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Archive Part B - Assassins 51-75, variants & other killers

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Post subject: Re: A51-75 Assassin Archive PART B

Posted: Sun Jul 06, 2008 5:42 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Old SSv3.2.1 scores:

Killer rating table      
Rounded Score from SSv3.2.1 
! = 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.63      1.00    1.05|A.64v2    1.75   !2.10|A.66      1.00    0.95|
|A.63v1.5  1.25    0.95|A.65      1.25    1.05|                      |
|A.63v2   H1.50    1.20|A.65v2   H1.50    2.65|                      |
|A.64      1.25    1.35|A.65v3    1.50    1.85|                      |
|====================================================================|
                              page #4

Old scores SSv3.3.0:

Rounded Score from SSv3.3.0 
! = 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.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

Killer rating table
SudokuSolver Target range v3.6.3

Rating.....Score
0.50   =   0.85
0.75   =   0.90-0.95
1.00   =   1.00-1.20
1.25   =   1.25-1.45
1.50   =   1.50-1.70   (E) = Easy  (H) = Hard

===========================================================================================
|A ##     by     Rate    Score|A ##     by     Rate    Score|A ##     by     Rate    Score|
|-----------------------------+-----------------------------+-----------------------------|
|A.63    Ruud    1.00     1.10|A.64v2  Ruud    1.75     1.85|A.66    Ruud    1.00     1.10|
|A63v1.5 mhp     1.25     1.15|A.65    Ruud    1.25     1.25|                             |
|A.63v2  mhp    H1.50     1.35|A.65v2  Ruud   H1.50     2.75|                             |
|A.64    Ruud    1.25     1.35|A.65v3  Ruud    1.50     1.75|                             |
|=========================================================================================|
                                         page #4

Assassin 63 by Ruud (Aug 07)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 9 7 1 | 5 6 3 | 2 8 4 |
| 5 8 2 | 1 9 4 | 7 3 6 |
| 3 4 6 | 8 2 7 | 5 9 1 |
+-------+-------+-------+
| 8 5 9 | 6 4 2 | 1 7 3 |
| 6 2 3 | 7 1 8 | 4 5 9 |
| 7 1 4 | 9 3 5 | 8 6 2 |
+-------+-------+-------+
| 1 9 8 | 4 5 6 | 3 2 7 |
| 2 6 5 | 3 7 1 | 9 4 8 |
| 4 3 7 | 2 8 9 | 6 1 5 |
+-------+-------+-------+

Quote:

goooders: isnt this very easy?
Andrew: This was a smooth puzzle except right at the end..about 0.75 which is probably about right
herschko: found this one relatively easy.... I just wouldn't call it an "assassin."
Andrew, after doing v1.5: in Mike's definition of ratings, that average Assassins now have a rating of 1.25, I would put A63 as 1.0.

Walkthrough by Andrew including (Hidden &) Killer pair:

Walkthrough by Para including Killer Triple:

Last edited by Ed on Sun Dec 28, 2008 9:03 am, edited 3 times in total.

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Post subject: Re: A51-100 Assassin Archive PART B

Posted: Sun Jul 06, 2008 5:45 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Assassin 63v1.5 by mhparker (Aug 07)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 2 9 8 | 7 4 5 | 3 1 6 |
| 6 4 1 | 8 3 2 | 9 5 7 |
| 3 7 5 | 1 6 9 | 4 8 2 |
+-------+-------+-------+
| 8 6 3 | 5 7 4 | 1 2 9 |
| 4 5 2 | 3 9 1 | 7 6 8 |
| 9 1 7 | 6 2 8 | 5 3 4 |
+-------+-------+-------+
| 1 2 9 | 4 5 6 | 8 7 3 |
| 5 3 4 | 2 8 7 | 6 9 1 |
| 7 8 6 | 9 1 3 | 2 4 5 |
+-------+-------+-------+

Quote:

Para: 1.5 seems overrated. Didn't have any more trouble with this one than with the V1. Nothing special needed...and one Killer Triple
Andrew: Para's step 21 was a powerful move...would probably be rated as 1.0 for Para's solving path...but 1.25 for the way that I solved it.

Walkthrough by Para including Killer Triple:

Walkthrough by Andrew:

Last edited by Ed on Sun Jul 06, 2008 10:34 pm, edited 1 time in total.

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Post subject: Re: A51-100 Assassin Archive PART B

Posted: Sun Jul 06, 2008 5:46 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Assassin 63v2 by mhparker (Aug 07)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 5 9 8 | 3 2 4 | 1 6 7 |
| 6 1 7 | 8 9 5 | 4 3 2 |
| 3 4 2 | 1 6 7 | 5 9 8 |
+-------+-------+-------+
| 7 3 4 | 5 8 6 | 9 2 1 |
| 2 6 1 | 7 4 9 | 8 5 3 |
| 8 5 9 | 2 1 3 | 6 7 4 |
+-------+-------+-------+
| 1 8 6 | 9 3 2 | 7 4 5 |
| 9 7 3 | 4 5 1 | 2 8 6 |
| 4 2 5 | 6 7 8 | 3 1 9 |
+-------+-------+-------+

Quote:

mhparker, lead-in: (Estimated rating: 1.75)
Andrew in June 2011: congratulations to nouggie for your first posted walkthrough. :applause:

... this was the only walkthrough posted at the time (where was everybody?

) ... I'll rate my walkthrough at Hard 1.5

Stream of consciousness, first effort ever Walkthrough by Nouggie:

2011 Walkthrough by Andrew:

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Post subject: Re: A51-100 Assassin Archive PART B

Posted: Sun Jul 06, 2008 5:53 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Assassin 64 by Ruud (Aug 07)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 4 6 3 | 5 8 2 | 7 9 1 |
| 9 1 2 | 7 3 6 | 8 4 5 |
| 8 7 5 | 9 4 1 | 2 3 6 |
+-------+-------+-------+
| 1 9 6 | 8 5 3 | 4 7 2 |
| 3 5 8 | 2 7 4 | 1 6 9 |
| 7 2 4 | 1 6 9 | 3 5 8 |
+-------+-------+-------+
| 5 3 7 | 6 2 8 | 9 1 4 |
| 2 4 9 | 3 1 5 | 6 8 7 |
| 6 8 1 | 4 9 7 | 5 2 3 |
+-------+-------+-------+

Quote:

Para: Was having some fun with this one. Also used a technique we don't get to use much in Assassins (LoL). Guess this assassin rates somewhere between 1.00 and 1.25
Andrew: I agree with Para that it's rated between 1.0 and 1.25
CathyW: Hmm - more a 1.5 in my book - quite a challenge
Andrew: Lots of killers

Walkthrough by Para:

Walkthrough by CathyW with xy-loop:

Walkthrough by Andrew:

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Post subject: Re: A51-100 Assassin Archive PART B

Posted: Sun Jul 06, 2008 5:57 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Assassin 64v2 by Ruud (Aug 07)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 2 1 7 | 9 6 3 | 4 8 5 |
| 9 5 3 | 4 8 1 | 2 6 7 |
| 4 6 8 | 2 5 7 | 9 3 1 |
+-------+-------+-------+
| 8 3 1 | 6 4 9 | 5 7 2 |
| 7 4 2 | 3 1 5 | 8 9 6 |
| 5 9 6 | 8 7 2 | 3 1 4 |
+-------+-------+-------+
| 1 7 4 | 5 3 8 | 6 2 9 |
| 3 2 5 | 1 9 6 | 7 4 8 |
| 6 8 9 | 7 2 4 | 1 5 3 |
+-------+-------+-------+

Quote:

CathyW: According to Ed's rating list from Sudoku Solver... the V2 has a marginally lower rating than the V1 - 1.28 compared to 1.29 presumably indicating that it shouldn't be any more difficult. But I beg to differ - completely stumped after 26 steps.
mhparker: Just shows that there's some more tweaking for Ed to do before we can replace the manual ratings with the automatic ones.
mhparker: it was considerably harder than the V1, because of the very narrow solving paths however it was no monster. I would give it a clear rating of 1.75
Tag solution: by CathyW, mhparker, Howard S, rcbroughton, Para, Glyn & goooders
Andrew (in 2014): When this puzzle was originally posted, I wrote the Consolidated Walkthrough but hadn't taken part in the "tag", so I've now tried this puzzle.
It's hard to know what rating to give my walkthrough. All I'll say is that it was harder than A65 V2 and A65 V3, both of which I've solved recently; also that my hardest step for this puzzle was more difficult than any steps I used for those two puzzles.
A 2021 Revisit thread here

Consolidated Walkthrough by Andrew:

Alternative ending to tag solution by mhparker:

How Solvers tackled A64v2 by mhparker:

Walkthrough by Andrew:

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Post subject: Re: A51-100 Assassin Archive PART B

Posted: Sun Jul 06, 2008 6:26 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

A64 thread Bifurcation/chain/T&E discussion

Post 1: goooders on A64v2:

Post 2: Glyn:

Post 3: mhparker:

This (unexpected) post is not going to be easy to write. But what I have to say has to be said. Sometimes remaining silent is not the most diplomatic approach.

Glyn wrote:

The chain supplied by Gooders =D> tore the problem right open and would have done so even right at the start, none of the programs is geared up to start a puzzle that way. Either human inspiration or a radically different type of computer solver would be required to investigate the hypotheticals.

They (i.e., the "computer solvers") can already do it: it's called bifurcation!

You know that of course, but what I'm trying to say is that if you allow a computer-based solver to simply save the grid state, try out the elimination or (as in this case) cage combination, continue with the puzzle using basic techniques until (potentially) some sort of conflict is found, restoring the old grid state (if so) and carrying out the original hypothesis, then even nightmarish puzzles like the A60RP and A50V2 are a breeze! For many people, myself included, using T&E based on simple techniques is not as satisfying as trying to solve a puzzle using advanced techniques without T&E.

A good example is TJK18. I originally spent days on this, unsuccessfully. There were 2 possibilities for everything (i.e., one solution, and one near-solution). If T&E were acceptable, I could have easily finished on one evening by doing (part of) the puzzle twice and publishing the walkthrough as such!

Going back to the implication chain in question, I (and probably others on this forum) find conflicts like the one Goooders did all the time, but unless they can be encapsulated in simpler, less T&E-based terms, I don't publish them, otherwise I'd be (metaphorically-speaking) torn apart limb-from-limb by the other forum members! For a newbie it may be forgivable, but for any one of the regulars here, their reputation as a solver would quickly be in tatters!

In that sense, one can indeed argue that newbies make for more effective (but not necessarily better) solvers than the experts, because (in general) the more experience one gets, the less willing one is to sacrifice all those great solving techniques one has picked up over the years and simply use a try-it-and-see approach instead. This certainly applies to me, where there are several moves I made some time back (e.g. step 26 in the A48Hevvie consolidated WT) that I would not make now, even if it means not being able to complete the puzzle.

Sure, we can start using extensive T&E in our WTs (although I won't), and I'm sure we'll often reach our "destination" faster if we do. But the end result is hardly likely to impress the Ruuds, Jean-Christophes, Myth Jellies or Andrew Stuarts of this world, is it?

As Ruud put it on the "Assassin 60 - the rejected pattern" thread:

Ruud wrote:

There is no value in trying to solve [the puzzle] with guesses.

Incidentally, Ruud, when posting a puzzle, often refers to us as the "advanced solvers on the forum". If we were to routinely use T&E to solve the puzzles he sets us, I don't think it would be long before this accolade is withdrawn...

Post 4: mhparker:

Post 5: CathyW:

Post 6: mhparker:

Post 7: goooders:

Post 8: Para:

Post 9: CathyW:

Post 10: Andrew:

CathyW wrote:

but it is a bifurcation with one route leading to conflict and one route leading to solution....

mhparker wrote:

Sounds like you may be misunderstanding the term bifurcation. It simply means forking the state of the puzzle, not simply going in one of two directions (possibly in turn). For example, all AICs are also based on a 2-state starting premise (i.e. premise is true or false). And yet AICs are not regarded as bifurcation.

and later in the same message

mhparker wrote:

This may seem obvious. But let's go back to the first example, namely AICs. Why isn't this bifurcation? Why isn't it T&E?

The crucial difference is that AICs, Nice Loops, X-Cycles, and so on, work purely by analysis of the strong and weak links currently present in the grid. No hypothesis or other intermediate results have to be committed, and no other solving technique (like conflicting combinations, etc.) needs to be invoked. No commitments implies that no copy of the grid needs to be made, therefore neither bifurcation nor backtracking is involved. They are therefore pure solving techniques and not T&E, as in the first case.

I hadn't planned to get involved in this discussion about bifurcation, T&E, etc. but I can't completely agree with what Mike has said.

In its original sense bifurcation means forking in two directions. The people who have invented advanced techniques in the last couple of years didn't like that. They have therefore taken the view that techniques that start with forking but are thereafter logical are not considered to be bifurcation even though they really are in the pure sense of that word.

To take an example, simple colouring (why I'll admit I don't yet understand well enough to use except in the very simplest case) has two chains from one cell to another cell. If one chain has an even number of links and the other an odd number of links, then a candidate in the destination cell can be eliminated. The simplest case, which can occur in jigsaw sudokus, has a two link chain and a single link chain. This is pure logic but still starts with bifurcation.

The same applies to the more advanced techniques that Mike has listed. They are not T&E but they are still bifurcation in the pure sense of that word. To repeat myself, they are not considered to be bifurcation because the people who have invented advanced techniques in the last couple of years didn't like that and consider it to be a dirty word.

I don't think that Cathy was misunderstanding the term bifurcation; she was just using it in a different sense than Mike does, in fact in the same way that I do.

Post 11: Glyn:

Post 12: Andrew:

Post 13: mhparker:

Andrew wrote:

In its original sense bifurcation means forking in two directions. The people who have invented advanced techniques in the last couple of years didn't like that. They have therefore taken the view that techniques that start with forking but are thereafter logical are not considered to be bifurcation even though they really are in the pure sense of that word.

Andrew wrote:

I've had Andrew Stuart's book since it first came out but, unlike Cathy and Mike who have well thumbed copies, I've only managed quick glances so far.

Yes, bifurcation does simply mean forking in its original sense. However, in Sudoku circles it's invariably reserved for a specific type of forking, namely forking of the entire grid state. For an example, see chapter 1 of Andrew Stuart's book, where he associates bifurcation with Ariadne's Thread. Another distinguishing feature of bifurcation in this sense is that the starting choice (e.g., cell candidate, cage combination, ...) is essentially arbitrary.

With the regular chain-based techniques in Sudoku, the situation is very different for a number of reasons:

The starting choice is not arbitrary. For example, for AICs, the starting choice is the candidate premise at one end of a strong link being false.
The grid is not modified. Note: This is important! Even the slightest modification to the grid would in general require saving the entire grid state at each branching point in the chain! I use AICs and Nice Loops quite a lot, so if anybody sees me using any strong links that weren't there at the start of the chain, I've made a mistake and would like to know about it!
The chain is built up "merely" by following weak and strong links, not by potentially using every solving technique under the sun. For automated solvers, this means using dedicated chain processing rather than simply allowing the solver to run further.
Although regular chains do often involve finding contradictions, one is looking out for particular termination conditions here, not simply responding to any unexpected error condition.

Glyn wrote:

...unless one is prepared to bite the bullet and allow the links to modify the cage values to a certain extent. Perhaps we could call them strong active links. The chains would preferably be short as any of the active links would start to make the grid unrecognisable and carry the strong odour of T&E.

I use the term dynamic links for these, because the strong links arise dynamically as a result of side effects of earlier links in the chain. But the difference between these dynamic links and the "active" links you describe is merely one of terminology. The concept is identical.

All chains containing dynamic ("active") links are hypotheticals in my book. Hypotheticals are generally regarded as limited T&E, or even "guessing" (as Ruud has just expressed it on the A65 thread). However, whilst this is often true, to uniformly apply this equation would belittle the tremendous aptitude humans have for recognizing promising patterns and cutting off unpromising avenues of exploration in order to dramatically reduce the amount of searching to be performed. The problem is, how can hypotheticals be formalized? I agree with Glyn that a lot of research work still needs to be done here (and that it's best to do all this on another thread).

Post 14: Ruud:

Post 15: mhparker:

Hi Ruud,

Thanks for the suggestions. Here are a few quick points to get the ball rolling. Maybe other forum members can add a few more.

Ruud wrote:

If you want to see bifurcation in action, take a puzzle that has no more logical solving steps and make an extra copy. Now pick a cell with 2 candidates or a cage with 2 combinations or a row, column or box where a certain number can only go in 2 places.

Actually (just in case anyone's getting the wrong impression), as far as the first two solving techniques you mentioned are concerned (Guess and Trial & Error), one can pick a cell with more than two candidates (or a cage with more than two combinations), and it's still only bifurcation (not trifurcation, etc.). As such, only one copy of the grid state needs to be made, and the two branches are essentially cell = chosen candidate (or cage = chosen combination) and cell <> chosen candidate (or cage <> chosen combination).

For the Tabling Verity technique, one clearly needs as many copies of the grid (including the original) as the number of candidates in the chosen cell, combinations in the chosen cage, or candidate positions in the chosen unit, respectively, in order to be able to compare the results. So this is real N-furcation. I presume this is what Andrew had in mind in his previous post.

Ruud wrote:

If you find the solution in one of the copies and you accept it, you have used a Guess.

Care must be taken here. Strictly speaking, one has found a solution, not necessarily the solution. So, by completing the grid after making a guess, one is also making the implicit assumption that the puzzle only has one solution.

Ruud wrote:

If you find a common truth in both copies, i.e. a candidate that is eliminated in both puzzles, or a placement made in both, you have used a Forcing Net.

Just for info: We also recently had a slightly more complicated case (Cathy's step 22 in her A61X WT), where trifurcation was involved that, whilst not yielding a common placement, nevertheless locked a digit into one of two positions within a unit, thus allowing that candidate digit to be eliminated elsewhere in that unit. A placement common to all branches can in this sense just be seen as being the special case where a particular digit is locked into a single candidate position within a particular unit.

Ruud wrote:

A solving technique is acceptable when it can be rewritten as a (reversible) sequence of implications where each node in this sequence is a coherent group of candidates. Because every sequence of implications is reversible, the use of this term is superfluous.

True, it should in theory be superfluous. However, this requirement is clearly intended to filter out chains with dynamic links (see my previous post), which are what I usually mean when I refer to the term hypothetical. For example, if a side effect of a link in the chain changes the grid state from G to G', then a subsequent link may not be reversible, because the underlying grid state in the forward direction (G') differs from that in the reverse direction (G).

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Post subject: Re: A51-100 Assassin Archive PART B

Posted: Sun Jul 06, 2008 6:30 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Assassin 65 by Ruud (Aug 07)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 4 3 2 | 6 1 8 | 5 9 7 |
| 7 6 9 | 5 4 2 | 1 3 8 |
| 8 1 5 | 9 7 3 | 2 4 6 |
+-------+-------+-------+
| 5 7 4 | 2 6 1 | 9 8 3 |
| 6 9 3 | 4 8 5 | 7 1 2 |
| 2 8 1 | 3 9 7 | 4 6 5 |
+-------+-------+-------+
| 3 4 7 | 1 5 6 | 8 2 9 |
| 9 2 8 | 7 3 4 | 6 5 1 |
| 1 5 6 | 8 2 9 | 3 7 4 |
+-------+-------+-------+

Quote:

CathyW: Excellent puzzle - kept me occupied most of this afternoon... Was stuck for quite a while
Andrew: not ..... particularly difficult..I rate this Assassin as 1.25..also 1.25 for the ways that Cathy and Para solved it.

Walkthrough by CathyW:

Walkthrough by Para:

Walkthrough by Andrew:

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Post subject: Re: A51-100 Assassin Archive PART B

Posted: Sun Jul 06, 2008 6:31 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Assassin 65 v2 by Ruud (Aug 07)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 6 3 7 | 5 1 8 | 2 9 4 |
| 2 1 4 | 6 3 9 | 7 5 8 |
| 8 5 9 | 7 2 4 | 1 3 6 |
+-------+-------+-------+
| 9 4 3 | 8 7 2 | 6 1 5 |
| 5 6 8 | 1 9 3 | 4 7 2 |
| 1 7 2 | 4 6 5 | 9 8 3 |
+-------+-------+-------+
| 4 9 1 | 3 8 6 | 5 2 7 |
| 3 2 6 | 9 5 7 | 8 4 1 |
| 7 8 5 | 2 4 1 | 3 6 9 |
+-------+-------+-------+

Quote:

Ruud, lead-in: Tough, but no hypotheticals (guesses) needed.
CathyW: Hmmph! Confused. Can't say that the V2 is a fun puzzle.
Howard S: Learnt a lot
Tag solution: Howard S and Para - moral support from CathyW and mhparker
Para: Step 29 isn't really a solver-step, more human creativity
Andrew (in 2014): In some ways my solving path was the other way round from the Tag solution. I used an unusual, possibly creative, step for my first key move but a more regular one for my final breakthrough. Rating Hard 1.5

Tag Walkthrough:

Alternative to tag solutions' step 29 by mhparker using discontinuous Nice Loop:

Para wrote:

Step 29 isn't really a solver-step, more human creativity.

Nice move, Para!

I agree with you here that it's extremely unlikely that an automated solver would (or could) find such a step. However, it's not inconceivable that a solver with a very good AIC/Nice Loop implementation could find the alternative move presented below that would serve as a replacement for your steps 29 - 29c:

Code:

.-----------------------.-----------.-----------------------------------.-----------.-----------------------.
| 12345678    12345678  | 23456789  | 2568        134         2568      | 123789    | 456789      456789    |
|           .-----------:           '-----------.-----------.-----------'           :-----------.           |
| 12345678  | 123456    | 23456789    68        | 1234      | 79          123789    | 123456    | 456789    |
:-----------:           '-----------.-----------:           :-----------.-----------'           :-----------:
| 56789     | 123456789   123456789 | 156789    | 123479    | 145       | 123456      123456    | 46        |
|           |           .-----------:           |           |           :-----------.-----------'           |
| 56789     | 123456789 | 13456789  | 156789    | 1279      | 125       | 23456789  | 1234567     1234567   |
|           :-----------'           |           '-----------'-----------:           '-----------.-----------:
| 56789     | 123456789   123456789 | 156789      79          13568     | 23456789    23456789  | 123456789 |
:-----------'-----------.           :-----------.-----------.           |           .-----------:           |
| 123567      1235679   | 12356789  | 4         | 568       | 13568     | 2356789   | 12356789  | 12356789  |
|           .-----------'-----------:           |           |           :-----------'           |           |
| 24        | 12456789    12456789  | 3         | 568       | 568       | 12456789    12456789  | 12456789  |
:-----------:           .-----------'-----------:           :-----------'-----------.           :-----------:
| 12345678  | 12345678  | 345678      79        | 568       | 79          12345678  | 12345678  | 12345678  |
|           '-----------:           .-----------'-----------'-----------.           :-----------'           |
| 35678       356789    | 356789    | 12          124         124       | 356789    | 356789      356789    |
'-----------------------'-----------'-----------------------------------'-----------'-----------------------'

29. Complex discontinuous Nice Loop (2 weak links at discontinuity) removes 9 from r12c3, as follows ("=>" implies strong link, "," implies direct link):
29a. if r12c3 = 9 -> r3c123 <> 9
29b. => r3c45 = 9 -> r2c6 <> 9
29c. => r2c6 = 7 -> r8c6 <> 7
29d. => r8c6 = 9 -> r8c4 <> 9
29e. => r8c4 = 7, r2c4 = 8 -> r12c3 <> 9 (contradiction)
29f. Conclusion: no 9 in r12c3

Note: Nice Loop notation avoided for clarity and due to difficulty representing direct link between 7 in r8c4 and 8 in r2c4

Walkthrough by Andrew:

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Post subject: Re: A51-100 Assassin Archive PART B

Posted: Sun Jul 06, 2008 6:34 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Assassin 65 v3 by Ruud (Aug 07)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 5 4 9 | 6 7 3 | 1 2 8 |
| 8 1 3 | 5 9 2 | 6 7 4 |
| 7 6 2 | 4 1 8 | 3 5 9 |
+-------+-------+-------+
| 2 3 8 | 1 5 4 | 9 6 7 |
| 6 5 1 | 9 8 7 | 2 4 3 |
| 9 7 4 | 2 3 6 | 8 1 5 |
+-------+-------+-------+
| 1 9 7 | 8 2 5 | 4 3 6 |
| 4 2 5 | 3 6 9 | 7 8 1 |
| 3 8 6 | 7 4 1 | 5 9 2 |
+-------+-------+-------+

Quote:

Ruud, lead-in: hot hot hot, probably needs some creative moves (guesses)
Para: That V3 is really deceiving, you think you're doing pretty well, placing digits, making eliminations and then all of the sudden you hit a dead end and there's seems to be no way out.
Caida: I've been pounding away at it for quite sometime and I think I'm going in circles. I've resorted to trial and error
Afmob: Rating: 1.75 it wasn't as difficult as A74 Brick Wall but a bit more complicated than M1, it's solvable without guesses or T&E
gary w: after a tough battle..rather more than 5 hours....managed to crack it

Andrew (in 2014): I've only just tried this puzzle. Not as hard as I'd expected from Ruud's and Para's comments. Strange that this puzzle was the V3; maybe Ruud's solver couldn't find the immediate placements from the starting grid (the V2 doesn't have any). Rating 1.5
A 2021 forum Revisit here

No contradiction moves Walkthrough by Afmob:

Fresh-eyes Walkthrough by Caida:

Beginning solution outline by gary w without any t&e:

Walkthrough by Andrew:

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Post subject: Re: A51-100 Assassin Archive PART B

Posted: Sun Jul 06, 2008 6:37 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Assassin 66 by Ruud (Aug 07)

Puzzle pic:

Code: Select, Copy & Paste into solver:

Solution:

+-------+-------+-------+
| 4 7 9 | 2 6 8 | 3 5 1 |
| 2 3 6 | 1 5 4 | 8 7 9 |
| 1 8 5 | 7 9 3 | 4 6 2 |
+-------+-------+-------+
| 3 5 2 | 6 4 1 | 9 8 7 |
| 9 4 1 | 3 8 7 | 5 2 6 |
| 8 6 7 | 9 2 5 | 1 4 3 |
+-------+-------+-------+
| 7 9 4 | 5 1 6 | 2 3 8 |
| 6 1 8 | 4 3 2 | 7 9 5 |
| 5 2 3 | 8 7 9 | 6 1 4 |
+-------+-------+-------+

Quote:

Howard S: One of the easier ones - I am torn between 0.75 and 1.0
Andrew: I think I'll rate this as 1.0. Step 32 isn't a difficult one but I found it was hard to spot
CathyW: 0.5 because I only used Innies, Outies, Outies-Innies, cage combinations, killer combos and combination analysis and because it only took me just over an hour including writing down my steps as I did them
azpaull: this was the first Assassin in several weeks that I have been able to do on my own....I'll give it a 0.75....let me thank you all for your walk-throughs and your commentary
gary w: both a66 and a67 took me about 1.5-2 hrs to do.A "deadly" killer in The Times normally takes me about 0.5 hrs so i'ld rate both of these as significantly harder

Walkthrough by Andrew:

Walkthrough by CathyW:

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