assassin 64

[mhparker]

Hi folks,

Yes, a great team effort.

Indeed. Highlights for me were the large number of people involved, and seeing two new members (Howard S and goooders) get actively involved for the first time. Also, it was good to see Glyn contributing again. Special thanks to Cathy for getting the ball rolling. Thanks also to Andrew for offering to consolidate our steps, which were fairly chaotic in some places! . I'm sure Ed is regretting not having been able to take part in the action...

Edit: the above paragraph is beginning to sound like part of a speech at an award ceremony!

I'll be interested to see what rating Ed eventually comes up with for this puzzle; it's clearly much, much harder than A64.

Yes, 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. In other words, about the same as the A60RP-Lite, which also had several forum members stumped. It's definitely not as hard as the A62V2 was, which I could eventually solve without hypotheticals, but only by using several grouped AICs. (BTW, I rated the A62V2 at 2.0. Haven't posted the WT for it yet, but plan to do so soon.)

Yes, we did use hypotheticals (several of them, me included!), but only because (having looked at how JS (JSudoku) and SS (SudokuSolver) did it) we missed a couple of critical moves that would have allowed us to complete the puzzle without any limited T&E whatsoever. JS found one, SS (which took a completely different path) found the other. Either one would have sufficed to break the deadlock, but unfortunately we found neither.

If as Mike suggested early on, this one might have a very narrow solving path, then a consolidated WT is probably almost the same as a condensed WT.

By condensed, I assume you mean what I usually refer to as optimized? In other words, where some steps (not on the solving path) may be dropped, and others re-ordered in order to ensure a more logical and coherent build-up, etc.

However, I would like to clarify something here. When I refer to the narrowness of a solving path, I'm referring to the situation without the use of any T&E-based techniques. As soon as one is prepared to use hypotheticals (as we did), then the number of possible solution paths skyrockets. For example, there may be only a couple of ways to solve this particular puzzle without T&E, but we could probably have found dozens of hypothetical chains leading to a conflict, given enough time. Thus, a consolidated WT in this case is not the same as a condensed/optimized WT, because merely completing the puzzle does not imply that we found (or were even close to finding) the optimum solving path.

BTW, the path taken by SS was particularly impressive. Gone are the days where we were regularly out-gunning the automated solvers! With the advent of SS and the quantum leap made by the new version of JS, the tables are often turned, and the solver logs can teach us a thing or two. From SS's point-of-view, this puzzle really was as easy as the low rating suggests. As I think I've said before, computer-based ratings can at best only reflect the difficulty level of the solving path they used to solve the puzzle. But if a human misses this path, and cannot easily find another way through, the perceived difficulty can be much higher. The trouble is, how does one objectively measure the narrowness of the solution paths and the resulting impact on the ergonomics of a puzzle?

That's all for now. If anybody's interested, I plan to make another post describing the moves that we missed, with some extra information and ideas for Ed and his ratings.

[CathyW]

Definitely interested Mike - please do post on what we missed.

I did try this puzzle in JSudoku afterwards - it seemed to get stuck on "Deduce all moves" and also when I tried deducing one move at a time! Surprisingly, the first move was an LOL on n46 creating an extra group. Not something I would have thought of!

Thanks Andrew for the offer of consolidated WT - and I do mean consolidated, not optimised or condensed, although Richard's 52 can be omitted and, as Glyn pointed out, Para's moves duplicated a couple that had already been given!

[Glyn]

Regarding Cathys comments I tried JSudoku 0.6b3 on it this morning and it stalled horribly I think it has entered some loop at least on my system. However as Ruud said it takes lots of steps I tried some earlier versions I have not erased, and 0.5 thru 0.6b1 can solve the problem.

The chain supplied by Gooders 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.

[mhparker]

Hi again folks,

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.

The chain supplied by Gooders 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:

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...

[mhparker]

Hi all,

Just want to clarify a few points:

Although I made it pretty clear yesterday how much I object to T&E, people may be asking themselves what the point is of trying to struggle through a puzzle using primitive logic, when a newbie like Goooders can quickly come up with a few T&E spoiler steps that crack the puzzle very quickly, by-passing and negating all those more complex moves the rest of us had been making up to that point.

How can this be? Isn't something wrong here? Is advanced logic failing us? Should we (heaven forbid!) acknowledge that T&E was better here?

Yes and no. Yes, something is wrong, but no, advanced logic is not failing us. The first point is that the rest of us were mainly concentrating on the wrong part of the grid (n258), where we should have been looking where Goooders was looking (c1/n7). The second point is that the fact that Goooders' T&E steps led to a quick contradiction indicates that there is a lot of "contention" in this part of the grid. In such cases, it is often possible to find advanced logical steps to replace the simpler T&E ones, with similar effect.

And so it is here. Indeed SudokuSolver did precisely this. It was using advanced non-T&E logic, in the same area that Goooders was looking at, to bust open the puzzle very quickly, thus accounting for its low rating.

To give Goooders the credit for a good basic idea, and to illustrate that the power of Goooders' steps can be achieved without T&E, I am including an alternative path, starting from our original step 27. The ideas are taken from Goooders, SudokuSolver (mainly) and some of my own (in particular, step 30). It should just be taken as an example of how we could/should have done it.

Marks pic after original step 27:

Code: Select all

.-----------.-----------------------------------.-----------.-----------------------------------.-----------.
| 23456789  | 123456789   123456789   456789    | 12345678  | 123456      123456789   123456789 | 345789    |
|           :-----------------------.-----------'           :-----------.-----------------------:           |
| 23456789  | 123456789   123456789 | 123456789   123456789 | 12356     | 123456789   123456789 | 345789    |
:-----------'-----------.           |           .-----------:           |           .-----------'-----------:
| 1234        12345678  | 23456789  | 23456789  | 23456789  | 23567     | 23456789  | 123456789   12346789  |
:-----------.           '-----------+-----------'           '-----------+-----------'           .-----------:
| 3456789   | 12345678    12345678  | 123456789   123456789   123456789 | 123456789   123456789 | 123456789 |
|           :-----------------------'-----------.           .-----------'-----------------------:           |
| 345678    | 123456      123456      23456     | 12345678  | 56789       56789       56789     | 12345678  |
|           :-----------------------.-----------'           '-----------.-----------------------:           |
| 3456789   | 456789      456789    | 123456789   123456789   123456789 | 123456      123456    | 123456789 |
:-----------'           .-----------+-----------.           .-----------+-----------.           '-----------:
| 1234        56789     | 12345678  | 1245      | 23456     | 23456789  | 123456789 | 123456789   12346789  |
:-----------.-----------'           |           :-----------'           |           '-----------.-----------:
| 345678    | 12345678    12345678  | 1245      | 23456789    23456789  | 123456789   123456789 | 56789     |
|           :-----------------------'-----------:           .-----------'-----------------------:           |
| 123456    | 789         789         789       | 23456     | 12345       123456      123456    | 23456     |
'-----------'-----------------------------------'-----------'-----------------------------------'-----------'

28. 9(2)n7 cannot be {45}. Here's how:
28a. Either 11(2)n1 = {(4/5)..}, or
28b. 11(2)n1 = {(2/3)..} -> h5(2) at r37c1 = {14}
28c. either way, {45} blocked for 9(2)n7

29. 9(2)n7 = {36}/[72]/[81] = {(1/3/7)..}
29a. -> {137} combo blocked for 11(3)n7
29b. -> 11(3)n7 = {128/146/236/245} (no 7)

30. 11(3)n7 cannot be {146}. Here's how:
30a. 1 in c1 locked in r379
30b. thus, either r9c1 = 1, or
30c. r37c1 = {14}
30d. either way, {146} is blocked for 11(3)n7

31. 11(3)n7 now = {128/236/245}
31a. 2 locked for n7
31a. cleanup: no 7 in r8c1, no 3 in r3c1

32. 9(2)n7 = {36}/[81] = {(1/3)..},{(3/8)...}
32a. -> {38} combo blocked for 11(2)n1
32b. -> {389} combo blocked for 20(3)n4 = {479/569/578} (no 3) = {(4/6/8)..}, {(5/9)..}, {(7/9)..}

33. 2 in c1 locked in n1 -> not elsewhere in n1

34. 3 in c1 locked in n7 -> not elsewhere in n7

35. 11(3)n7 now = {128/245} (no 6)

36. r7c12 cannot contain both of {45}. Here's how:
36a. r7c12 = [45] -> 23(4)n47 = {68}[45]
36b. but this is blocked by 20(3)n4 (step 32b)

37. only other place for {45} in n7 is 11(3)n7
37a. -> 11(3)n7 = {(4/5)..}
37b. -> 11(3)n7 = {245}, locked for n7
37c. cleanup: no 1 in r3c1

38. r7c2 cannot contain a 6. Here's how:
38a. r7c2 = 6 -> 23(4)n47 = {79}[16]/{59}[36]
38b. but both of these are blocked by 20(3)n4 (step 32b)
38c. -> no 6 in r7c2

39. 6 in n7 locked in 9(2)n7
39a. -> 9(2)n7 = {36}, locked for c1
39b. cleanup: no 5 in r12c1

40. HS in c1 at r7c1 = 1
40a. -> r3c1 = 4
40b. cleanup: no 7 in r12c1

41. 11(2)n1 = {29}
41a. 9 locked for c1 and n1

42. 20(3)n4) = {578}, locked for n4

43. Split 22(3) at r6c23+r7c2 = {679} (only possible combo)
43a. -> r7c2 = 7; r6c23 = {69}, locked for r6 and n4

44. HS in r7 at r7c4 = 7

...

[CathyW]

Appreciate the clarification Mike. I was still mulling over your previous post. It depends on how you define T&E, and where you draw the line for T&E. For myself, Goooders contradiction chain was perfectly logical but it is a bifurcation with one route leading to conflict and one route leading to solution.

Your post today has convinced me that the A64 V2 is indeed solvable without hypotheticals. I wouldn't like to say that one way is definitely better than the other but as a still (I hope!) improving solver I would also prefer not to use bifurcation or contradiction chains if possible. Having said that, I'm not going to rule it out from future puzzles if I can't find another way forward.

I'd be interested to read other members' views.

Cathy x

[mhparker]

Hi folks,

I don't want to dominate this forum, but I said above that I wanted to make a post on how automated solvers tackled this problem:

SudokuSolver (SS)

The key to the solution path used by SS were the conflicting partial combinations between 20(3)n4 and 23(4)n47, including several I did not list above. Although the two cages do not completely "see" each other (r7c2 is not a peer of r456c1), the interaction between them was greatly enhanced by the fact that there was no overlap between the candidates of r7c1 and r7c2. Thus, for any digit pair in r7c12, there was only one possible permutation.

However, SS did not use my step 30 above, and hence did not deduce 9(2)n7 = {36} by locking the 6 of n7 within these two cells. Instead it locked the 8 into the h25(4) n7 innies, thus eliminating [81] as an option for 9(2)n7, leaving {36} as the only remaining combo.


JSudoku (JS)

As mentioned by Glyn above, JSudoku (version 0.6b2 in my case) loops on this puzzle. So (as Ruud said), it does indeed require a "large number of steps" to solve this puzzle. An infinite number in fact!

But before it looped, it noticed the following move (which I've simplified quite a bit), which could have been used to break through the deadlock around our original step 53, where we could not find a way to progress without using hypotheticals (see marks pic below):

Code: Select all

.-----------.-----------------------------------.-----------.-----------------------------------.-----------.
| 23456789  | 123456789   123456789   689       | 1234678   | 234         23456789    23456789  | 345789    |
|           :-----------------------.-----------'           :-----------.-----------------------:           |
| 23456789  | 123456789   123456789 | 12346789    12346789  | 12356     | 123456789   123456789 | 345789    |
:-----------'-----------.           |           .-----------:           |           .-----------'-----------:
| 1234        5678      | 2346789   | 2346789   | 57        | 23567     | 2346789   | 1234        1234      |
:-----------.           '-----------+-----------'           '-----------+-----------'           .-----------:
| 3456789   | 123456      123456    | 123456789   123456789   1236789   | 345678      345678    | 1234568   |
|           :-----------------------'-----------.           .-----------'-----------------------:           |
| 345678    | 123456      123456      2345      | 12345678  | 567         6789        6789      | 1234568   |
|           :-----------------------.-----------'           '-----------.-----------------------:           |
| 3456789   | 56789       56789     | 123456789   123456789   1236789   | 12345       12345     | 1234568   |
:-----------'           .-----------+-----------.           .-----------+-----------.           '-----------:
| 1234        56789     | 12345678  | 1245      | 23456     | 2356789   | 123456789 | 1234        6789      |
:-----------.-----------'           |           :-----------'           |           '-----------.-----------:
| 3678      | 12345678    12345678  | 1245      | 23456789    2356789   | 123456789   123456789 | 789       |
|           :-----------------------'-----------:           .-----------'-----------------------:           |
| 1236      | 789         789         789       | 23456     | 1234        123456      123456    | 234       |
'-----------'-----------------------------------'-----------'-----------------------------------'-----------'

The key move (and its follow-up) JS found here can be simplified down as follows:

54. outies c123 = r159c4 = 19(3) cannot contain both of {67} ({667} not possible)
54a. -> split 20(4) at r2346c4 must contain at least 1 of {67}
54b. -> innies n2 (r1c46+r3c5) cannot contain both of {67}
54c. -> {467} blocked
54d. -> no 6 in r1c4
54e. r159c4 = [829/847/928/937]
54f. -> no 5 in r5c4

55. LoL(n5): r3c5 = r5c6, r5c4 = r7c5
55a. -> no 6 in r5c6; no 5,6 in r7c5
55b. cleanup: no 7 in r5c78

now continue as for step 59 in original tag WT


This begs the question as to why JS did not see the key conflicting partial combinations that SS did. Maybe it would have if it had not looped, but I doubt it. I suspect that the reason is that JS only detects conflicting partial combinations occuring within a single house. For example, if 20(3)n4 = {389/479/569/578} = {(5/9}..}, {(7/9}..}, {(8/9}..}, then JS would recognize that 23(4)n47 cannot have both of {59}, both of {79} or both of {89} within n4, but would ignore the fact that r7c1 (which is also a peer of all cells of 20(3)n4) also needs to be considered.

In that sense, it appears that SudokuSolver handles conflicting partial combinations better than JSudoku does. Congratulations, Richard, you seem to have gone one up there!

[mhparker]

but it is a bifurcation with one route leading to conflict and one route leading to solution.
...
I wouldn't like to say that one way is definitely better than the other but ... I would also prefer not to use bifurcation or contradiction chains if possible.

Hi, Cathy. 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. What is the crucial difference? I'll answer that below.

As a second example, consider Goooders' contradiction "chain":

1 will not go in the 9 because that requires542 for the 11(neither 641 nor 623 works) but if that is so columns 1 and 2 of row 7 are 63 which works with neither 68 nor 59 required by the bottom left outies of 22 (note 59 cant work with the 20 in middle left nonet)

Let me simply ask the questions:

Why doesn't {146} work for 11(3)n7?

Similarly why doesn't {236} work?

"But", I hear you say, "that's obvious! {146} can't work because we've already used the 1 in the 9(2)n7 cage. And {236} can't work, because a 1 in 9(2)n7 will force h5(2) at r37c1 to be {23}, thus blocking {236} for 11(3)n7".

If so, that would be correct. But let's think it through in a bit more detail first. The problem is, in order to know that the 1 is not available for the 11(3) cage, the hypothesis 9(2) = [81] must already have been committed in order that the candidates 1 and 8 are eliminated in the corresponding peer cells. Furthermore, in order to know that r37c1 is now {23}, the combinations must be re-evaluated. Not only that, but conflicting combination analysis needs to be performed to detect that {23} in r37c1 blocks the {236} in 11(3)n7. In an automated solver, all this updated information, needed for later parts of the "chain" has to be stored somewhere. Of course, at this stage we don't even know whether the original hypothesis is correct, so we can't "burn our bridges", as it were, in case we need to go back.

In computer terms, this means we need to bifurcate. In other words, the current grid state must be saved first. Then the initial hypothesis is committed. After that, the solver is simply allowed to run on, using every solving technique (naked/hidden singles, combinational analysis, conflicting combinations, etc., etc.) it has at its disposal until (if at all) a contradiction is reached. If this happens, the effects of applying the initial hypothesis (now known to be false) have to be reversed. This is done by restoring the original saved grid state, a process also known as backtracking. The word bifurcation implies (in computer terms) "forking", because when the state of the grid is saved, we initially have two identical copies of it (i.e., the working copy and the saved one).

This is the computer equivalent of making a photocopy of a puzzle being done on paper, making a guess and carrying on accordingly, throwing the working copy in the bin if a contradiction is reached, and returning to the saved photocopy.

Such bifurcation is almost universally regarded as trial-and-error. Of course one can try to distinguish between "limited T&E" (I use the term hypothetical for that) and full-blown T&E, but it's T&E all the same.

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.

[goooders]

i sort of agree with mhparker and sort of disagree

i agree theres no point in doing a puzzle based upon a guess also theres no point in trial and error however you then run into the issue of what is trial and error my own view is that if i can work through a combination in my head which leads to a contradiction that is fine but if i were to resort to pen and paper i have crossed a line(i fully accept this is "how long is a piece of string" but i feel comfortable with it)

i suspect i maybe do assassins slightly differently from some others my own rule is not to fill in all the numbers and then cut them back bit by bit however if there is 23 cage i will fill in a 689

i rely on combinations and patterns so for example in the 64v2 i noticed straightaway that in the bottom left nonet the 9 cage would not support a 54 because of the other numbers in column 1 nor then a 72 so given the 789 and the 22 outie i thought it was worth having a look at

in pure mathematics all proofs derive essentially from either induction or contradiction(for example that the square root of 2 is irrational) thus if there are only two paths and one is wrong then a fortiori the other is right

newbie or otherwise of the 64 assassins to date i thought 3 or 4 were very hard the last being 55

it is perhaps worth saying that the very fast solvers in the ordinary sudoku world champioships are all "pattern recognisers" rather than number eliminators(vis a vis devising a quick strategy to a solution)

finally finally some illustrious names are called in aid i wondered if anyone had come across "udosuk " whom i havent seen on this website but who demonstrated some brilliant logic in solving some of nate dorwards 10 puzzles

[CathyW]

Thanks Mike - sorry for confusing the terminology.

Goooders - udosuk is a regular on the djape forum which I also frequent. Perhaps he lurks without posting. I'm sure his input on the Assassins would be useful (perhaps I'll send him a PM). I never managed to solve Nate's puzzles when they were originally put on his site though I might give them another go having learned a lot from doing Ruud's Assassins.

Roll on no. 65!

[Para]

Hi

I guess for me it all has to do with the satisfaction of solving a puzzle. Implication chains are a sound form of logic which can solve any puzzle, but it's not really the most beautiful logic. I rather take a few hour more on a puzzle to find a nicer way to the solution. I guess it is the same as i feel about uniqueness moves. I rather solve a puzzle without uniqueness moves, so i can also prove the puzzle only has one solution.

it is perhaps worth saying that the very fast solvers in the ordinary sudoku world champioships are all "pattern recognisers" rather than number eliminators(vis a vis devising a quick strategy to a solution)

The big difference in this, is that on sudoku and logic puzzle championships it is all about speed, solving as many puzzle as possible in a certain time limit, or all puzzles as fast as possible. This of course gives a whole different attitude to solving. The solving techniques i use when speed solving are a lot different then when i do it for fun. In such championships use anything that will bring me closer to a solution. I sometimes solve these assassins on speed as well. Then i tend to use a lot of implication chains and uniqueness eliminations and don't work the same way as i normally do. This will always work faster.
When i solve puzzles for fun, i just want to reach a nice path to a solution. I have a lot of logic puzzles laying that i haven't solved yet, but if i wanted to could easily solve using a T&E/implication chain approach. But i choose to try and solve it using nicer logic.

So i guess it all comes down to a choice you make when solving logic puzzles. And i hope we can keep it at that, because these discussions have been going on everywhere and the arguments and discussions are always the same. Beauty vs speed, logic?, mathematicians use it to solve problems as well. Seen it, heard it and it all still keeps coming down to the choice you make as solver.

greetings

Para

[CathyW]

Well said Para. I expect discussions on what constitutes acceptable T&E techniques will continue from time to time. I certainly find it more satisfying to solve a puzzle without T&E but I still have a lot to learn on some of the advanced techniques that Mike mentioned, especially as they might apply in killers. So, for now at least, I choose not to rule out hypotheticals and UR moves.

Cathy x

[Andrew]

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

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

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.

[Glyn]

Hi everyone

Now that the thorny subject of bifurcation and T&E has come up there are always likely to be differences of opinion, however our goal must be to extend the number of solving methods available as we have a whole load of unsolvables which it would be nice to crack. It is quite possible that they may remain unsolvable without some sort form of chaining and maybe this chaining will be required to violate standard rules of AICs. (IMHO the word maybe can be deleted here).

I know that Mike is not entirely against AIC which formalises the processes involved. In vanilla Sudoku these chains can not only be long, but also be comprise of multithreads, groups, fish structures, ALS etc. They can usually be laid out fairly clearly on an unmodified grid. They do however require strong links for their construction and such relationships are sadly lacking in Killers 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. JC has already described killer variants of some chain structures and hinted at ALS extensions which I think may be have some similarities to what we might require.

Rather than continue the discussion here, which is not really the right place and where it will eventually get lost, we should perhaps open a new thread either in the Assassin forum or even better in the Solving Techniques & Tips forum (as they would apply to Texas Jigsaw Killers as well). Hopefully we can showcase the newly discovered tricks like the LOL pincer and develop a framework for building new ones where they will be available without hunting through the WTs. Also we might tempt some of the experts from the vanilla world, who sometimes drop in, and have already built on AIC methods and notation, to cross over to the dark side and helps us try to extend AIC further if that is the way to go on the unsolvables.

All the best

Glyn

PS I hope that mentioning AIC hasn't put people off, I think we would really only use it to encapsulate the tricky moves and a description of what was going on would be necessary. At the end of the day we are all meant to have fun

[Andrew]

I hope that mentioning AIC hasn't put people off, I think we would really only use it to encapsulate the tricky moves and a description of what was going on would be necessary. At the end of the day we are all meant to have fun

I've got no problems with advanced techniques being used so long as they are clearly presented and the outcomes, such as fixed cells, candidate eliminations or combo eliminations, are stated.

Like everyone else I want to improve my solving. 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. When it's a decision between studying advanced techniques, either from that book or a website guide, or solving more puzzles it's not difficult to guess which gets done first.