy work.

A85 (Original Version), in which I participated a little in the "tag" solution was a real brute. I don't understand how SS rates it as 1.94 but at the same time T&E is stated. If a software solver needs to use T&E how can the rating be that low?

Discrepancies for the very highest rated ones are hardly surprising. I think Afmob was suggesting that we shouldn't be concerned about that, which I agree with.

Finally Ed's NOTE 4. "We may need to have a discussion about adapting Mike's original rating definitions now that we have some firm numbers to work with". Sorry but I must disagree with that. After all the discussions and work that has been put in, surely it's too late for that unless some minor clarification changes are being suggested. Some existing ratings for individual puzzles in the sticky may need to be changed; that suggestion has been around for some time. I know for example that several people think that Mav 1 should be downgraded from 1.75 to 1.5. If that happens I'll accept the majority view but it won't change my personal view of that puzzle .

Thanks! At the risk of causing confusion, I've adapted the list - rounded to .05, and WITHIN 0.15 (not 0.25)and without any use of UR which makes a big difference to A71 Full Border (and A50 [edit:& A74 BrickWall]).

Trans X Lite is the one I'm least happy about getting into the 1.50 bracket. Many of the others that are HIGH tend to reflect (at least some) of the actual experience of solvers where there was a range of opinions.No UR makes a huge difference to this one.
Haven't looked into this one yet but sounds like SS needs to be taught something new. This one is an anomaly [edit:fluke is probably a better word]. Shutting down all the hidden & locked cage options in SS (to help with many) means that it finds a very efficient solution for this one using "45 Insane i/o". We might need to bump up the weighting given to that routine. Here are the stats.

BTW - I really like many of the "simple Bowman Bingo Lite" that SS finds. Feels like the sort that we often use.
Assassin 85 Original
I've left these ones alone for this list.

SS(v3)scores for Rating Sticky Killers NOTE:within 0.15

I would also go along with this view. Seems like far too much maintenance overhead for poor old Ed to me, who would not only have to append the latest SScore to the list each time a new version of SS is released, but would also have to re-categorize and re-sort the list accordingly each time.Probably not, but it is my experience that most people underestimate the complexity of the chains they use.Actually, AICs should strictly speaking be found by locating and linking up the (relatively few) strong links in the grid, rather than by assuming that a particular cell (which?) contains a particular digit (which?)...This is also the approach I take when posting a puzzle. If I think a puzzle is maybe a "1.4", I usually just post it as a "1.5" and be done with it. In this case, I just see the rating as being a rough guide.

Thanks Ed for the update to the SS scores, rounding them to 0.05. It's interesting that you have also chosen to narrow down your comparison from +/- 0.25 to +/- 0.15. It's good that you have the confidence to do that.

It's interesting how removing UR from the SS score has little effect on several puzzles, brings A71 "Full Border" almost spot on but massively increases the SS score for A74 Brick Wall.

I won't re-open any discussion about UR, which some find acceptable and others don't. However I would suggest that if UR is to be used it probably ought to be considered more difficult than in a 1.11 rating, which is what A71 "Full Border" scored with UR. Of course I may be biased in saying that because I'm one who refuses to use it; it may be fairly easy to spot for those who use it.A very good point Mike. If people use it that way then it certainly reduces the "what if" aspect. Of course there may well still be the "what if" aspect present when you re-write as AICs some steps that others have given as contradiction moves.

I'll have to try to remember that point about looking for the relatively few strong links if/when I learn AICs. I may take Andrew Stuart's book, which has been on a bookcase untouched for quite a long time, with me when we go on holiday in June. However I'm not sure how much I'll be able to learn about advanced techniques if I've only got the book without a computer to try out things on an Excel worksheet.

Found a bug in SS which could affect many puzzles & their scores. Back later - hopefully not 5 months this time!!

Cheers
Ed

Richard's SudokuSolver v3.0.0 rates this as 0.48 and also 0.60 depending on
how I open the file. However if a puzzle ever deserved a rating of 0 it is
this one. I have been very interested in SudokuSolver ratings and have
used it to rate many puzzles from different sites with fascinating results.
I applaud the effort to get a rating scheme is - it is well worthwhile.

But - let me know what happened to this one.



Text: 3x3::k:1024:769:1794:259:516:1285:1542:2311:2056:521:2314:267:2060:1805:1550:1295:1040:785:1298:1555:2068:789:1046:2327:1816:281:538:2331:284:1309:1054:1567:800:545:2082:1827:1828:1061:1574:551:1320:2089:2346:811:300:2093:558:815:1840:2353:306:1075:1332:1589:822:1847:1080:2361:2106:571:316:1597:1342:1599:2112:577:1346:323:1092:837:1862:2375:328:1353:2378:1611:844:1869:2126:591:1104:

Nice April Fool's Day post Frank!

Taking the point of rating this diagram, there are 81 Naked Singles so the score must be slightly greater than zero.

Ha, nice one Frank. Richard loves bug-finders! He'll enjoy that one.

0.48 is the equivalent of a zero rating. We've always called this an Assassin killer scoring project - not killers in general. As you can tell, SS is not so good at the bottom end and tends to squash them in pretty tight. Ruud's software method that he was working on with SumoCue (unreleased) was much more aimed at the lower end and spread those out much more.An update here on any generalizations/observations/results would be very interesting, especially as I'm a regular lurker elsewhere (sadly not Frank's for a long while ).Thanks! Richard has a long list of wish-list changes to SS(v3.0) (hidden killer triple, ALS cage block, killer quad etc) including many things for other formats, so the next V of scoring won't be for a good while.

Just to restate my last update - SSscore(v3) is only reasonably accurate up to about 1.40. It will usually err on the lower side. This is because "easier" puzzles that have a long solution set the maximum at about 1.40.

Thanks for your interest.

Cheers
Ed

3x3::k:3072:3072:3072:3843:3843:3843:4614:4614:4614:4617:2826:2826:2826:1293:5134:5134:5134:2321:4617:4115:4116:4116:1293:4375:4375:3609:2321:4617:4115:4115:4116:5151:4375:3609:3609:2321:1316:1316:2342:2342:5151:3113:3113:3371:3371:5421:4910:4910:4912:5151:3890:1587:1587:4149:5421:4910:4912:4912:1338:3890:3890:1587:4149:5421:2112:2112:2112:1338:5444:5444:5444:4149:3656:3656:3656:4683:4683:4683:3406:3406:3406:

It was enjoyable to solve. Just the right difficulty level for me. Definitly does not need T&E or big combination crushing like some others.

Here is my walkthrough & the solution:
1. Innies of R5 -> R5C5 = 6
2. Innies of R234 -> R4C5 = 9
3. Cage 20/3 in C5 -> R6C5 = 5

4. Innies of C5 -> R19C5 = 15 = {78}
5. Innies of C1234 -> R19C4 = 12
6. Innies of C6789 -> R19C6 = 6
7. Cage 18/3 in R9C456 = {9(18|27)} -> R9C4 = 9, R9C6 = {12}, R1C4 = 3
8. Cage 5/2 in R23C5 = {14} (NP @ N2, C5)
9. Cage 5/2 in R78C5 = {23} (NP @ N8)
10. R9C56 = [81], R1C56 = [75]

11. Cage 12/3 in R1C123 = {129|246} = {2..} -> no 2 elsewhere in N1, R1
12. 8 of R1 locked in Cage 18/3 = {8(19|46)} -> no 8 elsewhere in N3
13. Since R2C5 = {14} -> Cage 11/3 in R2C234 <> {146} = {128|236|245} = {2..} -> R2C4 = 2

14. Innies of C1 -> R159C1 = 6 = {123} (NT @ C1)
15. Cage 8/3 in R8C234 = {1(25|34)} -> no 1 elsewhere in N7, R8 -> R8C23 = {1(2|3)}, R8C4 = {45}
16. R8C23&R9C1 = NT {123} @ N7
17. R8C235 = NT {123} @ R8

18a. Cage 13/2 in R5C89 = {49|58}
18b. -> Cage 9/2 in R5C34 <> {45} = {18}|[27], Cage 12/2 in R5C67 <> {48} = [39|75]
19. 7 of R5 locked in R5C46 -> not elsewhere in N5

20a. Cage 16/3 in N125 = {169|178} = {1..}
20b. Since R3C4 <> {17} -> R3C3&R4C4 <> 8
20c. Since R4C4 <> {6789} -> R4C4 = 1, R3C34 = [78|96]

21. Cage 9/2 in R5C34 -> R5C3 = {12}
22. R5C3 & Cage 5/2 in R5C12 = complex naked pair on {12} -> not elsewhere in N4
23. R5C7 & Cage 13/2 in R5C89 = complex naked pair on {59} -> not elsewhere in N6

24a. Innies of R2 -> R2C159 = 14 = {149|158|167|347}
24b. Since each in R2C59 <= 6 -> R2C1 = {789}
25. Cage 18/3 in R234C1 -> R34C1 = {456}

26a. Outies of N1 -> R3C4+R4C123 = 25
26b. R3C4 = {68} -> R4C123 = 17|19 with 5 locked in R4C123 = {458|568} = {58(4|6)}
26c. Since R4C1 = {456} (step 25) -> 8 locked in R4C23 -> Cage 16/3 in N14 = {358}
26d. -> R4C23 = {58} (NP @ R4, N4), R3C2 = 3, R4C1 = {46}

27a. 7 of R4 locked in R4C78 -> Cage 14/3 in N36 = {167|257|347}
27b. Since R4C78 <> {57} -> R3C8 <> 2
28. Max R34C6=[94]=13 -> Min R3C7=17-13=4. Cannot repeat 4 in cage 17/3 -> Min R3C7=5
29. R3C9 = 2 (HS @ R3), R24C9 = [16]|{34}

30. 14/3 in R2C159 = {149|347} = {4(7|9)..} -> no 4 elsewhere in R2, R2C1 = {79}
31. R2C1&R3C4 = NP {79} @ N1
32. Cage 12/3 in R1 = {246} -> R159C1 = [213]
33. R5C234 = [427], R8C234 = [215], R78C5 = [23], R1C23 = [64]
...

Edit revised from step 21 I don't remember how I eliminated the combination {167} for R2C159 = 14 which Para noticed.
However there was a nice X Wing on 5 in there

I'll list that alternating path with the X-Wing because I think it's interesting:
24a. Innies of R2 -> R2C159 = 14 = {149|158|167|347}
24b. Did not remember how I eliminated {167} here. Assume this is the case
24c. R2C159 = 14 = {149|158|347} = {(4|5)..}
24d. Since each in R2C59 <= 6 -> R2C1 = {789}
24e. Since R2C159 = {(4|5)..} -> Cage 11/3 in R2 <> {245} = {128|236}
25. Cage 18/3 in R234C1 -> R34C1 = {456}
26. 5 of R2 locked in R2C789 -> not elsewhere in N3

27a. 5 of C2 locked in R3479C2, 5 of C3 locked in R479C3
27b. This forms a grouped X Wing on 5 with Cage 16/3 & N7
27c. -> no 5 elsewhere in N7, Cage 16/3 must include a 5
27d. -> Cage 16/3 in N14 = {5(38|47)} (no {169})

27e. Alternatively, there is also a grouped X Wing on 5 with R34 * Cage 18/3 in C1 & Cage 16/3 in N14
27f. -> both cages must include a 5

28. 5 of C1 locked in R34C1 -> Cage 18/3 in C1 = {5(49|67)} (no 8)
29. Cage 21/3 in C1 = {8(49|67)}
30. R2C1&R3C4 = NP {79} @ N1
...

Nothing elegant I'm afraid, using quite a lot of cage combination analysis and a couple of conflicting combinations, but this is how I managed A51:

1. Innies r5 -> r5c5 = 6 -> r46c5 = {59}, 59 not elsewhere in N5/c5
-> 9(2) r5c23 <>3, 13(2) r5c89 = {49/58}-> 12(2) r5c67 can’t be {48}, 9(2) can’t be {45}

2. r23c5, r78c5 = 5 = {14/23}, not elsewhere in c5 -> r19c5 = {78}

3. Innies c1: r159c1 = 6 = {123}, not elsewhere in c1 -> r5c2 <> 1.

4. Innies c9: r159c9 = 20 -> r159c9 <> 1,2

5. Innies c1234: r19c4 = 12 = {39/48/57}

6. Innies c6789: r19c6 = 6 = {15/24}

7. Innies r234: r4c5 = 9, -> r6c5 = 5 -> r5c6 = 3/7 -> r5c7 = 9/5 -> Killer pair {59} in r789c5, not elsewhere in N6.

8. 6(3) r6c78+r7c8 = {123}, r4c8 sees all cells <> 1,2,3

9. Innies r2: r2c159 = 14, r2c1 <> 4

10. Innies r8: r8c159 = 16 -> since r8c5 is max 4, r8c9 <> 1,2

11. Combinations for 18(3) r9c456 = 189/279 -> r9c4 = 789, r9c6 = 12, r1c4 = 345, r1c6 = 45
-> combinations for 15(3) in r1c456 = {357/348} -> r1c4 = 3, r9c4 = 9 -> 5(2) r23c5 = {14} not elsewhere in N2/c5, 5(2) r78c5 = {23} not elsewhere in N8 -> r1c6 = 5, r9c6 = 1, r9c5 = 8, r1c5 = 7
-> r8c4 = 4/5 -> r8c23 = {123} – forms naked triple within N7 and r8 -> r8c9 <> 3
-> 14(3) r9c123 = 257/347/356; 13(3) r9c789 = 247/256/346.

12. 12(3) r1c123 = 129/246, 2 not elsewhere in N1, r1
-> 18(3) r1c789 must have 8: {189/468} not elsewhere in N3
-> r2c4 <> 8

13. 11(3) r2c234 = {128/236/245}, not 146 since can’t have both 14 -> r2c23 <> 7 -> r2c4 = 2 -> r5c3 <> 7.

14. 16(3) r3c34+r4c4 = {169/178/367} -> r4c4 <> 4,8; r3c3 <> 4,5,6,8

15. 2 locked to r5c123, not elsewhere in N4.

16. 1 locked to r6c789, not elsewhere in N6.

17. 7 locked to r5c46, not elsewhere in N5 -> r4c4 = 1 -> r5c3 <> 8, r3c34 = 78/96.

18. 17(3) r3c67+r4c6: max from r34c6 = 14 -> r3c7 <> 1,2

19. Split 20(3) r159c9 = {389/479/569/578}. No 7 in r15c9 -> r9c9 <> 4

20. 21(3) r8c678 = {489/579/678} -> if {489}, r8c78 <> 4.

21. Split 16(3) r8c159 = {259/268/349/367}. {358} not possible since would leave no options for 8(3) r8c234.

22. 13(3) r9c789 = {247/256/346}. If {247}, r9c9 = 7 -> r9c78 <> 7.

23. Split 14(3) r2c159 = {149/158/167/347}. Combination analysis -> r2c1 <> 5,6
-> 18(3) r234c1 = {459/468/567} -> r34c1 = {456}

24. 14(3) r34c8+r4c7: since r4c78 = min 6 -> r3c8 <> 9.

25. 15(3) r6c6+r7c67 = {168/249/267/348/357/456}. Combination analysis -> r7c7 <> 2,4.

26. 14(3) r3c8+r4c78 = {167/248/257/347/356}. Combination analysis -> r3c8 <> 6.

27. 17(3) r3c67+r4c6 = {269/278/359/368/458/467}. Combination analysis -> r3c7 <> 4.

28. 19(3) r6c4+r7c34 = {469/478/568}
a) If {469}, r7c3 = 9, r6c4 = 4, r7c4 = 6
b) If {478}, r7c3 = 478, r6c4 = 48, r7c4 = 47
c) If {568}, r7c3 = 6, r6c4 = 8, r7c4 = 5
Conclusion: r7c3 <> 5, else would conflict with r3c4.

29. r3c34 = 78/96 -> r3c67 can’t be 67 -> 17(3) r3c67+r4c6 can’t be {467}
-> r3c67 can’t be 68 -> if 17(3) r3c67+r4c6 = {368}, r4c6 <> 3.

30. a) If r7c8 = 1: r6c67 = {23} -> r4c79, r6c9 <> 2
b) If r7c8 = 2: r6c67 = {13}, r3c8 <> 2, r3c9 = 2 -> r46c9 <> 2
c) If r7c8 = 3: r6c67 = {12} -> r4c79, r6c9 <> 2.
In each case r46c9 <> 2
-> combinations for 9(3) r234c9: r23c9 <> 6, r3c9 <> 3,4

31. Split 14(3) r2c159 = 743/815/914
11(3) r2c234 cannot be {45}2 else removes all options for split 14(3) -> r2c23 <> 4,5
-> 5 locked to r3c12 -> r3c789 <> 5
-> 17(3) r3c67+r4c6 now = {269/278/368} -> r4c6 <> 4
-> 4 locked to r6c46 -> r6c1239 <> 4
-> Killer pair (68) in r3c467: r3c4 = 6/8, r3c67 must have 6 or 8 -> r3c12 <> 6,8
-> 8 locked to r3c46 -> r2c6 <> 8
-> 20(3) r2c678 = 659/956/947 -> r2c78 <> 3.

32. 19(3) r6c23+r7c2 = {379/469/478/568}. Combination analysis -> r7c2 <> 6,8

33. In N1:
a) If r2c23 = {18} -> r1c2, r3c3 = {79} -> 12(3) = {246}, r3c1 = 5, r3c2 = 3 …
b) If r2c23 = {36} -> 12(3) = {129} -> r3c3 = 7, r2c1 = 8, r3c12 = {45} -> r3c5 = 1, r2c5 = 4 -> 20(3) r2c678 = {569} Conflict with r2c23
Conclusion: r2c23 = {18}

Straightforward from here on

I've now looked at the walkthroughs posted by J-C and Cathy. We all used fairly similar steps, although not in the same order, but each had slightly different breakthrough moves.

I looked at more combinations and outies than the others. Some of them didn't contribute directly to the final solution but I've left them in because they were how I worked through the puzzle.

Here is my walkthrough

First the obvious steps

1. 45 rule on R5 1 innie R5C5 = 6
1a. 45 rule on R1234 1 innie R4C5 = 9 -> R6C5 = 5 (cage sum)

Now for the usual preliminary steps

2. R23C5 = {14/23}

3. R5C12 = {14/23}

4. R5C34 = {18/27}/[54], no 3,9, no 4 in R5C3

5. R5C67 = [39]/{48}/[75], no 1,2, no 3,7 in R5C7

6. R5C89 = {49/58}
6a. R5C67 (step 5) = [39/75] (cannot be {48} which clashes with R5C89), no 4,8

7. Killer pair 5/9 in R5C7 and R5C89 for R5 and N6, clean-up: no 4 in R5C4

8. R78C5 = {14/23}

9. Naked quad {1234} in R23C5 and R78C5, locked for C5

10. R2C234 = {128/137/146/236/245}, no 9

11. R2C678 = {389/479/569/578}, no 1,2

12. R234C9 = {126/135/234}, no 7,8,9

13. R678C1 = {489/579/678}, no 1,2,3

14. 19(3) cage in N47 = {289/379/469/478/568}, no 1

15. 19(3) cage in N587 = {289/379/469/478/568}, no 1

16. 6(3) cage in N69 = {123} -> no 1,2,3 in R4C8

17. R8C234 = 1{25/34}, 1 locked for R8, clean-up: no 4 in R7C5

18. R8C678 = {489/579/678}, no 2,3

19. R1C456 with R1C5 = {78} = {168/258/267/348/357}, no 7,8,9 in R1C46

20. 45 rule on C1 3 innies R159C1 = 6 = {123}, locked for C1, clean-up: no 1 in R5C2

21. 45 rule on C9 3 innies R159C9 = 20 = {389/479/569/578}, no 1,2

22. 45 rule on R2 3 innies R2C159 = 14 = {149/158/167/239/248/257/347/356}
22a. 7,8,9 only in R2C1 -> no 4 in R2C1

23. 45 rule on R8 3 innies R8C159 = 16 = {259/268/349/367} (cannot be {358/457} which clash with R8C234)
23a. No 5,6,8,9 in R8C5 -> no 2 in R8C9

24. 45 rule on C1234 2 innies R19C4 = 12 = [39/48/57]

25. 45 rule on C6789 2 innies R19C6 = 6 = {15/24}

26. R9C456 = [972/981] -> R9C4 = 9, R9C6 = {12}, R1C4 = 3 (step 24), clean-up: no 2 in R23C5, R1C6 = {45} (step 25)

27. Naked pair {14} in R23C5, locked for C5 and N2 -> R1C6 = 5, R1C5 = 7 (cage sum), R9C5 = 8, R9C6 = 1 (step 25 or cage sum)

28. Naked pair {23} in R78C5, locked for N8

29. 1 in R6 locked in R6C789, locked for N6

30. R8C234 = 1{25/34} (step 17), R8C4 = {45} -> no 4,5 in R8C23

31. Naked triple {123} in R8C23 and R8C5, locked for R8

32. Naked triple {123} in R8C23 and R9C1, locked for N7

33. R159C9 (step 21) = {389/479/569/578}
33a. 7 only in R9C9 -> no 4 in R9C9

34. R2C234 (step 10) = {128/146/236/245} (cannot be {137} because no 1,3,7 in R2C4), no 7

35. 16(3) cage in N125 = {169/178/268/367} (cannot be {259} because 5,9 only in R3C3, cannot be {349/457} because no 3,4,5,7,9 in R3C4, cannot be {358} because 3,5 only in R3C3), no 4,5

36. 15(3) cage in N689 = {168/249/267/348/357/456} (cannot be {159} because 1,5,9 only in R7C7, cannot be {258} because no 2,5,8 in R7C6)
36a. 5 only in R7C7 and 4 required in R7C6 for {249/348} -> no 4 in R7C7

37. 19(3) cage in N587 = {469/478/568} (cannot be {289} because no 2,8,9 in R7C4), no 2

38. R1C789 = {189/468} = 8{19/46}, no 2, 8 locked for R1 and N3
38a. R1C123 = 2{19/46}, 2 locked for N1

39. R2C234 (step 10) = {128/236/245} (cannot be {146} which clashes with R2C5) = 2{18/36/45}
39a. No 2 in R2C23 -> R2C4 = 2; clean-up: no 7 in R5C3
[At this stage I missed 7 locked in R5C46 for N5. This would have allowed R4C4 to be fixed in step 45a instead of step 51. A strange oversight considering my next step!]

40. 2 in R5 locked in R5C123, locked for N4

41. R2C159 (step 22) = {149/158/167/347}
41a. 7,8 only in R2C1 -> no 5,6 in R2C1

42. R234C1 = {459/468/567}
42a. R2C1 = {789} -> no 7,8,9 in R34C1

43. R8C678 (step 18) = {489/579/678}
43a. 8,9 only in R8C78 -> no 4 in R8C78

44. 14(3) cage in N36 = {158/167/248/257/347/356} (cannot be {149} because 1,9 only in R3C8, cannot be {239} because no 2,3,9 in R4C8), no 9

45. 16(3) cage in N125 (step 35) = {169/178/367}
45a. All combinations require {68} in R3C4 -> no 6,8 in R3C3 + R4C4

46. 45 rule on N7 2 innies R7C23 – 2 = 2 outies R6C1 + R8C4
46a. Max R6C1 + R8C4 = 14 -> max R7C23 = 16 -> R78C1 must contain 8 and/or 9

47. 45 rule on N1 2 innies R3C23 - 6 = 1 outie R4C1
47a. R3C3 cannot be the same as R4C1 -> no 6 in R3C2

48. 45 rule on N9 6 outies R6C6789 + R78C6 = 26, R78C6 = 10, 11 or 13 -> R6C6789 = 13, 15 or 16 and must contain 1,2 = 12{37/46/48/67}
48a. If R78C6 = {47}, R6C6789 = 8{12}4 -> no 8 in R6C9

49. 45 rule on N8 4 innies R78C4 + R78C6 = 22, R78C6 = 10, 11 or 13 -> R78C4 = 9, 11 or 12
49a. 45 rule on N7 6 outies R6C1234 + R78C4 = 36, R78C4 = 9, 11 or 12 -> R6C1234 = 24, 25, or 27 and must contain 9 in R6C123 = {3489/3679/3789/4689}

50. 14(3) cage in N36 = {167/248/257/347/356} (cannot be {158} because 1,5 only in R3C8)
50a. R4C78 cannot be {48} (clashes with R5C89) -> no 2 in R3C8
50b. 2 only in R4C7 -> no 8 in R4C7
50c. 1,5 only in R3C8 -> no 6 in R3C8

51. 45 rule on N3 6 outies R23C6 + R4C6789 = 33, R23C6 = 15 or 17 -> R4C6789 = 16 or 18 = {2347/2367}, no 8, 2,3,7 locked for R4 -> R4C4 = 1, clean-up: no 8 in R5C3
51a. R4C4 = 1 -> R3C34 = 15 = [78/96], no 3

52. 8 in R4 locked in R4C23, locked for N4
52a. 16(3) cage in N14 = {358} (only remaining combination) -> R3C2 = 3, R4C23 = {58}, clean-up: no 6 in R2C23, no 2 in R5C1
52b. Naked pair {58} in R4C23, locked for R4

53. 14(3) cage in N36 (step 50) = {167/257/347/356}
53a. 3 only in R4C7 -> no 4 in R4C7

54. 8 in N1 locked in R2C123, locked for R2

55. No 8 in R2C678 -> no 3 in R2C78 -> R2C9 = 3 (hidden single in R2)
55a. R2C9 = 3 -> R34C9 = 6 = {24} (cannot be {15} because 1,5 only in R3C9), locked for C9, clean-up: no 9 in R5C8

56. 1 in C9 locked in R67C9 -> R678C9 = 1{69/78}, no 5

57. R159C9 (step 33) = 5{69/78}
57a. 7 only in R9C9 and only other 5 in R5C9 -> no 8 in R5C9, clean-up: no 5 in R5C8

58. R5C8 = 8 (hidden single in N6), R5C9 = 5
58a. R159C9 (step 58) = 5{69/78}, R9C9 = {67} -> R1C9 = {89}

59. R5C4 = 7, R5C67 = [39], R5C1 = 1, R5C3 = 2, R5C2 = 4, R1C1 = 2, R9C1 = 3, R4C1 = 6, R8C3 = 1, R8C2 = 2, R78C5 = [23] (naked singles), clean-up: no 9 in R1C2, no 6 in R1C3 (both step 38a), no 8 in R2C2, no 5 in R2C3 (both step 39)

60. 4 in N9 locked in R9C78, locked for R9
60a. R9C789 = {247} (only remaining combination), locked for R9 and N9 -> R9C9 = 7, R1C9 = 8 (step 57)

61. Naked pair {56} in R9C23, locked for N7

62. 9 in C9 locked in R78C9, locked for N9

63. R6C3 = 3 (hidden single in N4) -> R67C2 = 16 = {79}, no 8

64. Naked pair {12} in R6C78, locked for R6, N6 and 6(3) cage -> R7C8 = 3, R678C9 = [619]

65. R4C2 = 8 (hidden single in C2)

and the rest is naked singles, naked pairs and cage sums

3x3::k:2048:2048:3842:3842:6660:1285:1285:3591:3591:6665:2048:1803:1803:6660:4110:4110:3591:5393:6665:6665:6665:4629:6660:3607:5393:5393:5393:5147:2844:4629:4629:6660:3607:3607:4386:3619:5147:2844:4902:4902:4902:4902:4902:4386:3619:5147:2844:3887:3887:3633:2866:2866:4386:3619:4918:4918:4918:3887:3633:2866:5180:5180:5180:4918:4928:2625:2625:3633:2884:2884:2630:5180:4928:4928:2378:2378:3633:4173:4173:2630:2630:

V1 relatively straightforward. Good job it's a bank holiday weekend in the UK - an extra day off to contemplate the V2!

1. Innies c5: r5c5 = 5

2. 16(2) r2c67 = {79}, 16(2) r9c67 = {79} (x-wings on 7 and 9) -> 7, 9 not elsewhere in r29 or c67.

3. Innies N1: r12c3 = 11 = [92/83/74/65]
Outies N1: r12c4 = 11 = [92/83/74/65]

4. Innies N3: r12c7 = 10 = [37/19]
Outies N3: r12c6 = 11 = [29/47]

5. Innies N7: r89c3 = 7 = {16}/{34}/[25]
Outies N7: r89c4 = 12 = [93]/{48}/[75] -> r8c3 <> 4, r9c3 <> 3

6. Innies N9: r89c7 = 15 = [69/87]
Outies N9: r89c6 = 12 = [39/57]

7. Innies N4: r456c3 = 14

8. Innies N6: r456c7 = 14

9. Outies c12/Innies c3: r37c3 = 13 = {49/58/67}

10. Outies c89/Innies c7: r37c7 = 6 = {15/24}

11. 8(3) in N1 must have 1, not elsewhere in N1.

12. 26(4) r1234c5 can't have 1 -> 1 locked to r3c46 -> not elsewhere in r3: r3c7 <> 1 -> r7c7 <> 5.

13. Innies r1234: r4c1289 = 10 = {1234}
-> r4c1 = 3/4 -> 20(3) r456c1 = 389/479 -> 9 locked to r56c1, not elsewhere in c1/N4.
-> r4c3 = 5678, r4c45 = {6789}, r4c6 = 68, r4c7 = 568 -> combinations for 14(3) r3c6+r4c67 -> r4c7 = 5, r3c6 = 1/3 -> split 6(2) r37c7 = {24} -> split 14(3) r456c7 = 5{36/18}

14. Innies r6789: r6c1289 = 26 (can't have 1)

15. Innies c1234: r5c34 = 3 = {12} -> r5c67 = 11 = {38} -> r5c1 <> 8 -> r5c2 = 4/6/7, r5c89 = {4679}

16. Outies - Innies N2: r4c5 - r3c46 = 3
a) if r4c5 = 6, r3c46 = [21]
b) if r4c5 = 7, r3c46 = {13}
c) if r4c5 = 8, r3c46 = [41/23]
d) if r4c5 = 9, r3c46 = [51]
-> candidates for r3c4 = 1/2/3/4/5

17. 11(3) r6c67 + r7c6 = 128/146/236 -> HS r8c6 = 5
-> r8c7 = 6, r9c6 = 7, r9c7 = 9, r2c6 = 9, r2c7 = 7
-> r1c6 = 2, r1c7 = 3 -> r5c7 = 8, r5c6 = 3
-> r6c7 = 1 -> r67c6 = {46} -> r4c6 = 8, r3c6 = 1
Clean up from placements: 15(2) r1c34 = [96]/{78}; 7(2) r2c34 = [25]/{34};
10(2) r8c34 = [19/28]; 9(2) r9c34 = [63/54]

18. NP {12} r58c3, not elsewhere in c3 -> r2c3 <> 2 -> r2c4 <> 5, r1c4 <> 6, r1c3 <> 9
-> 7(2) r2c34 = {34} not elsewhere in r2, 15(2) r1c34 = {78} not elsewhere in r1, 8(3) in N1 = {125} not elsewhere in N1

19. NP {34} r29c4, not elsewhere in c4 -> r3c4 = 5 -> r4c5 = 9 -> r4c34 = {67} -> split 13(2) r37c3 <> {67}

20. HS r5c4 = 1 -> r5c3 = 2, r4c2 = 1 -> r1c1 = 1, r1c2 = 5, r2c2 = 2 … lots of singles

Hi all

I agree with Cathy, relatively straightforward. Nothing spectacular, one nice move i hoped to put to use in a walk-through for once. (Not that it was actually necessary, but sometimes it can break open puzzles, like one of my V2's)

Walk-through assassin 52

1. 45 on C5: 1 innie: R5C5 = 5

2. 8(3) in R1C1 = {125/134}: no 6,7,8,9; 1 locked for N1

3. R1C34 = {69/78}

4. 26(4) in R1C5 = {2789/3689/4679}: no 1; 9 locked for C5

5. R1C67 = {14/23}

6. Deleted: useless step

7. R2C34 = {25/34}/[61]: no 7,8,9; R2C4: no 6

8. R2C67 = {79}: locked for R2

9. 20(3) in R4C1 = {389/479/569/578}: no 1,2

10.11(3) in R4C2 and R6C6 = {128/137/146/236/245} : no 9

11. 19(5) in R5C3 = 5{1238/1247/1346}: 1 locked for R5

12. R8C34 = {19/28/37/46}: no 5

13. R8C67 = {29/38/47/56}: no 1

14. R9C34 = {18/27/36/45}: no 9

15. R9C67 = {79}: locked for R9
15a. Clean up: R9C34: no 2

16. 45 on N1: 2 outies: R12C4 = 11 = [65/74/83/92]: R2C4: no 1
16a. Clean up: R2C3: no 6
16b. CPE in 8(3) cage in R1C1 + 7(2) cage in R2C3: R2C1: no 2,3,4,5 (I love this move, it works because the combination of the 7(2) cage depends on the 8(3) cage, either way the cages contain the digits {12345})

17. 45 on N3: 2 outies: R12C6 = 11 = [29/47]: R1C6: no 1,3
17a. Clean up: R1C7: no 2,4
17b. 1in N2 locked for R3

18. 45 on N7: 2 outies: R89C4 = 12 = [48/75/84/93]: R8C4: no 1,2,3,6; R9C4: no 1,6
18a. Clean up: R8C3: no 4,7,8,9; R9C3: no 3,8

19. 45 on N9: 2 outies: R89C6 = [39/57]: R8C6 = {35}
19a. Clean up: R8C7 = {68}

20. 45 on R1234: 4 innies: R4C1289 = 10 = {1234}: no 5,6,7,8,9; {1234} locked for R4

21. 45 on R6789: 4 innies: R5C1289 = 26 = {2789/3689/4589/4679/5678}: no 1

22. Naked Pair {79} in R29C6: locked for C6

23. Naked Pair {79} in R29C7: locked for C7

24. 14(3) in R3C6 needs 2 of {568} in R4C67 -->> 14(3) = [185/365]: R3C6 = {13}; R4C7 = 5

25. 45 on N6: 2 innies: R56C7 = 9 = {18/36}: no 2,4

26. 11(3) in R6C6 needs one of {1368} in R6C7 -->> 11(3) = {128/146/236}: no 5
26a. R8C6 = 5(hidden single); R8C7 = 6; R9C67 = [79](step 19)
26b. R2C67 = [97]; R1C67 = [23](step 17)
26c. Clean up: R1C3: no 6; R2C3: no 5; R8C3: no 3; R8C4: no 4; R9C4: no 8(step 18); R9C3: no 1, 4

27. Naked pair {18} in R56C7: locked for C7 and N6
27a. R4C2 = 1(hidden single); R1C1 = 1(hidden single)

28. 17(3) in R4C8 = {269/467}: no 3; 6 locked for C8 and N6
28a. 3 in N6 locked for C9

Mistake in step 29. Edited from here on.

29. 11(3) in R6C6 = {146} (last possible combination)
29a. R6C7 = 1; R67C6 = {46}: locked for C6
29b. R5C7 = 8; R34C6 = [18]; R5C6 = 3
29c. R5C4 = 1(hidden single); R5C3 = 2; R8C34 = [19]; R9C34 = [63](step 18)

30. 18(3) in R3C4 needs 2 of {679} in R4C34 -->> 18(3) = [576](R3C4 = 5; R4C34 = [76])
30a. R4C5 = 9; R2C34 = [34]; R1C34 = [87]
30b. R123C5 = [683]; R12C2 = [52]; R2C1 = 6

31. R3C123 = {479}: locked for R3

32. 20(3) in R4C1 = [398] (last possible combination)

33. 19(3) in R8C2 = [748] (last possible combination): R8C2 = 7; R9C12 = [48]

And the rest is all singles.

greetings

Para

It's good to have a slightly easier Assassin at least once a month.I assume that is the opening move, unless I missed something else. Para's step 16b was a neat one! While he said that it wasn't actually necessary, in the sense that it didn't break open the puzzle, it was still the most powerful move for eliminating candidates from R2C1.

The solving route I used was fairly similar to Cathy's one. Here is my walkthrough.

First the obvious step

1. 45 rule on C5 1 innie R5C5 = 5

Now for the usual preliminary steps

2. R1C34 = {69/78}

3. R1C67 = {14/23}

4. R2C34 = {16/25/34}, no 7,8,9

5. R2C67 = {79}, locked for R2

6. R8C34 = {19/28/37/46}, no 5

7. R8C67 = {29/38/48/56}, no 1

8. R9C34 = {18/27/36/45}, no 9

9. R9C67 = {79}, locked for R9, clean-up: no 2 in R9C34

10. X-wing {79} in R29C67, no other 7,9 in C67, clean-up: no 2,4 in R8C67

11. 8(3) cage in N1 = 1{25/34}, 1 locked for N1, clean-up: no 6 in R2C4

12. R456C1 = {389/479/569/578}, no 1,2

13. R456C2 = {128/137/146/236/245}, no 9

14. 19(3) cage in N7 = {289/379/469/478/568}, no 1
14a. Max R9C12 = 14 -> min R8C2 = 5

15. 10(3) cage in N9 = {127/136/145/235}, no 8,9

16. R1234C5 = {2789/3689/4679} = 9{278/368/467}, no 1, 9 locked for C5

17. 1 in C5 locked in R6789C5 = 1{238/247/346}

18. 45 rule on N1 2 innies R12C3 = 11 = [65/74/83/92], no 6 in R2C3, clean-up: no 1 in R2C4

19. 45 rule on N3 2 innies R12C7 = 10 = [19/37], no 2,4 in R1C7, clean-up: no 1,3 in R1C6

20. 8(3) cage in N1, R1C12 cannot be {12/13} (which clash with R1C67) -> no 4,5 in R2C2
20a. Cannot be {34}1 (which clashes with R1C67); {25}1 is still valid

21. 45 rule on N7 2 innies R89C3 = 7 = {16}/[25]/{34}, no 7,8,9 in R8C3, no 8 in R9C3, clean-up: no 1,2,3 in R8C4, no 1 in R9C4
[I missed the obvious 2 outies R89C4 = 12, no 6]

22. 45 rule on N9 2 innies R89C7 = 15 = [69/87], no 3,5 in R8C7, clean-up: no 6,8 in R8C6

23. 8(3) cage in N1 = 1{25/34}, R2C3 = {2345} -> 26(4) cage in N1 contains one of 2,3,4,5 = {2789/3689/4679/5678} (cannot be {4589})

24. 45 rule on C1234 2 innies R5C34 = 3 = {12}, locked for R5
24a. R5C67 = 11 = {38} (only remaining combination), locked for R5

25. 45 rule on R1234 4 innies R4C1289 = 10 = {1234}, locked for R4

26. 45 rule on R6789 4 innies R6C1289 = 26 = {2789/3689/4589/4679/5678}, no 1

27. 45 rule on C12 2 innies R37C3 = 13 = {49/58/67}

28. 45 rule on C89 2 innies R37C7 = 6 = {15/24}

29. R4C1 = {34}, R456C1 (step 12) = {389/479} -> R5C1 = {79}, R6C1 = {789}, 9 locked for C1 and N4
29a. 9 in R4 locked in R4C45, locked for N4

30. 45 rule on N4 3 innies R456C3 = 14 with R5C3 = {12}, valid combinations {158/167/257} (cannot be {248} which clashes with R456C1), no 1,2,3,4 in R6C3

31. 14(3) cage in N245 = {158/356} (only remaining combinations) -> R3C6 = {13}, R4C7 = 5, clean-up: no 1 in R37C7

32. Naked pair {24} in R37C7, locked for C7

33. Killer pair 3/8 in R34C6 and R5C6, locked for C6 -> R8C67 = [56], clean-up: no 4 in R8C34, no 4 in R9C3
33a. 8 in C6 locked in R45C6, locked for N5

34. 4 in N5 locked in R6C456, locked for R6

35. 45 rule on N6 2 remaining 2 innies R56C7 = 9 = [81], R5C6 = 3, R1C67 = [23], R3C6 = 1, R4C6 = 8 (cage sum), clean-up: no 5 in R2C3, no 6 in R1C3 (step 18), no 9 in R1C4, R2C7 = 7 (step 19), R2C6 = 9, R9C67 = [79], clean-up: no 3 in R8C3
35a. R4C5 = 9 (hidden single in C5)

36. R12 = {14/15}, 1 locked for R1 and N1

37. Killer pair 2/3 in R2C2 and R2C34, locked for R2
37a. 2 in R2 locked in R2C23, locked for N1

38. Min R45C2 = 5 -> max R6C2 = 6
38a. R456C2 = {146/236/245} (cannot be {137} which clashes with R456C1), no 7
38b. 1 in R4C2 -> no 4 in R4C2

39. 8 in N9 locked in 20(4) cage = {1289/1478/2378/3458}
39a. R7C7 = {24} -> no 2,4 elsewhere in 20(4) cage

40. 45 rule on R123 1 outie R4C5 - 4 = 1 innie R3C4 -> R3C4 = 5, clean-up: no 2 in R3C3
[This could have been done after step 35a, when it would have simplified some of the steps after that one. Alternatively there was R4C34 = {67} -> R3C4 = 5.]

41. R5C4 = 1 (hidden single in N5), R5C3 = 2

42. R4C2 = 1 (hidden single in N4), R56C2 (step 38a) = [46], R4C1 = 3, R56C1 (step 12) = [98], R4C3 = 7, R4C4 = 6, R6C3 = 5, R67C6 = [46], R1C12 = [15], R2C2 = 2 (cage sum), clean-up: no 3 in R9C3, no 4 in R9C4, no 9 in R1C3, no 8 in R1C4 -> R1C34 = [87]

and the rest is naked singles, naked pairs and cage sums

3x3::k:4608:4608:1794:1794:5892:1797:1797:2055:2055:4617:4608:2571:2571:5892:3342:3342:2055:6673:4617:4617:4617:4373:5892:2839:6673:6673:6673:3099:5404:4373:4373:5892:2839:2839:5154:3107:3099:5404:5926:5926:5926:5926:5926:5154:3107:3099:5404:3119:3119:5425:4658:4658:5154:3107:6198:6198:6198:3119:5425:4658:4924:4924:4924:6198:2624:1601:1601:5425:3908:3908:3910:4924:2624:2624:2634:2634:5425:2381:2381:3910:3910:

Hi folks,

Here's the full walkthrough for the V2, based on our tag solution. I incorporated JC's hidden triple in R1, as well as making some minor alterations in the opening sequence.

I also added a couple of missed killer triples (steps 29 and 31c) that changed the course of the game a bit, making it less dependent on conflicting combinations.

Despite several comments to the contrary, the puzzle was not that difficult - certainly not "terrifying", and easily within range of ordinary mortals. Nevertheless, many thanks, Ruud, for providing this V2, thus giving us all a chance to get a small insight into the new JSudoku. Keep those V2's coming!

Talking of JSudoku (my favorite subject at the moment! ), it made heavy going of this puzzle, using no less than 12 XY-chains - despite JC's comment on the Solving Techniques forum that they are

. Not only that, it also hammered those conflicting combinations (especially in columns 4 - 6) time and time again, driving me almost into a state of delirium trying to follow it! Still, I'm looking forward to getting my paws on it as soon as it's out the door.

Now to the walkthrough, which is not in tiny text due to the next Assassin being just a few hours away and the fact that it was a tag solution anyway.

Enjoy!


Assassin 52V2 Walkthrough

1. Innie C5: R5C5 = 1

2. 7/2 at R1C3: no 7,8,9

3. 7/2 at R1C6: no 7,8,9

4. 8/3 at R1C8 = {1(25|34)} (no 6,7,8,9)
4a. 1 locked in 8/3 at R1C8 -> not elsewhere in N3
4b. Cleanup: no 6 in R1C6

5. Hidden triple on {789} in R1 at R1C125 -> R1C125 = {789}
5a. -> R1C125 forms split 24/3 cage in R1 -> R2C8 = 1 (outie, R1)

6. 18/3 at R1C1 = {(29|38)7}
6a. 7 locked in R1C12 -> not elsewhere in R1 and N1
6b. {23} only in R2C2 -> R2C2 = {23}
6c. Cleanup: no 3 in R2C4

7. 10/2 at R2C34 = {28|37|46}: no 5,9

8. 13/2 at R2C6 = {49|58|67}: no 2,3

9. 11/3 at R3C6 = {128|137|146|236|245}: no 9

10. 21/3 at R4C2 = {489|579|678}: no 1,2,3

11. 20/3 at R4C8 = {389|479|569|578}: no 2

12. 10/3 at R8C2 = {127|136|145|235}: no 8,9

13. 6/2 at R8C34 = {15|24}: no 3,6,7,8,9

14. 15/2 at R8C6 = {69|78}: no 1,2,3,4,5

15. 10/2 at R9C3 = {19|28|37|46}: no 5

16. 9/2 at R9C6 = {18|27|36|45}: no 9

17. Outies N1: R12C4 = 8/2 = [17]|{26} = {(1|2)..},{(2|7)..}
({35} blocked because both 3 and 5 unavailable in R2C4)
17a. -> R1C4 = {126} (no 3,4,5), R2C4 = {267} (no 4,8)
17b. Cleanup: R1C3 = {156} (no 2,3,4), R2C3 = {348} (no 2,6)

18. Outies N3: R12C6 = 9/2 = [18|27|36]|{45}: no 9 in R2C6
18a. Cleanup: no 4 in R2C7

19. Outies N7: R89C4 = 5/2 = {14}|[23] = {(1|2)..}
19a. -> R8C4 = {124} (no 5), R9C4 = {134} (no 2,6,7,8,9)
19b. Cleanup: R8C3 = {245} (no 1), R9C3 = {679} (no 1,2,3,4,8)
19c. 8 locked in 24/4 at R7C1 = {8..} (no eliminations yet)

20. Outies N9: R89C6 = 13/2 = {67}|[85|94]
20a. -> R9C6 = {4567} (no 1,2,3,8)
20b. Cleanup: R9C7 = {2345} (no 1,6,7,8)

21. Outies C12: R37C3 = 13/2 = {49|58}|[67] (no 1,2,3; no 6 in R7C3)

22. Outies C89: R37C7 = 10/2 = {28|37|46}|[91] (no 5; no 9 in R7C7)

23. Innies C1234: R5C34 = 15/2 = {69|78} (no 2,3,4,5)

24. Innies C6789: R5C67 = 7/2 = {25|34} (no 6,7,8,9)

25. Innies N4: R456C3 = 12/3
25a. min. R5C3 = 6 -> max. R46C3 = 6 -> R46C3 = {(1|2)..}

26. R12C4 and R89C4 form killer pair on {12} in C4 -> not elsewhere in C4

(27. {129} now unavailable for 12/3 at R6C3 ({12} only in R6C3)
27a. 12/3 at R6C3 = {138|147|237|156|246|345} (no 9)

[Andrew suggested that steps 27 and 28 should be replaced by
27. {129} now unavailable for 12/3 at R6C3 ({12} only in R6C3), {156} unavailable blocked by R1C3, {246} unavailable blocked by R89C3
27a. 12/3 at R6C3 = {138|147|237|345} (no 6,9)
27b. Cleanup: no 9 in R5C4

28. 9 in C4 now locked in 17/3 at R3C4 = {(17|26|35)9} (no 4,8)
28a and 28b deleted]

28. 9 in C4 now locked in 17/3 at R3C4 = {(17|26|35)9} (no 4,8)
28a. CPE: R5C4 sees all 9's in 17/3 at R3C4 -> no 9 in R5C4
28b. Cleanup: no 6 in R5C3

29. 21/3 at R4C2 must contain exactly 2 of {789} (step 10)
29a. -> R5C3 and 21/4 at R4C2 forms killer triple on {789} in N4
29b. -> no 7,8,9 elsewhere in N4

30. Similarly, R1C2 and 21/4 at R4C2 forms killer triple on {789} in C2
30a. -> no 7,8,9 elsewhere in C2

31. 12/3 at R4C1 = {156|246|345}
31a. -> 12/3 at R4C1 must contain exactly one of {123}
31b. {123} otherwise only available in R46C3
31c. -> 12/3 at R4C1 and R46C3 form hidden killer triple on {123} in N4
31d. -> R4C3 = {123} (no 5), R6C3 = {123} (no 4,5)
31e. Cleanup: no 3 in R34C4 ({359} only combo with 3 (step 28), and {59} now only in R34C4)

32. R12C4 must contain one of {27} (step 17)
32a. -> R12C6 (outies N3, step 18) cannot contain both of {27}
32b. -> no 2 in R1C6; no 7 in R2C6
32c. Cleanup: no 5 in R1C7; no 6 in R2C7

33. Innies - outies, R9: R9C5 (1 innie) = R8C28 (2 outies) + 1
33a. max. R9C5 = 9 -> max. R8C28 = 8 -> no 8,9 in R8C8
33b. min. R8C28 = 3 -> min. R9C5 = 4 -> no 2,3 in R9C5

34. Implication chain eliminates 8 in R2C3
34a. R2C3=8 -> R2C4=2 -> R2C2=3 -> R1C12={78} -> R2C3<>8 (contradiction)
34b. Conclusion: no 8 in R2C3
34c. Cleanup: no 2 in R2C4, no 6 in R1C4 (step 17), no 1 in R1C3

35. 1 in R1 locked in N2, not elsewhere in N2 (R3C6)
35a. min. R34C6 = 5 -> max. R4C7 = 6 (no 7,8)

36. 1 in C3 now locked in N4, not elsewhere in N4
36a. 12/3 at R4C1 = {(26|35)4}, 4 locked for C1 and N4

37. 21/3 at R4C2 = {(59|68)7}, 7 locked for C2 and N4
37a. Cleanup: no 8 in R5C4 (step 23)

38. Hidden single (HS) at R1C1 = 7

39. Naked pair (NP) on {67} in C4 at R25C4 -> no 6,7 elsewhere in C4

40. NP on {59} in C4 at R34C4 -> no 5,9 elsewhere in C4
40a. 17/3 at R3C4 = {359} (step 28)
40b. -> R4C3 = 3

This sets off an avalanche of hidden and naked singles that makes the rest of the puzzle a breeze.

Prelims

a) R1C34 = {16/25/34}, no 7,8,9
b) R1C67 = {16/25/34}, no 7,8,9
c) R2C34 = {19/28/37/46}, no 5
d) R2C67 = {49/58/67}, no 1,2,3
e) R8C34 = {15/24}
f) R8C67 = {69/78}
g) R9C34 = {19/28/37/46}, no 5
h) R9C67 = {18/27/36/45}, no 9
i) 8(3) cage at R1C8 = {125/134}
j) 11(3) cage at R3C6 = {128/137/146/236/245}, no 9
k) 21(3) cage at R4C2 = {489/579/678}, no 1,2,3
l) 20(3) cage at R4C8 = {389/479/569/578}, no 1,2
m) 10(3) cage at R8C2 = {127/136/145/235}, no 8,9
n) 26(4) cage at R2C9 = {2789/3689/4589/4679/5678}, no 1

1. 8(3) cage at R1C8 = {125/134}, 1 locked for N3, clean-up: no 6 in R1C6
1a. 45 rule on N3 2 innies R12C7 = 11 = [29/38/47/56/65], no 4 in R2C7, clean-up: no 9 in R2C6

2. 45 rule on C5 1 innie R5C5 = 1
2a. 45 rule on C1234 2 innies R5C34 = 15 = {69/78}
2b. 45 rule on C6789 2 innies R5C67 = 7 = {25/34}

3. R1C125 = {789} (hidden triple in R1)
3a. Min R1C12 = {78} = 15 -> max R2C2 = 3

4. 45 rule on N1 2 outies R12C4 = 8 = [17/26/53/62], R1C4 = {1256}, R2C4 = {2367}, clean-up: no 3,4 in R1C3, no 1,2,6,9 in R2C3

5. 45 rule on N7 2 outies R89C4 = 5 = [14/23/41], clean-up: R8C3 = {245}, R9C3 = {679}

6. 45 rule on N9 2 outies R89C6 = 13 = [67/76/85/94], clean-up: no 1,6,7,8 in R9C7

7. 6 in R1 only in R1C34 = {16} or R1C67 = [16] (locking cages), 1 locked for R1
7a. R2C8 = 1 (hidden single in N3)

8. R2C2 = {23} -> 18(3) cage at R1C1 = {279/378}, 7 locked for R1 and N1, clean-up: no 3 in R2C4, no 5 in R1C4 (step 3), no 2 in R1C3
8a. Killer pair 1,2 in R12C4 and R89C4, locked for C4
8b. Min R67C4 = 7 -> max R6C3 = 5
8c. Max R67C4 = 11, no 9 in R67C4

9. 45 rule on C12 2 outies R37C3 = 13 = {49/58}/[67], no 1,2,3, no 6 in R7C3

10. 45 rule on N4 3 innies R456C3 = 12 = {129/138/237} (cannot be {147} which clashes with 21(3) cage at R4C2, cannot be {156} which clashes with R1C3, cannot be {246} which clashes with R89C3, cannot be {345} because no 3,4,5 in R5C3), no 4,5,6, clean-up: no 9 in R5C4 (step 2a)
10a. R5C3 = {789} -> no 7,8,9 in R4C3
10b. Killer triple 7,8,9 in 21(3) cage at R4C2 and R5C3, locked for N4

11. 9 in C4 only in 17(3) cage at R3C4 = {179/269/359}, no 4,8
11a. 3 of {359} must be in R4C3 -> no 3 in R34C4

12. 45 rule on C89 2 outies R37C7 = 10 = {28/37/46}/[91], no 5, no 9 in R7C7

13. 45 rule on R89 4(3+1) innies R8C159 + R9C5 = 25
13a. Max R8C159 = 20 (cannot be {489/579/678/579/679/689} which clash with R8C67) -> min R9C5 = 5

14. Hidden killer pair 3,4 in R67C4 and R89C4 for C4, R89C4 contains one of 3,4 -> R67C4 must contain one of 3,4
14a. 12(3) cage at R6C3 = {138/147/237/246/345} (cannot be {129/156} which don’t contain 3 or 4)
14b. 1 in C4 only in R12C4 = [17] (step 3) or R89C4 = {14} (step 4) -> 12(3) cage = 138/237/246/345} (cannot be {147} = 1{47}, locking-out cages)

15. 45 rule on R6789 4 innies R6C1289 = 21 = {1389/1479/1569/1578/2379/2469/2478/2568/3459/3468/3567}
15a. R6C1289 contains at least one of 8,9 or R6C1289 = {3567} -> R6C34567 = {12489} but cannot be [142]{89} (because 12(3) cage at R6C3, step 14b, cannot contain both of 1,4) -> R6C67 cannot contain both of 8,9 -> 18(3) cage at R6C6 cannot be {89}1 -> no 1 in R7C6

16. 1 in N8 only in R89C4 = {14} (step 5), locked for C4, clean-up: no 6 in R1C3, no 7 in R2C4 (step 4), no 3 in R2C3, no 4 in R8C3, no 9 in R8C6 (step 6), no 6 in R8C7, no 7 in R9C3, no 5 in R9C7

17. 12(3) cage at R6C3 (step 14b) = {138/237}, no 5,6
17a. 1,2 only in R6C3 -> R6C3 = {12}

18. Naked pair {26} in R12C4, locked for C4 and N2, clean-up: no 5 in R1C7, no 7 in R2C7 no 9 in R5C3 (step 2a)
18a. R12C7 (step 1a) = [29/38/65], no 4 in R1C7, no 6 in R2C7, clean-up: no 3 in R1C6, no 7 in R2C6
18b. Killer pair 4,8 in R2C3 and R2C67, locked for R2

19. R34C4 = {59} (hidden pair in C4), R4C3 = 3 (cage sum)

20. Naked pair {78} in R5C34, locked for R5

21. R37C3 (step 9) = [49/67/94] (cannot be {58} which clashes with R12C3), no 5,8

22. R89C6 (step 6) = {67} (cannot be [85] which clashes with R12C6), locked for C6 and N8, clean-up: no 7 in R8C7, no 4 in R9C7

23. 26(4) cage at R2C9 = {2789/4679/5678} (cannot be {3689} which clashes with R12C7, cannot be {4589} which clashes with 8(3) cage at R1C8), no 3, clean-up: no 7 in R7C7 (step 12)

24. 45 rule on R123 2 innies R3C46 = 1 outie R4C5 + 5
24a. R3C46 cannot total 7,11,12 -> no 2,6,7 in R4C5
24b. R3C46 cannot total [91] = 10 (because R4C45 would both be 5) -> no 5 in R4C5
24c. R4C5 = {489} -> R3C46 = 9,13,14 = [54/58/94/95], no 1,3

25. 45 rule on N3 2 outies R12C6 = [18] (cannot be {45} which clashes with R3C46) -> R1C7 = 6, R2C7 = 5, R1C34 = [52], R2C34 = [46], R1C5 = 9, R3C46 = [54], R4C4 = 9, R8C3 = 2, R8C4 = 4, R9C4 = 1, R9C3 = 9, R3C3 = 6, R6C3 = 1, R7C3 = 7, R5C34 = [87]
25a. Naked pair {37} in R23C5, locked for C5, R4C5 = 4 (cage sum)
25b. Naked triple {258} in R789C5, locked for C5 and N8 -> R6C5 = 6, R7C4 = 3, R6C4 = 8, R6C6 = 9

26. 21(3) cage at R4C2 = {579} (only remaining combination), locked for C2 and N4 -> R1C12 = [78]

27. 10(3) cage at R8C2 = {136/145} -> R8C2 = 1, R9C12 = [36/54/63]
27a. Naked pair {23} in R23C2, locked for C2 and N1 -> R23C1 = [91]
27b. Naked pair {46} in R79C2, locked for N7

28. R3C6 = 4 -> R4C67 = 7 = [52], R9C7 = 3, R9C6 = 6, R9C12 = [54], R8C6 = 7, R8C7 = 8, R56C7 = [47]
28a. R9C89 = {27}, locked for N9, R8C8 = 6 (cage sum)

29. 20(3) cage at R4C8 = {389} (only remaining combination) -> R4C8 = 8, R56C8 = {39}, locked for C8 and N6 -> R1C89 = [43]

30. R1C12 = [78], R2C2 = 3 (cage sum)

and the rest is naked singles.

I’ll rate my walkthrough at 1.5 based on steps 15a and 24b.

3x3::k:4864:4864:4864:6659:6659:6659:4102:4102:4102:1033:1033:6155:6659:3597:6659:3599:3344:3344:2066:6155:6155:3349:3597:1303:3599:3599:2842:2066:6155:3349:3349:2079:1303:7457:3599:2842:6180:6180:6180:6180:2079:7457:7457:7457:7457:3629:5934:6180:3120:2079:4146:4146:4148:3381:3629:5934:5934:3120:3130:4146:4148:4148:3381:1855:1855:5934:6210:3130:6210:4148:3142:3142:3656:3656:3656:6210:6210:6210:3662:3662:3662:

Hi all

This was a quick puzzle. But as this is the first of the new assassin year, this one could get some newer players excited.

Walk-through Assassin 53

1. 19(3) in R1C1 = {289/279/469/478/568}: no 1

2. R2C12 = {13} -->> locked for R2 and N1

3. R23C5 and R67C1 = {59/68}: no 1,2,3,4,7

4. 14(4) in R2C7 = {1238/1247/1256/1346/2345}: no 9

5. R2C89 and R67C9 = {49/58/67}: no 1,2,3

6. R34C1 = {26/}/[53/71]: no 8,9; R4C1: no ,5,7

7. R34C6 = {14/23}: no 5,6,7,8,9

8. R34C9 = {29/38/47/56}: no 1

9. 8(3) in R4C5 = {125/134}: no 6,7,8,9; 1 locked for C5 and N5
9a. Clean up: R3C6: no 4

10. R67C4, R78C5 and R8C89 = {39/48/57}: no 1,2,6

11. R8C12 = {16/25/34}: no 7,8,9

12. 45 on R1: 2 outies: R2C46 = 16 = {79}: locked for R2 and N2
12a. R2C89 = {58}: locked for R2 and N3
12b. R23C5 = [68]
12c. Clean up: R4C9: no 3,6; R78C5: no 4
12d. R67C9: no {58}: clashes with R2C9

13. Killer Pair {35} in 8(3) in R4C5 + R7C5 locked for C5
13a. 7 in C5 locked for N8
13b. 9 of C5 locked for N8
13c. Hidden Killer Pair {79} in R78C5 + R9C5 for N8 -->> R9C5 = {79}
13d. Clean up: no 3,5

14. 26(5) in R1C4 = {14579/23579}: 5 locked in R1C46 -->> locked for R1 and N2

15. 8 in R1 locked in 19(3) cage in R1C1
15a.19(3) in R1C1 = {289/478}: no 6
15b. Killer Pair {24} in 19(3) in R1C1 + R1C5 -->> locked for R1
15c. Killer Pair {24} in 19(3) in R1C1 + R2C3 -->> locked for N1
15c. 6 in R1 locked for N3
15d. Clean up: R4C1: no 6; R4C9: no 5

16. 45 on R9: 2 outies: R8C46 = 7 = {16/25/34}: no 8

17. 45 on N1: 2 outies: R4C12 = 10 = [19/28/37] -->> R4C2 = {789}

18. 45 on N3: 2 outies: R4C89 = [18/27/54/72]: R4C8: no 3,4,6,8; R4C9: no 9
18a. Clean up: R3C9: no 2

19. 14(4) in R2C7 = {1247/2345}: {24} locked in 14(4)
19a. 4 in 14(4) locked for N3
19b. 2 in N3 locked for 14(4): R4C8: no 2
19c. Clean up: R4C9: no 7

20. 45 on N7: 2 outies: R6C12 = 13 = {58}/[67/94]: R6C2: no 1,2,3,6,9

21. 45 on N9: 2 outies: R6C89 = 10 = [19/37/46/64]: R6C8: no 2,5,7,8,9

22. 45 on N2: 2 innies: R3C46 = 5 = {23}/[41] -->> R3C4: no 1

23. 45 on N8: 2 innies: R7C46 = 9 = [36/45/54/81] -->> R7C6: no 2,3,8

24. 45 on R1234: 2 innies : R4C57 = 13 = [49/58]: R4C5 = {45}; R4C7 = {89}
24a. Clean up: R56C5: no 4,5

25. 45 on R6789: 2 innies: R6C35 = 3 = {12} -->> locked for R6
25a. Clean up: R6C9: no 9(step 21); R7C9: no 4

26. 45 on C789: 3 outies: R567C6 = 19 = {469/478/568}: no 1,2,3
26a. 45 on C789: 1 outie – 1 innie: R5C6 – R6C7 = 3: Max R5C6 = 9 -->> Max R6C7 = 6; Min R6C7 = 3 -->> Min R5C6 = 6: R5C6 = {6789}; R6C7 = {3456}
26b. 16(3) in R6C6 = {349/358/367/457}: needs 1 of {789}: only option for {789} is R6C6 -->> R6C6 = {789}
26c. Only place for 3 is R6C7 -->> R6C7: no 6
26d. Clean up: R5C6: no 9; R7C4: no 8; R6C4: no 4

27. Killer Triple {789} in R6C12 + R6C4 + R6C6 -->> locked for R6
27a. Clean up : R6C8: no 3; R7C9: no 6

28. Naked Pair {46} -->> locked for R6 and N6
28a. Clean up: R3C9: no 7; R4C8: no 5; R5C6: no 7; R6C1: no 9; R6C2: no 7; R7C1: no 5,8

29. Naked Pair {58} in R6C12 -->> locked for R6 and N4
29a. R6C7 = 3; R5C6 = 6; R9C6 = 8(hidden); R4C3 = 6(hidden)
29b. Clean up: R4C1: no 2; R3C1: no 6; R7C4: no 3,4
29c. R67C4 = [75]; R67C6 = [94]; R2C46 = [97]; R1C6 = 5(hidden); R4C5 = 5
29d. R4C7 = 8; R34C9 = [92]; R34C6 = [23]; R34C4 = [34]; R34C1 = [71]
29e. R2C12 = [31]; R1C45 = [14]; R3C23 = [65]; R4C8 = 7; R4C2 = 9
29f. R2C3 = 4; R2C7 = 2; R6C3 = 2; R5C4 = 8; R5C1 = 4; R56C5 = [21]
29g. R8C6 = 1; R67C9 = [67]; R6C8 = 4; R3C78 = [41]; R1C789 = [763]

30. R8C89 = [84](last remaining combination)
30a. R78C5 = {39}: locked for N8
30b. R8C12 = {25}: locked for R8 and N7
And finally all singles.

greetings

Para

Here's my V1 walkthrough:

1. Cage 4(2) r2c12 = {13}, not elsewhere in N1, r2 -> r4c1 <> 7,5.

2. Cage 8(3) r456c5 must have 1, not elsewhere in N5, c5 -> r3c6 <> 4.

3. Outies r1: r2c46 = 16 = {79}, not elsewhere in N2, r2 -> 13(2) at r2c89 = {58} not elsewhere in N3, r2 -> r2c5 = 6, r3c5 = 8 -> r2c37 = {24}, 19(3) at r1c123 must have 8, 12(2) at r78c5 = {39/57}, 13(2) at r67c9 <> {58}. Clean up r4c9 <> 6, 3

4 a) If 12(2) at r78c5 = {57} -> r9c5 = 9, 8(3) = {134} -> r1c5 = 2
b) If 12(2) at r78c5 = {39} -> r9c5 = 7, 8(3) = {125} -> r1c5 = 4
-> r9c5 = 7/9, r1c5 = 2/4 -> 7 and 9 locked to r789c5, not elsewhere in N8 -> r6c4 <> 3,5

5. Innies N2: r3c46 = 5 = [41]/{23} -> r1c456 must have 5, not elsewhere in r1 -> 5 locked to r3c123.

6. Outies N1: r4c12 = 10 = [19/28/37/64]

7. Outies N3: r4c89 = 9 = [18]/{45/27} -> r3c9 <> 2

8. Innies N8: r7c46 = 9 = [36/81]/{45}

9. Outies N7: r6c12 = 13 = [94/67]/{58}

10. Outies N9: r6c89 = 10 = [19/37]/{46}

11. Innies r1234: r4c57 = 13 = [49/58] -> split 9(2) at r4c89 <> [54] -> r3c9 <> 6,7

12. Innies r6789: r6c35 = 3 = {12}, not elsewhere in r6 -> 8(3) at r456c5 = 5{12}/[431] (r5c5 <> 4,5), r6c9 <> 9 -> r7c9 <> 4

13. Outies r9: r8c46 = 7 = {16/25/34} -> r8c357 = 19 (cannot have 1) -> either r8c12 or r8c46 = {16} -> r8c357 <> 6

14. Innies r9: r9c456 = 17 (must have 7 or 9, not both) -> Combination options are 7/{28/46}, 9/{26}-> r9c46 <> 3,5

15. Outies – Innies N4: r5c4 – r4c3 = 2 -> r4c3 is max 7, r5c4 is min 3

16. Outies – Innies N6: r5c6 – r6c7 = 3 -> r5c6 = 6/7/8/9, r6c7 = 3/4/5/6

17. Killer combination: 19(3) r1c123 = {289/478}, r2c3 = 2/4 -> 2,4 not in r3c123 -> r4c1 <> 6 -> r4c2 <> 4

18. Killer combinations: split 9(2) r4c89 = [18]/{27} -> split 10(2) r4c12 <> [28] -> r3c1 <> 6
-> NP {13} in r24c1, not elsewhere in c1 -> r8c2 <> 6,4
-> split 10(2) or split 9(2) in r4 must contain 1, not elsewhere in r4
-> split 10(2) or split 9(2) in r4 must contain 7, not elsewhere in r4

19. Combinations for 24(4) at r23c3+r34c2: 2679/4569 -> must have 6 which is locked to r3c23, not elsewhere in r3 -> 16(3) r1c789 must have 6 {169/367}.

20. Combinations for 13(3) at r3c4+ r4c34 = {238/256/346}
a) if {238}, r4c34 contains 8 -> r4c89 = {27}, r4c12 = [19] -> Conflict with r4c7 -> r4c34 <> 8
b) if {256}, r4c34 contains {56}, r4c5 = 4, … OK
c) if {346}, r4c34 contains 6, … OK
-> 13(3) = {256/346} -> r4c34 <> 2

21. 2 locked to r23c7+r3c8 of 14(4)/N3 -> r4c8 <> 2 -> r4c9 <> 7 -> r3c9 <> 4

22. 8 locked to r4c79, not elsewhere in N6

23. a) If 13(3) at r3c4+r4c34 = {256} -> r3c4 = 2, r1c5 = 4, r4c5 = 5 -> Conflict!
b) If 13(3) at r3c4+r4c34 = {346} -> r3c4 <> 2, r4c34 <> 5, r4c5 = 5 OK
-> r4c5 = 5, r56c5 = {12} -> r1c5 = 4, r3c4 = 3, r1c46 = {15}, r3c6 = 2, r4c6 = 3, r4c1 = 1, r3c1 = 7, … All singles and straightforward cage combinations.

I have tried really hard this time to include all the "not elsewhere in ..." so it's absolutely clear but no doubt someone will tell me if I've missed one! Seriously - I am grateful for comments and suggested edits if required.

A belated walkthrough for Assassin 53 V1. Because I'd been busy on my walkthrough for SampuZ4, including working through the tag solution and Ed's condensed walkthrough for the V2 of that puzzle, I only finished Assassin 53 yesterday and then worked through Para's and Cathy's walkthroughs.

All three of us had fairly similar solution paths but still had different steps or different ways at looking at them.

I missed Para's 3 outies from C789 and Cathy's killer combinations in R4. It's possible that those two steps, plus the corresponding ones for C123 and R6, may be more important for V2. Since I haven't yet finished that puzzle, I haven't worked through Para's walkthrough for it but noticed his comment about interaction between 2 hidden cages which I'll take as a hint when I try to finish V2.

Here is my walkthrough for V1. I could have used Cathy's killer pairs after step 34a. Those eliminations were done a different way in step 37.

1. R2C12 = {13}, locked for R2 and N1

2. R23C5 = {59/68}

3. R2C89 = {49/58/67}, no 2

4. R34C1 = {26}/[53/71]

5. R34C6 = {14/23}

6. R34C9 = {29/38/47/56}, no 1

7. R67C1 = {59/68}

8. R67C4 = {39/48/57}, no 1,2,6

9. R67C9 = {49/58/67}, no 1,2,3

10. R78C5 = {39/48/57}, no 1,2,6

11. R8C12 = {16/25/34}, no 7,8,9

12. R8C89 = {39/48/57}, no 1,2,6

13. R456C5 = 1{25/34}, 1 locked for C5 and N5, clean-up: no 4 in R3C6
13a. If R456C5 = {125} => R23C5 = {68};
....... if R456C5 = {134} => R78C5 = {57} => R23C5 = {68}
....... -> R23C5 = {68}, locked for C5 and N2, clean-up: no 4 in R78C5

14. 14(4) cage at R2C7 = {1238/1247/1256/1346/2345}, no 9

15. 45 rule on C5 2 innies R19C5 = 11 = {29/47}, no 3,5

16. 45 rule on R1 2 outies R2C46 = 16 = {79}, locked for R2 and N2, clean-up: no 4,6 in R2C89, no 2,4 in R9C5 (step 15)
16a. Naked pair {58} in R2C89, locked for R2 and N3 -> R23C5 = [68], clean-up: no 3,6 in R4C9
16b. Killer pair 7/9 in R78C5 and R9C5, locked for N8, clean-up: no 3,5 in R6C4

17. R2C46 = 16 (step 16) -> R1C456 = 10 = 5{14/23}, 5 locked for R1 and N2
17a. R1C5 = {24} -> no 2,4 in R1C46

18. 45 rule on R9 2 outies R8C46 = 7 = {16/25/34}, no 8
18a. R9C456 = 17 with R9C5 = {79} = {269/278/359/467} (cannot be {179} because 7,9 only in R9C5), no 1

19. 45 rule on N1 2 outies R4C12 = 10 = [19/28/37/64]

20. 45 rule on N3 2 outies R4C89 = 9, no 9, no 3,6,8 in R4C9, clean-up: no 2 in R3C9

21. 45 rule on N7 2 outies R6C12 = 13 = {58}/[67/94]

22. 45 rule on N9 2 outies R6C89 = 10 = [19/28/37]/{46}, clean-up: no 8 in R7C9

23. 45 rule on R1234 2 innies R4C57 = 13 = [49/58]
23a. R456C5 (step 13) = 1{25/34} -> no 4,5 in R56C5
23b. No {45} in R4C89 (clashes with R4C5), clean-up: no 6,7 in R3C9

24. 45 rule on R6789 2 innies R6C35 = 3 = {12}, locked for R6, clean-up: no 8,9 in R6C9 (step 22), no 4,5 in R7C9

25. 45 rule on N2 2 innies R3C46 = 5 = {23}/[41]

26. 45 rule on N8 2 innies R7C46 = 9 = [36]/{45}/[81]

27. 45 rule on R89 3 innies R8C357 = 19 = {289/379/469/478/568}, no 1
27a. R8C89 must contain 7/8/9 -> R8C357 must contain two of 7/8/9 = {289/379/478}, no 6
[Alternatively either R8C12 or R8C46 must be {16} -> no 1,6 in R8C357]

28. 45 rule on C123 1 outie R5C4 – 2 = 1 innie R4C3, no 2 in R5C4, no 8,9 in R4C3

29. 45 rule on C789 1 outie R5C6 – 3 = 1 innie R6C7, no 2,3,4,5 in R5C6, no 7,8,9 in R6C7

30. 16(3) cage at R6C6 = {169/349/358/367/457} (cannot be {178} because 7,8 only in R6C6)
30a. No 7,8,9 in R6C7 or R7C6 -> R6C6 = {789}

31. 45 rule on R4, R4C12 = 10 (step 19), R4C57 = 13 (step 23) and R4C89 = 9 (step 20) -> 3 innies R4C346 = 13 = {139/148/238/247/256/346} (cannot be {157} because no 1,5,7 in R4C6)

32. 45 rule on R6, R6C12 = 13 (step 21), R6C35 = 3 (step 24) and R6C89 = 10 (step 22) -> 3 innies R6C467 = 19 = {379/469/478} (cannot be {568} because 5,6 only in R6C7) [3/4, 6/7, 8/9], no 5
32a. R6C467 contains 8/9 -> R6C12 must contain 8/9 -> no 6,7 in R6C12, clean-up: no 8 in R7C1
32b. Killer pair 3/4 in R6C467 and R6C89, locked for R6, clean-up: no 9 in R6C1 (step 21), no 5 in R7C1
32c. 6 in R6 locked in R6C789, locked for N6

33. Naked pair {58} in R6C12, locked for R6 and N4, clean-up: no 2 in R4C1 (step 19), no 6 in R3C1, no 7 in R5C4 (step 28), no 4 in R7C4, no 5 in R7C6 (step 26)
33a. R6C467 (step 32) = {379/469} = 9{37/46}, 9 locked in R6C46 for N5, clean-up: no 7 in R4C3 (step 28)
33b. 6 only in R6C7 -> no 4 in R6C7
33c. 3 in R6 locked in R6C78, locked for N6
33d. Naked pair {79} in R26C6, locked for C6

34. 24(4) cage at R2C3 = {2679/4569} = 69{27/45}, 6 locked in R3C23, locked for R3 and N1
34a. R2C3 = {24} -> no 2,4 in rest of 24(4) cage, clean-up: no 6 in R4C1 (step 19), no 2 in R3C1
34b. R1C123 = 8{29/47}

35. 6 in R1 locked in R1C789
35a. R1C789 = 6{19/37}, no 2,4
[Alternatively killer pair 2/4 in R1C123 and R1C5, locked for R1]

36. 2 in N3 locked in 14(4) cage -> no 2 in R4C8, clean-up: no 7 in R4C9 (step 20), no 4 in R3C9
36a. 14(4) cage (step 14) = {1247}, no 3
[Alternatively killer pair 3/9 in R1C789 and R3C9, locked for N3]

37. 6 in R4 locked in R4C34, 13(3) cage at R3C4 = 6{25/34}, no 1,7,8
37a. 5 only in R4C4 and only other 6 in R4C3 -> no 2 in R4C34
37b. Clean-up: no 3,4 in R5C4 (step 28)

38. 5 in R4 locked in R4C45, locked for N5, clean-up: no 3 in R4C3 (step 28)
38a. Naked pair {68} in R5C46, locked for R5 and N5

39. R4C3 = 6 (hidden single in R4) -> R5C3 = 8 (step 28), R5C6 = 6, R6C7 = 3 (step 29), R9C6 = 8 (hidden single in C6), clean-up: no 4 in R6C4, no 3 in R7C4, no 1 in R7C6 (both step 26) -> R7C46 = [54], R6C46 = [79], R2C46 = [97], clean-up: no 7 in R78C5, no 6 in R7C9

40. Naked pair {46} in R6C89, locked for N6

41. Naked pair {39} in R78C5, locked for C5 and N8 -> R9C5 = 7, R1C5 = 4 (step 15), R4C5 = 5, clean-up: no 1 in R3C6 (step 25)

42. Naked pair {12} in R56C5, locked for N5 -> R34C6 = [23], R34C4 = [34] -> R4C1 = 1, R3C1 = 7, R2C12 = [31], R4C8 = 7, R4C2 = 9, R4C7 = 8, R4C9 = 2, R3C9 = 9, R3C23 = [65], R1C46 = [15], R8C6 = 1, R6C3 = 2, R5C1 = 4, R2C3 = 4, R2C7 = 2, R56C5 = [21], R7C9 = 7, R6C9 = 6, R6C8 = 4, R3C8 = 1, R3C7 = 4, R1C9 = 3, R1C8 = 6, R1C7 = 7, clean-up: no 6 in R8C1, no 3,4 in R8C2, no 3,5,9 in R8C8, no 5,8 in R8C9 -> R8C89 = [84], R2C89 = [58], R5C8 = 9
[R1C6 had been a hidden single for a few steps but I decided to go with the more obvious naked pairs and resulting naked singles.]

43. Naked pair {25} in R8C12, locked for R8 and N7

and the rest is naked singles

3x3::k:3584:3584:3584:5635:5635:5635:4614:4614:4614:2313:2313:6923:5635:3597:5635:3855:3088:3088:1810:6923:6923:3349:3597:1815:3855:3855:2330:1810:6923:3349:3349:4383:1815:7457:3855:2330:5668:5668:5668:5668:4383:7457:7457:7457:7457:2349:6446:5668:4400:4383:3122:3122:4148:1077:2349:6446:6446:4400:2362:3122:4148:4148:1077:1855:1855:6446:5442:2362:5442:4148:4422:4422:4168:4168:4168:5442:5442:5442:4430:4430:4430:

Hi all

With the practise of V1, this one goes smoothly.

Walk-through Assassin 53V2

1. R2C12, R34C9, R67C1 and R78C5 = {18/27/36/45}: no 9

2. 27(4) in R2C3 = {3789/4689/5679}: no 1,2

3. R23C5 = {59/68}: no 1,2,3,4,7

4. R2C89 = {39/48/57}: no 1,2,6

5. R34C1, R34C6 and R8C12 = {16/25/34}: no 7,8,9

6. R67C4 = {89} -->> locked for C4

7. R67C9 = {13} -->> locked for C9
7a. Clean up: R2C8: no 9; R34C9: no 6,8

8. R8C89 = {89} -->> locked for R8 and N9
8a. Clean up: R7C5: no 1

9. 17(3) in R9C7 = {467} -->> locked for R9 and N9

10. 16(3) in R9C1 = {259/358}: no 1; 5 locked for R9 and N7
10a. 1 in R9 locked for N8
10b. Clean up: R7C5: no 8; R8C12: no 2; R6C1: no 4

11. 45 on C5: 2 innies: R19C5 = 5 = {23}/[41] -->> R1C5 = {234}; R9C5 = {123}

12. 45 on R9: 3 innies: R9C456 = 12 = {129/138} -->> R9C6 = {89}(only place for {89})
12a. Naked Pair {89} in R7C4 + R9C6 -->> locked for N8
12b. 45 on R9: 2 outies: R8C46 = 9 = {27/45}: ({36} clashes with R8C12): no {36}

13. 45 on N3: 2 outies: R4C89 = 9 = {27/45}: R4C8: no 1,3,6,8,9

14. 45 on N1: 2 outies: R4C12 = 12 = [39/48] ([57] clashes with R4C89); R4C1 = {34}; R4C2 = {89}
14a. Clean up: R3C1 = {34}
14b. Naked Pair {34} in R34C1 -->> locked for C1
14c. Clean up: R8C2: no 3,4
14d. Naked Pair {16} in R8C12 -->> locked for R8 and N7
14e. Clean up: R2C2: no 5,6; R6C1: no 5,6,8; R7C5: no 3

15. 45 on N7: 2 outies: R6C12 = 12 = [75]
15a. R7C1 = 2
15b. 16(3) in R9C1 = {358} -->> locked for R9 and N7
15c. R9C6 = 9; R67C4 = [98]

16. Naked Pair {12} in R9C45 -->> locked for N8
16a. R8C46 = {45} (step 12b) -->> locked for R8 and N8
16b. R8C3 = 7; R78C5 = [63]; R7C6 = 7; R8C7 = 2
16c. R19C5 = [41] (step 11); R9C4 = 2
16d. R23C5 = {59} -->> locked for C5 and N2
16e. R456C5 = {278} -->> locked for N5
16f. Clean up: R2C2: no 2,7

17. 45 on N9: 2 outies: R6C89 = 9 = [63/81]; R6C8 = {68}

18. 45 on R6789: 2 innies: R6C35 = {28} -->> locked for R6
18a. R6C89 = [63]; R7C9 = 1

19. 45 on R1234: 2 innies: R4C57 = 13 = [85]
19a. R4C12 = [39]; R3C1 = 4; R56C5= [72]; R6C3 = 8; R7C78 = [35]; R7C23 = [49]
19b. Naked Pair {16} in R58C1 -->> locked for C1
19c. R2C12 = [81](last possible combination); R9C123 = [583]; R8C12 = [16]
19d. R1C1 = 9; R5C12 = [62]
19e. Clean up: R4C89: no 4; R2C8: no 4 ; R2C9: no 4,7; R3C9: no 5

Now it is all singles:
20. R2C7 = 4(hidden); R6C67 = [41]; R4C3 = 4(hidden); R5C3 = 1; R5C46 = [53]; R8C46 = [45]
20a. R1C3 = 2(hidden); R1C2 = 3; R3C2 = 7; R34C9 = [27]; R4C8 = 2;
20b. R2C6 = 2(hidden), R1C6 =8(hidden); R1C9 = 5(hidden); R2C89 = [39]
20c. R8C89 = [98]; R5C789 = [984]; R9C789 = [746]; R23C5 = [59]
20d. R23C3 = [65]; R1C78 = [67]; R12C4 = [17]; R34C4 = [36]; R34C6 = [61]; R3C78 = [81]




This is mostly because Sumocue misses one elimination because it is made between 2 hidden cages. I never seen Sumocue makes these types of eliminations. If you make this elimination Sumocue can solve the rest.

greetings

Para

Initially I'd got stuck on Assassin 53V2. Then after completing V1 and working through Cathy's and Para's V1 walkthroughs I started V2 again.

Here is my walkthrough

1. R2C12 = {18/27/36/45}, no 9

2. R23C5 = {59/68}

3. R2C89 = {39/48/57}, no 1,2,6

4. R34C1 = {16/25/34}, no 7,8,9

5. R34C6 = {16/25/34}, no 7,8,9

6. R34C9 = {18/27/36/45}, no 9

7. R67C1 = {18/27/36/45}, no 9

8. R67C4 = {89}, locked for C4

9. R67C9 = {13}, locked for C9, clean-up: no 9 in R2C8, no 6,8 in R34C9

10. R78C5 = {18/27/36/45}, no 9

11. R8C12 = {16/25/34}, no 7,8,9

12. R8C89 = {89}, locked for R8 and N9, clean-up: no 1 in R7C5

13. 27(4) cage at R2C3 = 9{378/468/567}, no 1,2

14. 45 rule on C5 2 innies R19C5 = 5 = {14/23}

15. 45 rule on N1 2 outies R4C12 = 12 = [39/48/57], clean-up: no 1,5,6 in R3C1

16. 45 rule on N3 2 outies R4C89 = 9 = {27/45} -> no 5,7 in R4C12 (clashes with R4C89), clean-up: no 2 in R3C1
[The elimination of 5,7 from R4C12, which is what I'd missed earlier , is I think the key move for V2. I assume this is the move that Para referred to at the end of his walkthrough. Without it I'd done about 30 moves and was stuck. After this elimination and the resulting naked pair it went very smoothly.]

17. Naked pair {34} in R34C1, locked for C1, clean-up: no 5,6 in R2C2, no 5,6 in R67C1, no 3,4 in R8C2

18. 45 rule on N7 2 outies R6C12 = 12 = [75/84], clean-up: no 7,8 in R7C1

19. Killer pair 1/2 in R7C1 and R8C12, locked for N7

20. 45 rule on N9 2 outies R6C89 = 9 = [63/81]

21. 45 rule on N2 2 innies R3C46 = 9 = {36/45}/[72], clean-up: no 6 in R4C6

22. 45 rule on N8 2 innies R7C46 = 15 = [87/96]

23. 45 rule on R1234 2 innies R4C57 = 13 = {49/58/67}, no 1,2,3

24. 45 rule on R6789 2 innies R6C35 = 10 = {19/28/37/46}, no 5

25. 45 rule on R4, R4C12 = 12 (step 15), R4C57 = 13 (step 23) and R4C89 = 9 (step 16) -> R4C346 = 11 = {128/137/146/236/245}, no 9

26. 45 rule on R6, R6C12 = 12 (step 18), R6C35 = 10 (step 24) and R6C89 = 9 (step 20) -> R6C467 = 14 with R6C4 = {89} = 8{15}/8{24}/9{14}/9{23}, no 6,7,8,9 in
R6C67
[Alternatively this result comes from combinations for 12(3) cage at R6C6]

27. 45 rule on C123 1 outie R5C4 – 1 = 1 innie R4C3 -> no 7,8 in R4C3, no 1 in R5C4

28. 45 rule on C789 1 outie R5C6 – 2 = 1 innie R6C7 -> R5C6 = {34567}

29. 45 rule on R1 2 outies R2C46 = 9 -> no 1,9 in R2C6

30. 45 rule on R9 2 outies R8C46 = 9 -> {27/36/45}, no 1

31. 45 rule on R12, 3 innies R2C357 = 15
31a. Min R2C35 = 8 -> max R2C7 = 7

32. R9C789 = {467} (only remaining combination), locked for R9 and N9, clean-up: no 1 in R1C5 (step 14)

33. R9C123 = {358} (only remaining combination), locked for R9 and N7, clean-up: no 2 in R1C5 (step 14), no 2 in R8C12

34. Naked pair {12} in R9C45, locked for R9 and N8 -> R9C6 = 9, R7C4 = 8, R6C4 = 9, R7C6 = 7 (step 22), clean-up: no 2 in R2C4 (step 29), no 7,8 in R78C5

35. Killer pair 5/6 in R23C5 and R78C5, locked for C5

36. Naked pair {16} in R8C12, locked for R8 and N7 -> R7C1 = 2, R6C1 = 7, clean-up: no 2,7 in R2C2, no 3 in R7C5

37. R7C5 = 6 (hidden single in R7) -> R8C5 = 3, R1C5 = 4, R9C5 = 1 (step 14), R9C4 = 2, clean-up: no 8 in R23C5, no 5 in R2C46 (step 29), no 5 in R3C46 (step 21), no 2,3 in R4C6, no 1 in R4C3 (step 27), no 5 in R6C7 (step 28)

38. Naked pair {49} in R7C23, locked for 25(4) cage -> R6C2 = 5, R8C3 = 7, clean-up: no 6 in R5C4 (step 27)

39. R8C7 = 2 (hidden single in R8), clean-up: no 4 in R5C6 (step 28)

40. Naked pair {59} in R23C5, locked for N2

41. Naked triple {278} in R456C5, locked for N5, clean-up: no 6 in R4C3 (step 27)

42. R7C6 = 7 -> R6C67 = 5 = {14}, no 3, clean-up: no 5 in R5C6 (step 28)

43. Naked pair {14} in R6C67, locked for R6 -> R67C9 = [31], R6C8 = 6 (cage sum)

44. 1 in N4 locked in R5C123, locked for R5

45. 1 in R4 locked in R4C46, locked for N5 -> R6C67 = [41], R8C46 = [45], R4C6 = 1, R3C6 = 6, R3C4 = 3 (step 21), R5C6 = 3, R5C4 = 5, R4C4 = 6, R4C3 = 4 (cage sum), R34C1 = [43], R7C23 = [49], clean-up: no 5 in R2C1, no 5 in R34C9

46. Naked pair {27} in R34C9, locked for C9, clean-up: no 5 in R2C8

47. 2 in R4 locked in R4C89 = {27} (step 16), locked for R4 and N6 -> R456C5 = [872], R4C2 = 9, R4C7 = 5, R6C3 = 8, R3C3 = 5, R23C5 = [59], R7C78 = [35], R9C3 = 3

48. R3C7 = 8 (hidden single in R3)

49. Naked pair {78} in R3C27, locked for R3 -> R3C9 = 2, R4C89 = [27]

50. 27(4) cage at R2C3 (step 13) = {5679} (only remaining combination) -> R2C3 = 6, R3C2 = 7, R3C7 = 8, R2C7 = 4 (cage sum), R2C9 = 9, R2C8 = 3, R1C789 = [675], R8C89 = [98], R5C789 = [984], R9C789 = [746]

51. R2C12 = {18}, locked for R2 and N1

and the rest is naked singles

Please note that the numbering of the A53 variants is rather misleading. The V2 and V2.5 aren't much harder than A53. Anyone comfortable with solving V1s should consider trying these variants. V3 and the definitely misleading V0.1 are much harder; they are both of traditional V2 difficulty.

3x3::k:3584:3584:3584:5635:5635:5635:4358:4358:4358:3337:3337:4363:5635:2573:5635:5135:1296:1296:3090:4363:4363:5397:2573:3607:5135:5135:2074:3090:4363:5397:5397:3615:3607:7713:5135:2074:4900:4900:4900:4900:3615:7713:7713:7713:7713:2861:5422:4900:1584:3615:3634:3634:5684:2613:2861:5422:5422:1584:2618:3634:5684:5684:2613:2367:2367:5422:5954:2618:5954:5684:3654:3654:3912:3912:3912:5954:5954:5954:3662:3662:3662:

Hi all

As Ed remarked in his post 53V2.5 doesn't have a walk-through yet. Here it is.

Walk-through Assassin 53V2.5

1. R2C12 = {49/58/67}: no 1,2,3

2. R23C5, R67C9 and R78C5 = {19/28/37/46}: no 5

3. R2C89 = {14/23}: no 5,6,7,8,9

4. R34C1 = {39/48/57}: no 1,2,6

5. 21(3) at R3C4 = {489/579/678}: no 1,2,3

6. R34C6 and R8C89 = {59/68}: no 1,2,3,4,7

7. R34C9 = {17/26/35}: no 4,8,9

8. R67C1 = {29/38/47/56}: no 1

9. R67C4 = {15/24}: no 3,6,7,8,9

10. R8C12 = {18/27/36/45}: no 9

11. 45 on R1: 2 outies: R2C46 = 8 = {17/26/35}: no 4,8,9

12. 45 on R12: 3 innies: R2C357 = 19 = {289/379/469/578}({478} blocked by R2C12): no 1
12a. Clean up: R3C5: no 9

13. 45 on R1234: 2 innies: R4C57 = 7 = {16/25/34}: no 7,8,9

14. 45 on R9: 2 outies: R8C46 = 7 = {16/25/34}= {3|5|6..}: no 7,8,9
14a. R8C89 = {5|6..} and R8C46 = {3|5|6..} -->> R8C12: {36} blocked(R8C4689 needs at least one of {36}) -->> R8C12 = {18/27/45}: no 3,6 = {2|5|8..}
14b. R8C89 = {5|8..} and R8C12 = {2|5|8..} -->> R8C46 = {25} blocked(R8C1289 needs at least one of {25}) -->> R8C46 = {16/34} = {4|6..}: no 2,5
14c. R78C5 = {19/28/37}: {46} blocked by R8C46: no 4,6
14d. R8C46 = {4|6..} and R8C89 = {5|6..} -->> R8C12 = {18/27}:{45} blocked by R8C4689(needs at least one of {45}): no 4,5

15. 45 on R6789: 2 innies: R6C35 = 11 = {29/38/47/56}: no 1

16. 45 on N1: 2 outies: R4C12 = 11 = [92]/{38}/{47}/[56] -->> R4C2: no 1,5,9

17. 45 on N2: 3 outies: R4C346 = 22 = {589/679}: no 4; 9 locked for R4
17a. Clean up: R3C1: no 3; R4C2: no 2
17b. R4C12 = [56] blocked by R4C346 -->> R4C1: no 5; R4C2: no 6
17c. R4C12 = {38/47} = {7|8..}/{3|4..}
17d. Killer Pair {78} in R4C12 + R4C346 -->> locked for R4
17e. R4C57 = {16/25}: {34} blocked by R4C12: no 3,4

18. 45 on N2: 2 innies: R3C46 = 13 = [49/58/76/85]: R3C4: no 6,9

19. 45 on N3: 2 outies: R4C89 = 5 = [41]/{23}-->> R4C8 = {234}; R4C9 = {123}
19a. Clean up: R3C9 = {567}

20. 45 on N7: 2 outies: R6C12 = 11 = {29/38/47/56}: no 1
20a. 1 in N4 locked for R5

21. 45 on N8: 3 outies: R6C467 = 8 = {125/134}: no 6,7,8,9; 1 locked for R6
21a. Clean up: R7C9: no 9

22. 45 on N8: 2 innies: R7C46 = 12 = [48/57]: R7C4 = {45}; R7C6 = {78}
22a. Clean up: R6C4: no 4,5

23. 45 on N9: R6C89 = 15 = {69/78}: no 2,3,4,5
23a. Clean up: R7C9: no 6,7,8

24. 45 on C123: 1 innie and 1 outie: R4C3 = R5C4 + 4 -->> R4C3 = {6789}; R5C4 = {2345}

25. 45 on C5: 2 innies: R19C5 = {29/38/47/56}: no 1

26. 45 on C789: 1 innie and 1 outie: R5C6 = R6C7 + 5 -->> R5C6 = {6789}; R6C7 = {1234}

27. 45 on C789: 3 outies: R567C6 = 19 = [658/748/847/937]:[928] blocked by R34C6: no 1,2
27a. Combined with step 26: R6C67 = [51/43/34]: [42] blocked by step 21: R6C7: no 2
27b. Clean up: R5C6: no 7(step 26)

28. 45 on C123: 3 outies: R345C4 = 17 = {78}[2]/[593]/[863]/[764]: {269} blocked by R3C4, {458} blocked by R7C4 -->> R3C4 = {578}; R4C4 = {6789}; R5C4 = {234}
28a. Clean up: R4C3: no 9
28b. 9 in R4 locked for N5
28c. R567C6 = [658/847]: 8 locked for C6; R6C6: no 3
28d. Clean up: R6C7: no 4(step 26); R34C6: no 6

29. R34C6 = {59} -->> locked for C6
29a. R6C6 = 4; R57C6 = [87](step 28c); R6C7 = 3
29b. R7C4 = 5(step 22); R6C4 = 1; R4C89 = [41](step 19); R3C9 = 7
29c. R3C4 = 8

30. Whole lot of clean up: R4C12 = {38}(step 16) -->> locked for R4 and N4
30a. R4C57 = {25}(step 13) -->> locked for R4
30b. R34C6 = [59]
30c. R2C46: no 3(step 13); R6C12: no 7(step 20); R6C3: no 2,7 and R6C5: no 7(step 15)
30d. R6C8 = 7(hidden); R6C9 = 8(hidden); R7C9 = 2; R9C7 = 7(hidden)
30e. R8C4: no 3; R8C6: no 6(step 14); R7C5: no 3; R8C5: no 3,8
30f. R23C5: no 2; R2C5: no 3; R1C5: no 4,6; R9C5: no 3,6(step 25)
30g. R2C8: no 3

31. 13(2) at R2C12 = {58}: {49} blocked by R3C1, {67} blocked by R2C46(R2C46 = {26}/[71] = {6|7..}) -->> {58} locked for R2 and N1
31a. 8 in C3 locked for N7
31b. Clean up: R8C12 = {27} -->> locked for R8 and N7
31c. Clean up: R78C5 = {19} -->> locked for C5 and N8
31d. R8C46 = [43](step 14); R9C5 = 8(hidden); R1C5 = 3(step 25)
31e. R1C4 = 9(hidden); R5C4 = 3(hidden)
31f. Clean up: R2C5: no 7
31g. R2C4 = 7(hidden); R4C34 = [76]; R9C46 = [26]; R5C5 = 7(hidden)

32. 20(4) at R2C7 = 4{169}(last remaining combo) R2C7 + R3C78 = {169} -->> locked for N3
32a. R2C89 = [23]; R12C6 = [21]

33. 14(3) at R9C7 = 7[34](last remaining combo) -->> R9C89 = [34]
33a. R1C789 = [485]

34. R1C123 = {167} -->> locked for N1

35. 17(4) at R2C3 = {2348}(last remaining combo): no 9
35a. R2C3 = 4; R23C5 = [64]; R2C7 = 9; R34C1 = [93]; R4C2 = 8

36. R67C1 = [56](last remaining combo)

37. R8C89 = [59](last remaining combo)

And the rest is all naked singles.

greetings

Para

Prelims
a). R2C12 = {49/58/67}, no 1,2,3
b). R23C5 = {19/28/37/46}, no 5
c). R2C89 = {14/23}
d). R34C1 = {39/48/57}, no 1,2,6
e). R34C6 = {59/68}
f). R34C9 = {17/26/35}, no 4,8,9
g). R67C1 = {29/38/47/56}, no 1
h). R67C4 = {15/24}
i). R67C9 = {19/28/37/46}, no 5
j). R78C5 = {19/28/37/46}, no 5
k). R8C12 = {18/27/36/45}, no 9
l). R8C89 = {59/68}
m) 21(3) cage at R3C4 = {489/579/678}, no 1,2,3

1. 45 rule on R1 2 outies R2C46 = 8 = {17/26/35}, no 4 8,9

2.45 rule on R9 2 outies R8C46 = 7 = {16/25/34}, no 7,8,9

3. 45 rule on N1 2 outies R4C12 = 11 = {38/47}/[56/92], no 1,5,9 in R4C2

4. 45 rule on N3 2 outies R4C89 = 5 = [23/32/41], clean-up: no 1,2,3 in R3C9

5. 45 rule on N7 2 outies R6C12 = 11 = {29/38/47/56}, no 1

6. 45 rule on N9 2 outies R6C89 = 15 = {69/78}, clean-up: no 6,7,8,9 in R7C9

7. 45 rule on R12 3 innies R2C357 = 19 = {289/379/469/568} (cannot be {478} which clashes with R2C12), no 1, clean-up: no 9 in R3C5

8. 45 rule on R1234 2 innies R4C57 = 7 = {16/25} (cannot be {34} which clashes with R4C89)
8a. Killer pair 1,2 in R4C57 and R4C89, locked for R4, clean-up: no 9 in R4C1 (step 3), no 3 in R3C1
8b. R4C12 (step 3) = {38/47} (cannot be [56] which clashes with R4C57), no 5,6, clean-up: no 7 in R3C1
8c. Killer pair 3,4 in R4C12 and R4C89, locked for R4

9. 45 rule on R6789 2 innies R6C35 = 11 = {29/38/47/56}, no 1
9a. Killer quad 6,7,8,9 in R6C12, R6C35 and R6C89, locked for R6

10. 14(3) cage at R6C6 must contain one of 6,7,8,9 -> R7C6 = {6789}

11. 45 rule on C123 1 innie R4C3 = 1 outie R5C4 + 4, no 6,7,8,9 in R5C4

12. 45 rule on C789 1 outie R5C6 = 1 innie R6C7 + 5, no 1,2,3,4,5 in R5C6, no 5 in R6C7

13. 45 rule on N2 2 innies R3C46 = 13 = [49/58/76/85], no 6,9 in R3C4

14. 45 rule on N8 2 innies R7C46 = 12 = [48/57], clean-up: no 4,5 in R6C4

15. 45 rule on C6789 4 innies R1289C6 = 12 = {1236/1245}, no 7,8,9, 1,2 locked for C6, clean-up: no 1 in R2C4 (step 1)

16. Killer pair 5,6 in R1289C6 and R34C6, locked for C6, clean-up: no 1 in R6C7 (step 12)

17. 45 rule on C5 2 innies R19C5 = 11 = {29/38/47/56}, no 1

18. 45 rule on N8 2 outies R6C67 = 1 innie R7C4 + 2
18a. R7C4 = {45} -> R6C67 = 6,7 = {24/34}, 4 locked for R6, clean-up: no 7 in R6C12 (step 5), no 7 in R6C35 (step 9), no 4,7 in R7C1

19. R6C4 = 1 (hidden single in R6), R7C4 = 5, R7C6 = 7 (step 14), clean-up: no 4,6 in R1C5 (step 17), no 3 in R2C6 (step 1), no 8 in R3C6 (step 13), no 5,9 in R4C3 (step 11), no 6 in R4C6, no 6 in R4C7 (step 8), no 6 in R6C1, no 5 in R6C2 (step 5), no 2 in R6C7 (step 12), no 3 in R78C5, no 2 in R8C4, no 2,6 in R8C6 (both step 2)

20. Naked pair {34} in R6C67, locked for R6, clean-up: no 8 in R6C12 (step 5), no 8 in R6C35 (step 9), no 3,8 in R7C1

21. R6C89 = {78} (hidden pair in R6), locked for N6, clean-up: no 1,4 in R7C9

22. 5,6,9 in N6 only in 30(5) cage at R4C7, 6,9 locked for R5 -> R5C6 = 8, clean-up: no 6 in R3C6, no 7 in R3C4 (step 13)
22a. 30(5) cage = {25689} (only remaining combination), no 1,3,4

23. Naked pair {59} in R34C6, locked for C6

24. R4C89 = [41] (hidden pair in R4), R3C9 = 7, R6C67 = [43], R6C89 = [78], R7C9 = 2, clean-up: no 3 in R2C5, no 3 in R2C8, no 9 in R6C1, no 2 in R6C2 (step 5), no 3 in R8C4 (step 2), no 8 in R8C5, no 6 in R8C8

25. 14(3) cage at R4C5 = {257/356} (cannot be {239} which clashes with R5C4), no 9, 5 locked for C5 and N5 -> R4C6 = 9, R3C6 = 5, R3C4 = 8 (step 13), clean-up: no 3 in R2C4 (step 1), no 2 in R23C5, no 7 in R4C1, no 2 in R6C3 (step 9), no 3,6 in R9C5 (step 17)

[From here onward, some clean-ups and/or CPEs have been omitted when they follow quickly from normal steps.]

26. Naked pair {67} in R4C34, locked for R4

27. 6 in N4 only in R4C3 + R6C23, CPE no 6 in R78C3
27a. 9 in N4 only in R6C23, CPE no 9 in R78C3

28. R2C12 = {58} (only remaining combination, cannot be {49} which clashes with R3C1, cannot be {67} which clashes with R2C46), locked for R2 and N1

29. 5,8 in R1 only in 17(3) cage at R1C7 = {458}, locked for R1 and N3 -> R2C9 = 3, R2C8 = 2, clean-up: no 6 in R2C46 (step 1)

30. R2C46 = [71], R4C34 = [76], R8C46 = [43], clean-up: no 9 in R2C5, no 3 in R3C5, no 5 in R6C3 (step 9), no 5,6 in R8C12, no 6 in R78C5

31. Naked pair {25} in R46C5, locked for C5 and N5 -> R5C45 = [37], clean-up: no 8 in R7C5

32. Naked pair {46} in R23C5, locked for N2 -> R1C456 = [932], R9C46 = [26], R9C5 = 8 (hidden single in N8)

33. Naked triple {167} in 14(3) cage at R1C1, locked for N1
33a. Naked pair {49} in R2C3 + R3C1, locked for N1

34. Naked pair {23} in R3C23, locked for 17(4) cage at R2C3 -> R4C2 = 8, R4C1 = 3, R3C1 = 9, R2C3 = 4, R7C1 = 6, R6C1 = 5, R6C2 = 6 (step 5), R6C35 = [92], R4C57 = [52], R2C12 = [85], clean-up: no 1 in R8C12

35. Naked pair {27} in R8C12, locked for N7

36. 15(3) cage at R9C1 = {159} (only remaining combination) = [195], R8C3 = 8, clean-up: no 6 in R8C9

37. R9C9 = 4

and the rest is naked singles.

[I didn’t spot 45 rule on N2 3 outies R4C346 = 22 = {589/679} and 45 rule on N8 3 outies R6C467 = 8 = {125/134}, but steps 8 and 9 give the same results. Steps 18 and 19 would have been a bit simpler with outies for N8.]

I'll rate my walkthrough for A53 V2.5 at Easy 1.25. I used a killer quad. If I'd spotted Outies for N8, I'd have rated it lower.

3x3::k:4096:4096:4096:5123:5123:5123:4102:4102:4102:1289:1289:5899:5123:6992:5123:4623:6737:6737:2834:5899:5899:2837:6992:6992:4623:4623:6737:2834:5899:2837:2837:3359:6992:4641:4623:6737:6948:6948:6948:6948:3359:4641:4641:4641:4641:6482:3630:6948:5711:3359:5170:5170:5428:2357:6482:3630:3630:5711:5711:5170:5428:5428:2357:6482:6482:3630:6210:5711:6210:5428:2886:2886:3912:3912:3912:6210:6210:6210:3406:3406:3406:

Thanks!

Here is the complete walk-through to Assassin 53V3 - a really tough one. After the early breakthrough contradictions moves, some difficult hurdles remain. There were so many bi-value cells that felt sure one of those fun fishy moves would be there. Just couldn't find it. Had to use one tricky combination move to crack it in the end (step 38b,39).

Please let me know of any corrections or improvements. Thanks.
Ed

Assassin 53 V3
1. "45" r6789: r6c35 = 6 = h6(2)r6 = {15/24}
1a. = [4/5]

2. "45" n7: r6c12 = 9 = h9(2)n4
2a. no 9

3. "45" n9: r6c89 = 9 = h9(2)n6
3a. no 9

4. "45" n8: r6c467 = 21 = h21(3)r6
4a. must have 9 for r6
4b. = 9{48/57}(no 1236)
4c. = [4/5]

5. Killer Pair 4/5 in h21(3)r6 and h5(2)r6
5a. 4 and 5 locked for r6

6. "45" n3: r4c89 = 15 = h15(2)n6
6a. = {69/78}

7. "45" n369: r5c6 + 3 = r6c7
7a. r5c6 = 1,2,4,5,6

8. 4 and 5 cannot be in r5c6. Here's how.
8a. 4 or 5 in r5c6 -> only place for 4/5 in n6 is in r6c7
8b. but this is impossible since r5c6 + 3 = r6c7 = 7/8(step 7)
8c. -> no 4 or 5 in r5c6
8d. -> no 7/8 r6c7 (step 7)

9. 1 cannot be in r5c6. Here's how.
9a. 1 in r5c6 -> 4 in r6c7 (step 7) and 1 in n6 in r6c89.
9b. -> r6c789 = {14}
9c. but this clashes with h6(2) r6 = [1/4..]
9d. no 1 r5c6
9e. no 4 r6c7 (step 7)

10. 2 cannot be in r5c6. You've probably guessed how by now.
10a. 2 in r5c6 -> r6c7 = 5 (step 7) and 2 for n6 in r6c89
10b. -> r6c789 = {25}
10c. but this clashes with h6(2)r6 = [2/5..]
10d. no 2 r5c6

11. r5c6 = 6, r6c7 = 9 (step 7)
11a. split-cage 11(2)r6c6 = [83]/{47}
11b. r6c6 = 478, r6c7 = 347

12. split-cage 12(4)r4c7 = {1245}: all locked for n6

13. h15(2)n6 = {78}: both locked for n6 & r4

14. r6c89 = {36}: both locked for r6

15. 9(2)r6c9 = {36}: both locked for c9

16. "45" r1234: r4c57 = 7 = h7(2)r4
16a. = {25}/[34], r4c5 = 235, r4c7 no 1
16b. -> 1 in n6 only in r5: 1 locked for r5

17. "45" n8: r6c46 = 12 = {48}/[57](no 7 r6c4)
17a. = [4/7..]

18. 13(3)n5 = [391/571/382] ({247} blocked by r6c46 step 17a)
18a. r4c5 = {35}, r5c5 = {789}, r6c5 = {12}
18b. r6c3 = {45} (h6(2)r6)
18c. r4c7 = {24} (h7(2)r4)

19. 5 in n6 only in r5: 5 locked for r5

20. 27(5)n4 = 5{...}
20a. ->r6c3 = 5

21. r6c5 = 1 (h6(2)r5)
21a. r45c5 = [39/57](no 8)
21b. 8 in r5 only in split-cage 22(4)r5c1 = 8{239/347}

22. r6c12 = h9(2) = {27}: both locked for n4, r6

23. r6c46 = naked pair {48}: both locked for n5
23. r67c6 = [83/47]

24. "45" n147: r5c4 - 1 = r4c3
24a. r5c4 = {27}, r4c3 = {16}

25. "45" n1: r4c12 = 10 = [91]/{46} (no 3)

26. 2 in n5 only in c4: 2 locked for c4

27. "45" n2: 3 outies r4c346 = 13 = [139/625] ([652] blocked by no 1 or 2 in a 27(4) cage: or blocked by combinations for 11(3)r3c4)
27a. r4c4={23}, r4c6 = {59}

28. "45" n2: r4c6 - 2 = r3c4
28a. r3c4 = {37}

29. naked triple {237} r345c4: all locked for c4

30. 5(2)n1 = {14/23}
30a. = [3/4..]

31. "45" r1: 2 outies r2c46 = 7 = h7(2)n2
31a. = [61/52] ([43] blocked by 5(2)n1 step 30a)

32. 27(4)n2: no 1 or 2 and must have 9
32a. ->no 9 r1c6
32b. ->20(5)n2 must have 1&2 for n2 = 12{359/368/458/467}
32c. -> r1c456 = 13 (because of h7(2)n2 step 31a)
32d. = {139/238/148/247}(no 5,6)

33. 27(4)n2 must have 5/6 for n2 (only other place in n2 apart from r2c4)
33a. 27(4) = {4689/5679} = 69{48/57}(no 3)
33b. 6 in this cage only in n2 and c5: 6 locked for n2 & c5
33c. no 9 r1c6

34. r2c46 = [52]
34a. r1c456 = {139/148}(no 7) = [3/8,3/4..]

35. 5(2)n1 = {14}: both locked for r2 & n1

36. 1 in r3 only in n3 in 18(3)
36a. 1 locked for n3
36b. 18(3) must have 1 and 7/8 (r4c8)
36c. = 1{278/368/467}(no 5,9) ({1458} blocked by 1,4,5 only in r3c78)
36d. only combo with both 7 & 8 in {1278} with {12} only in r3c78
36e. all other combo's = 7/8, not both -> only in r4c8
36f. ->no 7 or 8 r3c78

37. 16(3)n1 = {259/268/367} ({358} blocked by r1c456 step 34a)

38. 26(4)n3 = {2789/4679/5678} (no 3) ({3689} blocked by 3,6 only in r2c8: {4589} blocked by 4,5 only in r3c9)
38a. 26(4) = [2/4/5] not more than 1 off -> r3c9 = {245}
38b. r2c89 + r3c9 = {79}[2]/{89}[2]/[694]/[685]/[675]

39. 16(3)n3 = {367/457} ({259/268} blocked by r2c89 + r3c9 step 38b: {349/358} blocked by r1c456} step 34a)
39a. 16(3) = 7{36/45} (no 2,8,9)
39b. 7 locked for n3, r1

40. 16(3)n1 = {259/268} = 2{59/68}(no 3)
40a. 2 locked n1

41. 11(2)n1 = [74/56]
41a. r3c1 = {57}, r4c1 = {46}

42. "45" n1: r4c2 + 1 = r3c1
42a. r4c2 = {46}

43. r4c6 = 9 (hsingle r4)
43a. split cage 18(3)r2c5 = {468}: all locked for n2

44. Naked pair {46} r4c12: both locked for r4

45. r45c5 = [57], r45c4 = [32], r4c3 = 1, r4c7 = 2, r3c4 = 7

46. 11(2)n1 = [56], r4c2 = 4, r2c12 = [41]

47. naked pair {48} r36c6: both locked for c6

48. r1c456 = {139}: all locked for r1

49. 16(3)n1 = {268}: all locked for n1 and r1

50. r2c3 = 7 (hsingle n1)

51. r3c23 = {39}: both locked for r3

52. 16(3)n3 = {457}: all locked for n3

53. 26(4)n3 = [2]789}
53a. r4c9 = 7 (only 7 available in cage)

54. 14(4)r6c2 = {2345} (only valid combo)
54a. r67c2 = [25]
54b. r78c3 = {34}: both locked for n7 & c3

55. "45" r9: r8c46 = 7 = [61] ([43] blocked by r8c3)

the rest are singles and last valid combo's

Prelims
a). R2C12 = {14/23}
b). R34C1 = {29/38/47/56}, no 1
c). R67C9 = {18/27/36/45}, no 9
d). R8C89 = {29/38/47/56}, no 1
e). 11(3) cage at R3C4 = {128/137/146/236/245}, no 9
f). 20(3) cage at R6C6 = {389/479/569/578}, no 1,2
f). 27(4) cage at R2C5 = {3789/4689/5679}, no 1,2
g) 26(4) cage at R2C8 = {2789/3689/4589/4679/5678}, no 1
h) 14(4) cage at R6C2 = {1238/1247/1256/1346/2345}, no 9
i). 18(5) cage at R4C7 = {12348/12357/12456}, no 9

1. 27(4) cage at R2C5 = {3789/4689/5679}, CPE no 9 in R12C6

2. 45 rule on R1 2 outies R2C46 = {16/25} (cannot be {34} which clashes with R2C12)
2a. Killer pair 1,2 in R2C12 and R2C46, locked for R2

3. 45 rule on R9 2 outies R8C46 = 7 = {16/25/34}, no 7,8,9

4. 45 rule on N1 2 outies R4C12 = 10 = {28/37/46}/[91], no 5, no 9 in R4C2, clean-up: no 6 in R3C1

5. 45 rule on N3 2 outies R4C89 = 15 = {69/78}

6. 45 rule on N7 2 outies R6C12 = 9 = {18/27/36/45}, no 9

7. 45 rule on N9 2 outies R6C89 = 9 = {18/27/36/45}, no 9

8. 45 rule on N2 1 outie R4C6 = 1 innie R3C4 + 2, no 8 in R3C4

9. 45 rule on N8 1 outie R6C4 = 1 innie R7C6 + 1, no 1,2,3 in R6C4, no 9 in R7C6

10. 45 rule on C123 1 outie R5C4 = 1 innie R4C3 + 1, no 1 in R5C4

11. 45 rule on C789 1 innie R6C7 = 1 outie R5C6 + 3, no 7,8 in R5C6, no 3 in R6C7

12. 45 rule on R1234 2 innies R4C57 = 7 = {16/25/34}, no 7,8,9

13. 45 rule on R6789 2 innies R6C35 = 6 = {15/24}

14. R6C12 (step 5) = {18/27/36} (cannot be {45} which clashes with R6C35), no 4,5

15. R6C89 (step 6) = {18/27/36} (cannot be {45} which clashes with R6C35), no 4,5, clean-up: no 4,5 in R7C9

16. Killer triple 1,2,3 in R6C12, R6C35 and R6C89, locked for R6

17. 45 rule on N8 3 outies R6C467 = 21 = {489/579} (cannot be {678} which clashes with R6C12), no 6, clean-up: no 3 in R5C6 (step 11), no 5 in R7C6 (step 9)
[Alternatively 3 in R6 only in R6C12 or R6C89 -> one of these hidden cages must be {36}, locked for R6.]

18. 18(5) cage at R4C7 = {12348/12357/12456}
18a. 1 or 2 of {12348/12357} must be in R5C6 (cannot have all of 1,2,3 in N6 which would clash with R6C89), 6 of {12456} must be in R5C6 (6 of {12456} cannot be in N6 which would clash with R6C89 = {36}, only remaining place for 3 in N6 when 18(5) cage = {12456}) -> R5C6 = {126}, clean-up no 7,8 in R6C7 (step 11)
18b. 6 of {12456} must be in R5C6 (step 18a) -> no 6 in R4C7 + R5C789, clean-up: no 1 in R4C5 (step 12)

19. 13(3) cage at R4C5 = {139/148/157/238/247/256/346}
19a. Max R46C5 = 11 -> min R5C5 = 2
19b. 7,8 of {148/247} must be in R5C5, 4 of {346} must be in R6C5 -> no 4 in R5C5

20. 45 rule on C789 3 outies R567C6 = 17 = {179/269/278/368/467} (cannot be {359/458} because R5C6 only contains 1,2,6), no 5

21. Consider combinations for 18(5) cage at R4C7 (step 18) = {12348/12357/12456}
18(5) cage = {12348/12357} => R4C89 (step 5) = {69}
or 18(5) cage = {12456} => R5C6 = 6
-> 6 must be in R4C89 or R5C6, CPE no 6 in R4C456, clean-up: no 4 in R3C4 (step 8), no 1 in R4C7 (step 12)
21a. 1 in 18(5) cage only in R5C6789, locked for R5
21b. 6 in N5 only in R5C456, locked for R5

22. 13(3) cage at R4C5 = {139/148/157/238/247/256/346}
22a. 6,7,8,9 only in R5C5 -> R5C5 = {6789}

23. 45 rule on N2 3 outies R4C346 = 13 = {139/148/157/256/346} (cannot be {238/247} which clash with R4C57)
23a. 7 of {157} must be in R4C34 (R4C34 cannot be {15} because 11(3) cage at R3C4 cannot be 5{15}), no 7 in R4C6, clean-up: no 5 in R3C4 (step 8)
23b. 5 of {157/256} must be in R4C6 -> no 5 in R4C34, clean-up: no 6 in R5C4 (step 10)
23c. 6 of {256} must be in R4C3 -> no 2 in R4C3, clean-up: no 3 in R5C4 (step 10)

24. 3 in N5 only in R4C456, locked for R4, clean-up: no 7 in R4C12 (step 4), no 4,8 in R3C1, no 4 in R4C5 (step 12), no 4 in R5C4 (step 10)

25. 45 rule on C123 3 outies R345C4 = 12 = {129/138/147/156/237/246} (cannot be {345} because 11(3) cage at R3C4 cannot be [344])
25a. 8 of {138} must be in R5C4 -> no 8 in R4C4

26. 5 in N4 only in R5C123 + R6C3, locked for 27(5) cage at R5C1, no 5 in R5C4, clean-up: no 4 in R4C3 (step 10)

27. R4C346 (step 23) = {139/157/256/346} (cannot be {148} which clashes with R4C12), no 8, clean-up: no 6 in R3C4 (step 8), no 9 in R5C4 (step 10)

28. 5 in N4 only in 27(5) cage at R5C1 = {14589/23589/24579/34578}
28a. Consider combinations for R6C467 (step 17) = {489/579}
R6C467 = {489} => no 8 in R5C4
or R6C467 = {579}, locked for R6 => R6C35 (step 13) = {24}, no 1
-> 27(5) cage at R5C1 = {23589/24579/34578} (cannot be {14589} = {459}[81] because no 8 in R5C4 or no 1 in R6C3), no 1, clean-up: no 5 in R6C5 (step 13)

29. R4C346 (step 27) = {139/157/256/346}
29a. 5 of {157} must be in R4C6 => R4C57 (step 12) = [34] => 2 in 18(5) cage at R4C7 must be in R5C6789, locked for R5 => no 2 in R5C4 => no 1 in R4C3 (step 10) => 7 of {157} must be in R4C3 -> no 7 in R4C4

30. Consider combinations for R4C346 (step 27) = {139/157/256/346}
R4C346 = {139} => R4C89 (step 5) = {78} => 6 in N6 only in R6C89 (step 7) = {36}, 3 locked for R6 => 3 in N4 only in 27(5) cage at R5C1
or R4C346 = {157} = [715] (step 29a) => R5C4 = 8 (step 10) => 27(5) cage at R5C1 contains 8
or R4C346 = {256/346} => R4C3 = 6 => R6C12 (step 6) = {18/27}, no 3 => 3 in N4 only in 27(5) cage at R5C1
-> 27(5) cage at R5C1 (step 28a) must contain 3 and/or 8 = {23589/34578}, 3 locked for R5 and N6, clean-up: no 6 in R6C12 (step 6)

31. R6C89 = {36} (hidden pair in R6), locked for N6, R7C9 = {36}, clean-up: no 9 in R4C89 (step 5)
31a. Naked pair {36} in R67C9, locked for C9, clean-up: no 5,8 in R8C8

32. Naked pair {78} in R4C89, locked for R4 and N6, CPE no 7,8 in R2C8, clean-up: no 2 in R4C12 (step 4), no 3,9 in R3C1, no 8 in R5C4 (step 10)

33. Killer pair 1,6 in R4C12 and R4C3, locked for R4 and N4, clean-up: no 8 in R6C12 (step 6)

34. Naked pair {27} in R6C12, locked for R6 and N4, CPE no 2,7 in R8C2, clean-up: no 4 in R6C35 (step 13), no 6 in R7C6 (step 9)

35. R6C35 = [51], clean-up: no 4 in R7C6 (step 9)

36. R6C7 = 9 (hidden single in N6), R5C6 = 6 (step 11), clean-up: no 1 in R2C4 (step 2), no 8 in R7C6 (step 9), no 1 in R8C4 (step 3)
36a. Naked pair {48} in R6C46, locked for N5, clean-up: no 2 in R3C4 (step 8)

37. 11(3) cage at R3C4 = {137/236}, 3 locked for C4, clean-up: no 4 in R8C6 (step 3)
37a. R4C3 = {16} -> no 1 in R3C4, clean-up: no 3 in R4C6 (step 8)

38. 13(3) cage at R4C5 = {139/157}, no 2, clean-up: no 5 in R4C7 (step 12)

39. Naked triple {237} in R234C4, locked for C4, clean-up: no 5 in R2C6 (step 2), no 5 in R8C6 (step 3)

40. 26(4) cage at R2C8 = {2789/4589/4679/5678} (cannot be {3689} because 3,6 only in R2C8), no 3

41. 27(4) cage at R2C5 = {4689/5679} (cannot be {3789} which clashes with R3C4), no 3, 6 locked for C5 and N2 -> R2C4 = 5, R2C6 = 2 (step 2), clean-up: no 3 in R2C12

42. Naked pair {14} in R2C12, locked for R2 and N1

43. 20(5) cage at R1C4 contains 2,5 = {12359/12458}, no 7, 1 locked for R1

44. 26(4) cage at R2C8 (step 40) = {2789/4679/5678} (cannot be {4589} because 4,5 only in R3C9), 7 locked for C9, clean-up: no 4 in R8C8
44a. 2,4,5 only in R3C9 -> R3C9 = {245}

45. 1 in N3 only in 18(4) cage at R2C7 = {1278/1368/1467} (cannot be {1269/1359} because R4C8 only contains 7,8, cannot be {1458} because 1,4,5 only in R3C78), no 5,9
45a. 1,2 of {1278} must be in R3C78, 7,8 of other combinations must be in R4C8 -> no 7,8 in R3C78

46. 16(3) cage at R1C1 = {259/268/367} (cannot be {358} which clashes with 20(5) cage at R1C4)

47. Hidden killer pair 5,6 in 16(3) cage at R1C1 and 16(3) cage at R1C7 for R1, 16(3) cage at R1C1 contains one of 5,6 -> 16(3) cage at R1C7 must contain one of 5,6
47a. 26(4) cage at R2C8 (step 44) = {2789/4679} (cannot be {5678} which clashes with 16(3) cage at R1C7, no 5, 9 locked for R2 and N3

48. 5 in R3 only in R3C23, locked for N1
48a. 16(3) cage at R1C1 (step 46) = {268/367}, no 9, 6 locked for N1

49. 9 in N1 only in R3C23, locked for R3

50. 27(4) cage at R2C5 (step 41) = {4689/5679} -> R4C6 = 9, R2C5 + R3C56 = {468}, locked for N2

51. Naked triple {139} in R1C456, locked for R1 and N1 -> R3C4 = 7, R4C34 = [13] (step 37)

52. 16(3) cage at R1C1 (step 48a) = {268} (only remaining combination), locked for R1 and N1

53. Naked triple {457} in 16(3) cage at R1C7, locked for N3 -> R3C9 = 2

54. R3C1 = 5, R4C1 = 6, R4C2 = 4, R4C7 = 2, R2C12 = [41]

55. 26(4) cage at R2C8 (step 47a) = {2789} (only remaining combination) -> R2C8 = 9, R24C9 = [87], R4C8 = 8, R2C5 = 6, R2C7 = 3, R2C3 = 7, clean-up: no 3 in R8C8

56. Naked pair {13} in R18C6, locked for C6 -> R7C6 = 7, R6C6 = 4 (cage sum), R6C4 = 8, R3C56 = [48], R9C5 = 8 (hidden single in N8)

57. R9C5 = 8, R8C46 = 7 (step 3) -> R9C46 = 9 = [45], R8C4 = 6, R8C6 = 1 (step 3), R7C4 = 9, clean-up: no 5 in R8C9

58. 13(3) cage at R9C7 = {139} (only remaining combination) = [139], R8C9 = 4, R8C8 = 7

59. 1,9 in N7 only in 25(4) cage at R6C1 -> R67C1 = [71], R8C12 = {89}, locked for R8 and N7

and the rest is naked singles.

I'll rate my walkthrough for A53 V3 at 1.75. I used several forcing chains.

3x3::k:4096:4096:4096:5891:5891:5891:3078:3078:3078:4691:4691:5131:5891:6480:5891:3855:7249:7249:4691:5131:5131:3093:6480:6480:3855:3855:7249:4691:5131:3093:3093:3103:6480:7713:3855:7249:6948:6948:6948:6948:3103:7713:7713:7713:7713:5458:5934:6948:5199:3103:3634:3634:5172:3156:5458:5934:5934:5199:5199:3634:5172:5172:3156:5458:5458:5934:8002:5199:8002:5172:3156:3156:2120:2120:2120:8002:8002:8002:4686:4686:4686:

Prelims
a). 8(3) cage at R9C1 = {125/134}
b). 28(4) cage at R2C8 = {4789/5689}, no 1,2,3
c). 12(4) cage at R6C9 = {1236/1245}, no 7,8,9

Steps resulting from Prelims
1. 8(3) cage at R9C1 = {125/134}, 1 locked for R9 and N7
1a. 28(4) cage at R2C8 = {4789/5689}, CPE no 8,9 in R1C9
1b. 12(4) cage at R6C9 = {1236/1245}, CPE no 2 in R9C9

2. 45 rule on R1 2 outies R2C46 = 6 = {15/24}

3. 45 rule on R8 2 outies R8C46 = 12 = {39/48/57}, no 1,2,6

4. 45 rule on N1 2 outies R4C12 = 9 = {18/27/36/45}, no 9

5. 45 rule on N3 2 outies R4C89 = 10 = [19/28/37/46/64], no 5, no 7,8,9 in R4C8

6. 45 rule on N7 2 outies R6C12 = 7 = {16/25/34}, no 7,8,9

7. 45 rule on N9 2 outies R6C89 = 5 = {14/23}
7a. R6C12 (step 6) = {16/25} (cannot be {34} which clashes with R6C89), no 3,4
7b. Killer pair 1,2 in R6C12 and R6C89, locked for R6

8. 45 rule on N2 1 outie R4C6 = 1 innie R3C4 + 3, no 7,8,9 in R3C4, no 1,2,3 in R4C6

9. 45 rule on N8 1 outie R6C4 = 1 innie R7C6 + 6, R6C4 = {789}, R7C6 = {123}

10. 45 rule on N8 4 innies R7C456 + R8C5 = 14 = {1238/1247/1256/1346/2345}, no 9

11. 45 rule on R1234 2 innies R4C57 = 11 = {29/38/47/56}

12. 45 rule on R6789 2 innies R6C35 = 13 = {49/58/67}, no 1,2,3

13. 45 rule on C123 1 innie R4C3 = 1 outie R5C4 + 2, no 1,2 in R4C3, no 8,9 in R5C4

14. 45 rule on C789 1 outie R5C6 = 1 innie R6C7, no 1,2 in R5C6

15. 45 rule on C123 3 outies R345C4 = 10 = {127/136/145/235}, no 8,9

16. 45 rule on N8 3 outies R6C467 = 20 = {389/479/578} (cannot be {569} which clashes with R6C12), no 6, clean-up: no 6 in R5C6 (step 14)

17. 18(3) cage at R9C7 = {279/369/378/468} (cannot be {459} which clashes with 8(3) cage at R9C1, cannot be {567} which clashes with 12(4) cage at R6C9), no 5

18. 45 rule on R9 3 innies R9C456 = 19 = {379/469/478/568} (cannot be {289} which clashes with 18(3) cage at R9C7), no 2

19. R6C467 (step 16) = {389/479/578}, R5C6 = R6C7 (step 14) -> R5C6 + R6C46 = 20 = {389/479/578}
19a. 12(3) cage at R4C5 = {129/138/147/156/246} (cannot be {237/345} which clash with R5C6 + R6C46)
19b. 8,9 of {129/138} must be in R6C5 -> no 8,9 in R45C5, clean-up: no 2,3 in R4C7 (step 11)
19c. 1 of {129/138/147/156} must be in R5C5 or 12(3) cage = {246} -> R5C5 = {1246}, no 3,5,7

20. 45 rule on C123 3 innies R4C3 + R5C123 + R6C3 = 29 contains 9 for N4 = {14789/23789/34589/34679} (cannot be {15689/24689/25679} which clash with R6C12)
20a. Consider combinations for R4C3 + R5C123 + R6C3
R4C3 + R5C123 + R6C3 = {14789/23789/34679} => 7 in R4C3 or 7 in R5C123 + R6C3 => no 7 in R5C4 => no 9 in R4C3 (step 13)
or R4C3 + R5C123 + R6C3 = {34589} => R6C12 (step 6) = {16} => R6C89 (step 7) = {23} => R6C467 (step 16) = {479/578} => R5C6 + R6C46 (step 19) = {479/578} => no 7 in R5C4 => no 9 in R4C3 (step 13)
-> no 7 in R5C4, clean-up: no 9 in R4C3 (step 13)

21. R4C3 = R5C4 + 2 (step 13) -> R4C3 cannot be 2 more than R4C4 or R4C6 which would clash with R5C4
21a. 45 rule on N2 3 outies R4C346 = 15 = {159/267/348/357/456} (cannot be {168} = [618] because R45C4 = [14] clashes with 12(3) cage at R4C5, cannot be {168} = [816] because R4C3 2 more than R4C6, cannot be {249} because R4C3 2 more than R4C4, cannot be {258} because 12(3) cage at R3C4 cannot be [282/552])
21b. 6 of {627} must be in R4C6 (cannot be [627] because 12(3) cage at R3C4 = [426] clashes with R4C3 + R5C4 = [64]), 6 of {456} must be in R4C46 (cannot be [645/654] because R4C3 would be 2 more than one of R4C46) -> no 6 in R4C3, clean-up: no 4 in R5C4 (step 13)

22. Consider combinations for R4C346 (step 21a) = {159/267/348/357/456}
R4C346 = {519} = [519] => R6C12 (step 6) = {16}, locked for N4
or R4C346 = {267/348/357/456} contains 3 or 6 for R4 = R4C12 (step 4) cannot be {36}
-> R4C12 = {18/27/45}, no 3,6
22a. R4C346 = {519} => R4C12 = {27}, locked for R4
or R4C346 = {267/348/357/456} contains 4 or 7 for R4 = R4C57 (step 11) cannot be {47}
-> R4C57 = [29/38/56/65], no 4,7
22b. R4C346 = {159} => R4C12 = {27}, locked for R4
or R4C346 = {267/348} contains 2 or 8 for R4 = R4C89 (step 5) cannot be [28]
or R4C346 = {357} = R4C12 = {18}, locked for R4
or R4C346 = {456} => R4C12 = {18/27} => R4C89 cannot be [28] which clashes with R4C12
-> R4C89 (step 5) = [19/37/46/64], no 2,8

23. 45 rule on C789 3 innies R4C7 + R5C789 + R6C7 = 30 contains 5,8 for N6 = {15789/25689/45678}, no 3, clean-up: no 3 in R5C6 (step 14)
23a. 3 in N6 only in R5C8 + R6C89, CPE no 3 in R8C8

24. 3 in N4 only in R4C3 + R5C123 + R6C3 (step 20) = {23789/34589/34679}, no 1

25. 12(3) cage at R4C5 (step 19a) = {129/138/156/246} (cannot be {147} because no 1,4,7 in R4C5), no 7, clean-up: no 6 in R6C3 (step 12)

26. R4C6 = R3C4 + 3 (step 8)
26a. 45 rule on N1247 3 outies R4C46 + R5C4 = 13 = {139/157/238/247/256/346} (cannot be {148} which clashes with 12(3) cage at R4C5)
26b. 4 of {247} must be in R4C6 (cannot be [472] because R345C4 cannot be [442]), 4 of {346} must be in R4C6 (cannot be [463] because R345C4 cannot be [343]) -> no 4 in R4C4

27. 3 in R5 only in R5C1234
27a. 3 in R5C123, locked for N4 or 3 in R5C4 -> R4C3 = 5 (step 13)
-> no 3 in R4C3, clean-up: no 1 in R5C4 (step 13)
27b. 3 in N4 only in R5C123, locked for R5, clean-up: no 5 in R4C3 (step 13)

28. R4C346 (step 21a) = {267/348/357/456} (cannot be {159} because R4C3 only contains 4,7,8), no 1,9, clean-up: no 6 in R3C4 (step 8)
28a. 7 of {267/357} must be in R4C3 -> no 7 in R4C46, clean-up: no 4 in R3C4 (step 8)

29. R5C5 = 1 (hidden single in N5)
29a. 12(3) cage at R4C5 (step 25) = {129/138/156}, no 4, clean-up: no 9 in R6C3 (step 12)
29b. 4 in N5 only in R456C6, locked for C6, clean-up: no 2 in R2C4 (step 2), no 8 in R8C4 (step 3)

30. R345C4 (step 15) = {136/235}, 3 locked for C4, clean-up: no 9 in R8C6 (step 3)

31. 12(3) cage at R3C4 contains 3 = {138/237/345}, no 6

32. R4C6 = R3C4 + 3 (step 8)
32a. R4C46 + R5C4 (step 26a) = {238/256/346}
32a. 5 of {256} must be in R45C4 (cannot be [256] because R345C4 cannot be [226]) -> no 5 in R4C6, clean-up: no 2 in R3C4 (step 8)

33. R4C7 + R5C789 + R6C7 (step 23) = {25689/45678}, 6 locked for N6, clean-up: no 4 in R4C89 (step 5)
[Alternatively hidden killer pair 1,3 in R4C89 and R6C89 for N6 …]

[Just spotted …]
34. 9 in R4 only in R4C79, locked for N6, clean-up: no 9 in R5C6 (step 14)

35. 7 in N5 only in R5C4 + R6C46 = {479/578} (step 19), no 3

36. 3 in N5 only in R4C45, locked for R4 -> R4C8 = 1, R4C9 = 9 (step 5), clean-up: no 8 in R4C12 (step 4), no 4 in R6C89 (step 7)

37. Naked pair {23} in R6C89, locked for R6 and N6, CPE no 2 in R8C8, clean-up: no 5 in R6C12 (step 6)

38. Naked pair {16} in R6C12, locked for R6 and N4, CPE no 6 in R8C2, clean-up: no 5 in R4C5 (step 29a), no 7 in R6C3 (step 6)

39. 12(4) cage at R6C9 = {1236/1245}, 1,2 locked for C9, 1 also locked for N9

[Missed a couple of useful clean-ups …]
40. R4C57 (step 22a) = [38/65], no 2 in R4C5, no 6 in R4C7, clean-up: no 9 in R6C5 (step 29a), no 4 in R6C3 (step 12)

41. Naked pair {58} in R6C35, locked for R6, clean-up: no 5,8 in R5C6 (step 14), no 2 in R7C6 (step 9)

42. Naked triple {479} in R5C6 + R6C46, locked for N5

43. R4C46 + R5C4 (step 32a) = {238/256}, 2 locked for C4
43a. R4C6 = {68} -> no 6 in R5C4, clean-up: no 8 in R4C3 (step 13)

44. R345C4 (step 30) = {235} (only remaining combination), locked for C4, clean-up: no 1 in R2C6 (step 2), no 7 in R8C6 (step 3)

45. Killer pair 4,7 in R4C12 and R4C3, locked for N4
[Alternatively naked quint {45678} in 30(5) cage at R4C7, 4,7 locked for R5.]

46. R1C7 = 1 (hidden single in N3)
46a. 12(3) cage at R1C7 = {138/147/156} (cannot be {129} because 2,9 only in R1C8), no 2,9
46b. 8 of {138} must be in R1C8 -> no 3 in R1C8

47. 9 in N3 only in 15(4) cage at R2C7 = {1239} (only remaining combination), 3 locked for N3, clean-up: no 8 in R1C8 (step 46a)

48. 45 rule on R1 3 innies R1C456 = 17 = {269/278/368} (cannot be {359} which clashes with R3C4, cannot be {458} which clashes with R2C46, cannot be {467} which clashes with 12(3) cage at R1C7), no 4,5
48a. Killer pair 6,7 in R1C456 and 12(3) cage at R1C7, locked for R1
48b. Killer triple 2,3,5 in R1C456, R2C6 and R3C4, locked for N2

49. 25(4) cage at R2C5 = {1789/4678}, 7 locked for N2
49a. R1C456 (step 48) = {269/368}, 6 locked for R1 and N2, clean-up: no 5 in R1C89 (step 46a)
49b. Naked pair {47} in R1C89, locked for R1 and N3
49c. 5 in R1 only in 16(3) cage at R1C1, locked for N1

50. 8 in N5 only in R4C6 + R6C5, CPE no 8 in R23C5

51. 25(4) cage at R2C5 (step 49) = {1789/4678}, 8 locked for C6, clean-up: no 4 in R8C4 (step 3)
51a. 1 of {1789} must be in R3C6, [86] of {4678} must be in R34C6 -> no 7,9 in R3C6
51b. 7 in N2 only in R23C5, locked for C5

52. R8C9 = 1 (hidden single in R8)
52a. R6C4 = R7C6 + 6 (step 9)
52b. 1,2 in N8 only in R7C456 + R8C5 (step 10) = {1238/1256} (cannot be {1247} which clashes with R6C4 + R7C6 = [71]), no 4,7
52b. 6 of {1256} must be in R7C4 -> no 6 in R78C5

53. 4 in N8 only in R9C45, locked for R9, clean-up: no 3 in 8(3) cage at R9C1

54. Naked triple {125} in 8(3) cage at R9C1, locked for R9 and N7

55. 18(3) cage at R9C7 (step 17) = {369/378}, 3 locked for N9

56. Naked pair {79} in R68C4, locked for C4

57. 21(4) cage at R6C1 = {1389/1479/3468}
57a. R6C1 = {16} -> no 6 in R78C1

58. 6 in N7 only in R7C23 + R8C3, locked for 23(3) cage at R6C2 -> no 6 in R6C2

59. R6C2 = 1, R6C1 = 6
59a. 21(4) cage at R6C1 (step 57) = {3468} (only remaining combination), 3,4,8 locked for N7

[Missed this at step 41 …]
60. R6C35 = {58}, CPE no 5 in R5C4 -> R5C4 = 2, R4C3 = 4 (step 13)

61. R4C12 = {27} (hidden pair in N4), CPE no 2,7 in R2C2

62. 18(4) cage at R2C1 = {1269/1278/1467/2367} (cannot be {1368} because R4C1 only contains 2,7, cannot be {2349} which clashes with 16(3) cage at R1C1)
62a. 8 of {1278} must be in R2C2 -> no 8 in R23C1
62b. 6,8 only in R2C2 -> R2C2 = {68}

63. Naked triple {568} in R2C289, locked for R2, 5 also locked for N3 -> R2C6 = 2, R2C4 = 4 (step 2)

64. 25(4) cage at R2C5 (step 49) = {1789} (only remaining combination) -> R3C6 = 1, R4C6 = 8, R7C6 = 3, R8C6 = 5, R8C4 = 7 (step 3), R4C7 = 5, R34C4 = [53], R4C5 = 6, R6C5 = 5 (step 29a), R6C3 = 8

65. Naked pair {79} in R23C5, locked for C5 and N2 -> R1C6 = 6, R1C45 = [83], R9C46 = [69], R9C5 = 4 (hidden single in N8)

66. Naked triple {259} in 16(3) cage at R1C1, locked for N1

67. Naked triple {378} in 18(3) cage at R9C7, locked for N9

68. 20(4) cage at R2C3 = {2378/3467} (cannot be {1568/3458} because R4C2 only contains 2,7, cannot be {1478/2468} because 4,8 only in R3C2), no 1
68a. 4,8 only in R3C2 -> R3C2 = {48}
68b. 20(4) cage = {2378/3467}, 3 locked for C3 and N1
68c. 8 in N1 only in R23C2, locked for C2

69. R2C1 = 1 (hidden single in N1)
69a. R9C3 = 1 (hidden single in N7)

70. R1C3 = 2, R5C3 = 5 (hidden singles in C3)
70a. 9 in C3 only in R78C3, locked for N7

71. 12(4) cage at R6C9 = {1236/1245}
71a. R8C8 = {46} -> no 4,6 in R7C9

72. 20(4) cage at R6C8 = {2369/2459}
72a. 6 of {2369} must be in R78C7 (R78C7 cannot be {29} which clashes with R23C7, ALS block), no 6 in R7C8
72b. 5 of {2459} must be in R7C8 -> no 4 in R7C8
72c. R78C7 = {26/69/49} -> R23C7 + R78C7 = [32]{49}/[32]{69}/{39}{26}, 3 locked for C7 and N3

[This puzzle was stubborn right to the end; all I can see now is …]
73. Consider combinations for 20(4) cage at R6C8 (step 72) = {2369/2459}
20(4) cage = {2369} => R8C8 = 4 (hidden single in N9), R8C12 = [83], R8C5 = 2
or 20(4) cage = {2459} => R6C2 = 2, no 2 in R8C7
-> no 2 in R8C7

74. R8C5 = 2, R7C5 = 8, R7C1 = 4, R8C12 = [83], R5C12 = [39], R3C1 = 7, R2C3 = 3, R2C7 = 9, R3C8 = 2, R6C8 = 3, R6C9 = 2, R7C9 = 5, R8C8 = 4 (cage sum)

and the rest is naked singles.

I'll rate my walkthrough for A53 V0.1 at (Very) Hard 1.75. In addition to forcing chains I did some difficult permutation analysis involving interactions with innie-outie differences. It also deserves a high rating by being stubborn right to the end.

sudokuEd
Hi all.
Been thinking about how we are going as a forum. Things are really taking off with lots of new forum members, posters and puzzles. Lots of great stuff!! Now comes the 'but'.

We've had two extremes last week. Andrews follow-up of a puzzle months old (SampuZ4), since he likes each puzzle on this forum to have a walk-through. On the other hand, Assassin 53 + 3 versions within 24 hours and a 4th thrown in for good measure even before all the previous 3 have been solved. The pace has certainly picked up! Lots of puzzles gives lots of free choice and decisions.

But, there are also negatives in having a number of versions of the one puzzle. Personally, I like one really hard extra version - though understand the need to cater for a wide audience. Hence, thanks to Ruud & Para for posting A53V2 + walk-through.

But no one has posted about Jean-Christophe's V2.5 or V0.1. I don't like puzzles having no response. But it shows that we probably had too many versions this week and in hindsight, didn't need those two.

I really value the (mainly) hand-solving ethic of this forum, including that we are mostly working on the same puzzles. Too many versions, (especially if they have not been hand-solved first - Ruud excluded of course!) doesn't fit in with this ethos in my opinion. We could burn out or lose too much of the group feeling. I enjoy you guys too much to risk that. :colors:

I'm not suggesting putting a number figure on how many versions/puzzles per week. But am asking that we think about the (slower?) pace of this forum before posting a puzzle.

Thanks
Ed


Andrew
Some interesting thoughts from Ed. If there are too many variants each week then people will limit the number of puzzles that they try to solve. For Assassin 53 I've solved Ruud's original and am part way through his V2. I probably won't try the other ones as they are clearly much harder and because we now have Assassin 54. I'm pleased to see that Ed then posted his walkthrough for J-C's V3. I'll try to find time to look at that.

Since we don't want to discourage any forum member from posting variants, I would suggest that anyone except Ruud should limit themselves to one variant each week.

One other point. I only attempt variants and extra puzzles that have diagrams posted. I expect those who are using SumoCue import puzzles using the code string. Even so I would think that people are more likely to be tempted to try a puzzle when they can see a diagram first.

I'll be interested to see what other group members think.


mhparker
I agree. In retrospect, we didn't need the V2.5. I suspect what happened is that JC first of all tried to use an identical cage pattern to the original. But, as he said at the time, the cage pattern made it impossible to produce a much more difficult puzzle. I can confirm this, because I also experimented with generating several random V2's based directly on this design. Despite lengthy efforts, my program couldn't come up with a single one that Sumocue couldn't easily solve. Seems like JC had the same problems, explaining why he shortly afterwards took a different approach and posted a second puzzle (the V3), with some cages having been merged.

As for the V0.1, I don't know why JC posted it so early after Ed announced the breakthrough move for the V3, before we were even through with the V3. But I sense some informal competition between man and machine (i.e., JSudoku) here. I hope not. That would be like comparing apples and oranges.

BTW, I'm not sure how seriously JC intended us to take the V0.1. After all, why call it a V0.1 and not a V4, if not to stress its inofficiality? Well, whatever, at least Para's made a start with it now.Agree again. Too much competition between us and JSudoku (or any other computer-based solver for that matter) can only be detrimental to the popularity of this forum.On reflection, I don't think a limit is a good idea, since there may be bone-fide reasons for somebody to post multiple puzzles in a particular week (e.g., to train particular skills). But, in general, one or two variants a week may be a good guideline. Also, it's a good idea to wait a while until the previous puzzles have been solved, unless the new puzzle is intended to appeal to different forum members. For example, posting a very difficult V2 up front when Ruud has only produced a single, relatively straightforward Assassin, would be considered OK.

On a final note, many thanks to JC for an excellent A53V3. Keep 'em coming!


Andrew
Maybe I didn't make myself clear. What I meant was that, in general, forum members should voluntarily limit themselves unless there is a particular reason for more than one.I'll support Mike on that!