## Help to solve hardest puzzles

Post the puzzle or solving technique that's causing you trouble and someone will help

### Re: Help to solve hardest puzzles

Hi SpAce,

First of all this is an exocet our friend totuan had something else in mind when he wrote "almost exocet"

The exocet base logic is very simple and widely open.

Take 2 cells in the same unit containing n possible digits. This is the base
Take 2 other cells anywhere this is the target

If for any digit of the base one target cell must contain this digit then we have an exocet
the target can only contains digits form the base
For any pair in the base, we have the same pair in the target

This is the trivial base rule.
The 2 target cells can be replaced by 3 target cells having a locked digit ....

For a manual player, an exocet is of interest if it can be easily seen and if it has good chances to bring some solving tools.

The first reduction is to have an exocet located in a band with, usually the base in one mini row and the targets in the 2 other boxes.
The second reduction is to have an easy proof of the digit per digit constraint. For me, the proof is easy when for each digit it comes from the digit pm.

The exocet here fits with these reductions. So if you suspect that you have a potential exocet, You can apply the simple proof

champagne wrote:Step 1 check that this is an exocet pattern for each digit:
a) force the digit in the base
b) clear the digit in the target
c) check that you have no solution

BTW, when you have a locked digit, "platinum blonde" as example, the proof is very similar, point b) is clear the digit in the 3 target cells

David made a huge work to define the subset Jexocets where the exocet property can be derived easily from the given. With my computer, I stick to the general definition (restricted normally within a band) so I let him comment on the Jexocet.

Next step is the solving rules offered by an exocet.

Again, we have an open space with the basic logic. If a cell sees both target (/all targets), it can not contain the base digits.
A more specific clearing rule has been seen using a UR threat (see "abi loop" in the documentation)
And many more specific derived rules have been written here and there.

In our example 2 basic cleaning moves have been done

If the base contains the digit 4, then both targets would contain the digit 4, no pair can be valid with the digit 4.

The second is just a consequence of the basic properties applied to the box 1 pattern.
the cell r1c3 sees the 2 targets and contains only the 3 digits of the base
the cell r3c1 sees the base and r1c3
r3c1 can not contain the base pair (sees the base)
the third digit is forced in r3c1
so r3 c1 can not contain any of the base digits
champagne
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### Re: Help to solve hardest puzzles

champagne wrote:First of all this is an exocet our friend totuan had something else in mind when he wrote "almost exocet"

Ok, thanks for the clarification!

The exocet base logic is very simple and widely open.

Take 2 cells in the same unit containing n possible digits. This is the base
Take 2 other cells anywhere this is the target

If for any digit of the base one target cell must contain this digit then we have an exocet
the target can only contains digits form the base
For any pair in the base, we have the same pair in the target

Awesome! This is the kind of general rule I can work with. So, is it fair to say that most of the parts of the JExocet, such as the companion cells, mirror cells, S-cells, cover sets, etc, aren't at all necessary to understand the general Exocet logic? They're only there to help find and validate that specific (albeit the most common and useful) Exocet variant, and to provide well-defined elimination rules for the same? If one understands the general definition and the resulting inferences, there's no need to memorize all those specific rules (except to use it effectively in practice, I guess)?

In our example 2 basic cleaning moves have been done

If the base contains the digit 4, then both targets would contain the digit 4, no pair can be valid with the digit 4.

This one was pretty easy, once I understood the basic rule.

The second is just a consequence of the basic properties applied to the box 1 pattern.
the cell r1c3 sees the 2 targets and contains only the 3 digits of the base
the cell r3c1 sees the base and r1c3
r3c1 can not contain the base pair (sees the base)
the third digit is forced in r3c1
so r3 c1 can not contain any of the base digits

A bit more complicated but still easy to see as a direct result of the basic rule. Could it be seen like this:

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`.--------------------.--------------------.--------------------.| 9     8     123    | 7      6      4    | 5    t123    123   || 7    t123   1236   | 8      235    1235 | 4     9      1236  || 136   4     5      |b123   b23     9    | 167   12367  8     |:--------------------+--------------------+--------------------:| 5     9     1237   | 1234   2347   6    | 17    8      127   || 168   127   4      | 1259   25789  1258 | 3     1267   12679 || 1368  1237  123678 | 1239   23789  1238 | 1679  4      5     |:--------------------+--------------------+--------------------:| 4     6     1389   | 239    2389   7    | 189   5      139   || 2     357   3789   | 3569   1      358  | 6789  367    4     || 138   1357  13789  | 34569  34589  358  | 2     1367   13679 |'--------------------'--------------------'--------------------'Case base(12): (12)(r3c45* & r1c8,r2c2) - (12=3)r1c3 - *(13=6)r3c1Case base(13): (13)r3c45 - (13=6)r3c1Case base(23): (23)(r3c45* & r1c8,r2c2) - (23=1)r1c3 - *(13=6)r3c1=> 6r3c1`

Or something like that?
-SpAce-: Show
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2514
Joined: 22 May 2017

### Re: Help to solve hardest puzzles

SpAce wrote:
Case base(12): (12)(r3c45* & r1c8,r2c2) - (12=3)r1c3 - *(13=6)r3c1

Case base(13): (13)r3c45 - (13=6)r3c1

Case base(23): (23)(r3c45* & r1c8,r2c2) - (23=1)r1c3 - *(13=6)r3c1

=> 6r3c1[/code]
Or something like that?

Yes you have plenty of ways to express this very simple logic. The merit of players like abi and totuan is to detect them. My solver try to clear pairs. It works, but nothing attractive for a player (long nets), except for the well known "abi loop" so common with exocets
champagne
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Location: France Brittany

### Re: Help to solve hardest puzzles

Thanks again, champagne! Is there a collection of puzzles containing Exocets? I'd like to see if I could spot some on my own, preferably starting with some trivial samples. This is how I imagine the process:

1. Spot a possible base pair
2. Find possible targets
3. Validate it's an Exocet
4. See what kind of eliminations are available

At first I'd be happy to complete steps 1-3 and find some basic eliminations, and then start learning about the more complicated possibilities.
-SpAce-: Show
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2514
Joined: 22 May 2017

### Re: Help to solve hardest puzzles

Hi SpAce,

You have in my "google drive space" with the name ph_1409_exocets.zip a relatively old file giving examples of all kinds of exocets based on the status of the PH data base in 2014.

the link to that storage place is here

I did not update the files meantime, but this is enough to start
champagne
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Location: France Brittany

### Re: Help to solve hardest puzzles

Thanks a lot, champagne! I really appreciate it.

champagne wrote:...but this is enough to start

Are you sure? 1 529 417 puzzles doesn't seem that much

One more question. Which publicly available software solvers can help with Exocets? SudokuWiki has some parts implemented, but I would imagine it probably misses many variants and finer details. I also know Phil's solver has Exocets. Is that a more complete implementation?
-SpAce-: Show
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2514
Joined: 22 May 2017

### Re: Help to solve hardest puzzles

Those are the only released ones with them implemented space.

Allans can somewhat show them when reverse constructed into xsudo but dosent find them on its own.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1163
Joined: 05 September 2006

### Re: Help to solve hardest puzzles

SpAce wrote:One more question. Which publicly available software solvers can help with Exocets? SudokuWiki has some parts implemented, but I would imagine it probably misses many variants and finer details. I also know Phil's solver has Exocets. Is that a more complete implementation?

Hi SpAce,
The reason why I opened this thread is exactly the core of your question. If you read the help files of both solvers you mention, you see that they implement the JExocet pattern, as it is presented in David P Bird's "JExocet compendium" here

JExocet pattern has a few more requirements than the "general" exocet defined by champagne in his post above. These extra requirements are:
- base cells and target cells in the same band or stack
- no more than two cover houses for base digits in "S" cells.
These conditions alone are enough to give assurance that the pattern is an exocet. Moreover, they are easy to spot "manually". JExocet is therefore a pattern for P&P players and this is the great interest of DPB's Jexocet compendium.
A large part of exocets are JExocets (I read somewhere about 80%, to be confirmed).

This last requirement (about "S" cells cover houses) is not met for the puzzle WU#299 which I asked help for. This is the reason why the exocet found by champagne, abi and totuan is not detected by Phil's and Andrew's solvers. It is also the case for further "Weekly Unsolvables" which David Filmer seems to have raised the level of ...

I don't know any other public solver implementing the most comprehensive exocet. I am still in search of a teaching document...

So, even if JExocet do not solve all puzzles having an exocet, it solves a large proportion of them, and it is easy to spot on PM. My advice, FWIW, would be: start with JExocet, try to find them manually in champagne database, leave aside puzzles having a more general exocet and study these later.
Cenoman
Cenoman

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### Re: Help to solve hardest puzzles

champagne's file '03 E1 exo je.txt' in 'ph_1409_exocets.zip' is entirely made up of puzzles from his 'potential hardest' list that contain Junior Exocet [JE2].
The file '03 ED exo double.txt' has puzzles from the same list that contain a double Junior Exocet [JE4]. The much rarer JE3 and JE+ are also found in these files.
The other files contain puzzles that have exocets that typically require detailed checking of the exocet property. David P. Bird [in his JE compendium thread] has recently expanded the 'Almost Exocet' group to some further 'patterns' that avoid the checking step.
The current definition of 'potential hardest' is based on Nicolas Juillerat's 2007 scoring of puzzle strategies used in his Sudoku Explainer. Back in 2007, Exocet, SK Loops, MSLS and others were not known [I think so, anyhow]. One can now speculate how Nicolas might have scored the JE2. I might think a score of around 7.0 for JE2 might be about right. The XY Chain is 6.9 [I recall].
I took David Filmer's U304 as an example. The minimal puzzle is 11.4 / 1.2 / 1.2 but this puzzle has a JE2 that eventually yields 3 more placements. If these 3 are added to the puzzle, one gets an SE of 9.8 / 9.8 / 2.6. If one could add the JE2 as a 7.0 to SE, one would then get a rating of 9.8 /1.2 / 1.2. Still very hard.
There are though many examples in '03 E1 exo je.txt' which solve easily after the JE2. In 2018, I think we would say that these puzzles are no longer in the PH group.

Best
Gordon
ghfick

Posts: 92
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### Re: Help to solve hardest puzzles

ghfick wrote: I think we would say that these puzzles are no longer in the PH group.

Thank you, Gordon, for recalling the historical background of SE rating. Debates about puzzle classification are recurring, and other systems are proposed from time to time. I agree with you that puzzles whose difficulty rating is dramatically lowered by a JE2 or a double JE or a MSLS are "easy" hardest. But this doesn't make the question in my opening post purposeless.
I recall my question : how to solve puzzles that are not solved by well documented patterns (JExocet, MSLS, SK Loops) ?

I got a nice answer for WU#299.
A few days later, I posted WU#303. Just a terse response from champagne.
ghfick wrote:I took David Filmer's U304 as an example. The minimal puzzle is 11.4 / 1.2 / 1.2 but this puzzle has a JE2 that eventually yields 3 more placements. If these 3 are added to the puzzle, one gets an SE of 9.8 / 9.8 / 2.6. If one could add the JE2 as a 7.0 to SE, one would then get a rating of 9.8 /1.2 / 1.2. Still very hard.

Relevant example : the remaining SE 9.8 is still too hard for my solver (as well as for Andew's)

I am also stuck with recent WU#300, 301, 302. In total I am stuck on WU#300 to 304.

In this part of the forum, detailed explanations are given to beginers on X-wing or XY-wing, sometimes on basics. Isn't it also the right place to ask help for hardest strategies ?

Can someone help to solve WU#303 here (and the others later) ?
Cenoman
Cenoman

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### Re: Help to solve hardest puzzles

Cenoman wrote:If you read the help files of both solvers you mention, you see that they implement the JExocet pattern, as it is presented in David P Bird's "JExocet compendium"

That's not very clear, actually. Both call their implementations "Exocet", which is misleading. They do mention "jExocet" as well but imply it's a synonym, which is clearly not the case (besides the incorrect spelling). As far as I understand, the descriptions of the pattern are also more limited than the full JExocet, which makes them seem like an even smaller subset of Exocet. Then again, it seems that at least the SudokuWiki solver implements more of the spec than what is described -- maybe it's close to a full JExocet, I wouldn't know. What is really annoying is that the help page describes just one elimination rule, but the solver uses more and refers to them with numbers (defined where?).

The SudokuWiki description is quite confusing anyhow, as it does mention the various JExocet-specific details, such mirror cells and escape cells, but never explains what they're used for (but the solver uses at least the mirror cells for eliminations). It's also unclear if it includes the JE+(+) variants or not. All of that confusion leaves one wondering which checks are really needed to know you have an "Exocet" (actually a JExocet) and what to do if you do have one. It left me with such disgust that I didn't want to touch the pattern for a long time. Of course the compendium answers most of those questions, but since SudokuWiki is more accessible to most, it's a pity it does such a poor job of presenting the JExocet unambiguously.

The compendium, on the other hand, does a very good job of presenting the JE and its variants, as I would expect from David, but it jumps right into the details and skips explaining how the JE fits into the context of the generic Exocet family. Like I said, my learning style would have really benefited from that kind of an introduction, which is why I was grateful for champagne's answer. Now I have a better idea of how the JE fits into the big picture.

I have one specific question about the SudokuWiki description:

"We then check if there are two Target cells (T) that contain all the digits of the Base cell (plus any extras)."

Is that "all the digits" rule valid? Can't we have a target that doesn't have all the base candidates, which would automatically imply those candidates aren't true in the base? (By "target" I mean all the target cells together.) It's probably answered somewhere but I can't find it now.

This last requirement (about "S" cells cover houses) is not met for the puzzle WU#299 which I asked help for. This is the reason why the exocet found by champagne, abi and totuan is not detected by Phil's and Andrew's solvers. It is also the case for further "Weekly Unsolvables" which David Filmer seems to have raised the level of ...

Which is why I think it's beneficial to understand the general Exocet rule even when almost fully concentrating on JExocets (which is clearly a good general strategy). I would imagine that a skilled JE hunter would spot your example as an almost-JE, and then it would be a simple matter of conducting a few more checks to see if it has the Exocet property despite the non-standard S-cell pattern. (Well, in *this case* it was a rather simple matter, but I do imagine situations when it's not. There's also the question of how do you document a non-standard Exocet? How do others know it really has the property if it's not obvious from the pattern?)

So, even if JExocet do not solve all puzzles having an exocet, it solves a large proportion of them, and it is easy to spot on PM. My advice, FWIW, would be: start with JExocet, try to find them manually in champagne database, leave aside puzzles having a more general exocet and study these later.

That's exactly what I'm planning to do. Studying the JE has clearly the highest payoff, which I knew from the start. My point was that I needed to understand the general definition first so I could understand why we have a "Junior" version of it and how they're related. The really confusing part, however, is the concept of a "Senior Exocet". When I first saw that in the compendium files, I thought it was indeed the *full* Exocet. Seems that it's not.
-SpAce-: Show
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2514
Joined: 22 May 2017

### Re: Help to solve hardest puzzles

ghfick wrote:champagne's file '03 E1 exo je.txt' in 'ph_1409_exocets.zip' is entirely made up of puzzles from his 'potential hardest' list that contain Junior Exocet [JE2].
The file '03 ED exo double.txt' has puzzles from the same list that contain a double Junior Exocet [JE4]. The much rarer JE3 and JE+ are also found in these files.
The other files contain puzzles that have exocets that typically require detailed checking of the exocet property. David P. Bird [in his JE compendium thread] has recently expanded the 'Almost Exocet' group to some further 'patterns' that avoid the checking step.

Thanks for the info, Gordon!

The current definition of 'potential hardest' is based on Nicolas Juillerat's 2007 scoring of puzzle strategies used in his Sudoku Explainer. Back in 2007, Exocet, SK Loops, MSLS and others were not known [I think so, anyhow]. One can now speculate how Nicolas might have scored the JE2. I might think a score of around 7.0 for JE2 might be about right. The XY Chain is 6.9 [I recall].

Has anyone tried to build such an extension to SE? It would be really interesting to see how it would affect the ratings if those known exotic patterns were added.

I took David Filmer's U304 as an example. The minimal puzzle is 11.4 / 1.2 / 1.2 but this puzzle has a JE2 that eventually yields 3 more placements. If these 3 are added to the puzzle, one gets an SE of 9.8 / 9.8 / 2.6. If one could add the JE2 as a 7.0 to SE, one would then get a rating of 9.8 /1.2 / 1.2. Still very hard.

Since you're an experienced manual solver, how would you continue solving such a puzzle after any and all exotic patterns have been harvested and it's still very hard? What about hard puzzles that don't have such patterns at all? I think this is what Cenoman is interested in as well.
-SpAce-: Show
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

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Joined: 22 May 2017

### Re: Help to solve hardest puzzles

Cenoman wrote:I recall my question : how to solve puzzles that are not solved by well documented patterns (JExocet, MSLS, SK Loops) ?

I'm also very interested in answers to this, though I haven't even used any of those three yet. Btw, can someone point to the most definite sources on the last two? Also, how are "multi-fish" (also often mentioned) related to these? What other "exotic" solving methods are there, besides those related to symmetries? The three above seem to always be listed as the most important ones, so I would guess they cover the most ground, but that can't be the whole picture, right?

In this part of the forum, detailed explanations are given to beginers on X-wing or XY-wing, sometimes on basics. Isn't it also the right place to ask help for hardest strategies ?

I hope so. I for one would be very happy to read such discussions.
-SpAce-: Show
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

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Joined: 22 May 2017

### Re: Help to solve hardest puzzles

One comment from a poor manual solver.

Searching for exotic patterns takes resources = function(techniques zoo <=> knowledge, techniques complexity to apply) and surely there is a point where these resources exceed those for applying the guess (blind backdoor guess or informed guess for particular cell/pair/triplet/house/digit template).

Now-days the guessing is taboo. The manual and computer-assisted solvers prefer large forcing nets just to simulate logic and claim that these techniques have nothing in common to the guessing. Kind of dancing with the puzzle for a whole night and never putting it into bed.

This doesn't answer the question, but suggests a reformulation to "At which point a manual solver should stop searching for more and more complex known patterns and gracefully switch to applying effective to a manual solver guesses?". Are there known puzzles that require this? IMHO yes.

In this forum there is a discussion which informed-guessing steps a manual solver applied to one of the top hardest puzzles and solved it in about half an hour. The approach led to silent excommunication of the author from the community of The True Logic Only Manual Sudoku Solvers.

Other key point is "known pattern" and all would agree that any newly discovered effective and simple to identify/apply shortcut is welcome. But the question is for the known shortcuts.

Again, I am not against any incredible attempt to break a puzzle using a very complex exotic technique, but in terms of resources spent, there is a threshold and the techniques beyond it are less human-friendly than the informed guessing. And the hardest known puzzles are beyond this threshold.

Keep dancing
dobrichev
2016 Supporter

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### Re: Help to solve hardest puzzles

Searching for exotic patterns takes resources = function(techniques zoo <=> knowledge, techniques complexity to apply) and surely there is a point where these resources exceed those for applying the guess (blind backdoor guess or informed guess for particular cell/pair/triplet/house/digit template).

If you play in a turnaments, this is true around naked hidden pairs, StrmCkhr could tell more

and to make it short, if you are a manual solver, forget puzzles rating over 8 to 9 in sudoku explainer unless you are looking for exotic patterns, and if you can't find an exotic pattern, give up.

Beeing a poor manual solver, I would fully agree in this .
champagne
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