## JExocet Pattern Definition

Advanced methods and approaches for solving Sudoku puzzles

### Re: JExocet Pattern Defintion

Hi logel,

I'm (now) noting David's post, which has materialized while I've been editing this one.
FWIW, I agree with what he's saying.

logel wrote:Hi David
Yet another discussion rule vs pattern.

Inventing/finding new rules seem to be an endless story without any prospect to be completed.

If I summarize the discussion correctly, the JExocet fit to a precise rule definition now.

The JE+ looks like some hybrid, neither rule nor pattern.

This is very confusing.
JE and JE+ are both well defined patterns with associated elimination rules.

Maybe a better elucidation of the differences between JE+ and JE is called for (?). The basic idea is that one target cell, can be replaced by two, as long as there is a non-base digit that is forced to occupy one of the two cells, after considering where it can be placed in the "S" column, associated with the target pair. There's a possible variation where rather then considering where it can go in the column, one considers where it can go in the box containing the target pair. Whether that's supposed to be covered by the definition, I can't say.

This is the main thing I wanted say: (ignore the rest, if you like)

logel wrote:b) If you instead intend to use JE+ in a pragmatic way to find some more eliminations you can't get otherwise, its completely OK. In this case I would rather start with assuming the potential targets TRUE and perform a limited number of local eliminations. If you find a contradiction there is a hit.

I invite you to try this approach for a few JE (not JE+) instances, and report the findings (perhaps) in your "Universal Elimination Pattern" thread. (Maybe here will be fine as well).
Try to find a general pattern of logic.
I'm curious whether you might come up with something that differs fundamentally, from a particular "general pattern of logic" that I discussed in PMs with Denis.

Regards,
Blue.
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### Re: JExocet Pattern Defintion

blue wrote:
logel wrote:Yet another discussion rule vs pattern.
[...]If I summarize the discussion correctly, the JExocet fit to a precise rule definition now.
The JE+ looks like some hybrid, neither rule nor pattern.

This is very confusing. JE and JE+ are both well defined patterns with associated elimination rules.

I fully agree with Blue.
I don't know if my re-writing of David's definition of JE and not that of JE+ played a part in the difference you make in your post, but you should know that the only reason for me was a matter of time. JE+ is a pattern and resolution rule in exactly the same sense JE is.
As for David, in spite of our different views on many topics, our ideas of a pattern are much closer than he thinks.

BTW, I don't consider I took any noticeable part in the definition of JE. My re-writing was merely cosmetic. So I think I can make a short history of JE. I think this is the ideal example for showing the difference between a real pattern/rule (JExocet) and something else (Exocet).
- years ago, Allan Barker found some common configuration of candidates allowing some elimination(s) in a few hard puzzles;
- Champagne dug into this; he defined the "Exocet", part of which is a partial pattern (not enough to justify any eliminations) and part of which is a verification procedure (much in the spirit of your approach); he spent much time popularising it and finding it in hard puzzles; he undoubtedly played a major role in this history;
- however, for many people, the Exocet definition was not satisfactory;
- on the Programmer's Forum, Blue proposed a logical description that could turn this procedure into a real pattern;
- after tweaking Blue's definition, David finally proposed the JE (and JE+) pattern(s).

JExocet is less general than Exocet (how much less remains an open question as we currently have no estimate of JE's presence neither in champagne's hardest list nor for easier puzzles).
But, contrary to Exocet, you can be shown a JE in a grid and you can immediately say "yes, I see it" and conclude "I can eliminate these candidates" - without checking thousands of possible truth value assignments (what you call permutations) to the relevant set of candidates. Well, I feel like paraphrasing something Blue said somewhere.
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### Re: JExocet Pattern Defintion

Blue wrote:Maybe a better elucidation of the differences between JE+ and JE is called for (?). The basic idea is that one target cell, can be replaced by two, as long as there is a non-base digit that is forced to occupy one of the two cells, after considering where it can be placed in the "S" column, associated with the target pair. There's a possible variation where rather then considering where it can go in the column, one considers where it can go in the box containing the target pair. Whether that's supposed to be covered by the definition, I can't say.

With the JE definition as it stands there are occasions where it's possible to have a choice of target cells on different cross lines in one particular box. This produces two candidate JE patterns to check, but an instance where both alternative cross lines comply with the partial fish requirements has never yet come to light. If additionally these two target options contain a locked candidate, I think we then get to the JE+ circumstances you're considering. However, then proof of the eliminations wouldn’t depend on the existence of the locked candidate.

Is that right? If not a diagram would help.

Denis Berthier wrote:JExocet is less general than Exocet (how much less remains an open question as we currently have no estimate of JE's presence neither in champagne's hardest list nor for easier puzzles).

In JE or JE+ if the partial fish requirement isn't met the case is closed, but for not for Exocet which continues to hunt for justification using templates and/or inference following. What would be interesting to me is how often this extra work is required, and how often it produces a hit.

Regards David
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### Re: JExocet Pattern Defintion

David P Bird wrote:
If additionally these two target options contain a locked candidate, I think we then get to the JE+ circumstances you're considering. However, then proof of the eliminations wouldn’t depend on the existence of the locked candidate.

Is that right? If not a diagram would help.

Regards David

Hi David,

For me the logic of the exocet is requiring a locked candidate in that situation.
The basic for an Exocet are

if any of the base digit must be in the target, then
the target can only contain the base digits
the solution has the same couple of digits in the base and the target.

to extend that rule to a twin exocet, you need the locked candidate.

David P Bird wrote:
Denis Berthier wrote:JExocet is less general than Exocet (how much less remains an open question as we currently have no estimate of JE's presence neither in champagne's hardest list nor for easier puzzles).

In JE or JE+ if the partial fish requirement isn't met the case is closed, but for not for Exocet which continues to hunt for justification using templates and/or inference following. What would be interesting to me is how often this extra work is required, and how often it produces a hit.

Regards David

this is very easy to do, but requires cycles. The way things are going, I see no reason to change my priorities trying to answer to that question. I prefer to go ahead with investigations in the "potential hardest" area
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### Re: JExocet Pattern Defintion

champagne wrote:
David P Bird wrote:
Denis Berthier wrote:JExocet is less general than Exocet (how much less remains an open question as we currently have no estimate of JE's presence neither in champagne's hardest list nor for easier puzzles).

In JE or JE+ if the partial fish requirement isn't met the case is closed, but for not for Exocet which continues to hunt for justification using templates and/or inference following. What would be interesting to me is how often this extra work is required, and how often it produces a hit.
this is very easy to do, but requires cycles. The way things are going, I see no reason to change my priorities trying to answer to that question. I prefer to go ahead with investigations in the "potential hardest" area

There is a big expectation about the frequency of JExocet. The question is about how much the scope of a general non-pattern-based procedure has to be restricted when one wants to define a real pattern (or real patterns, JE and JE+) inspired by it.
You can continue to enlarge the list of puzzles having Exocets, but as we know that part of these do not correspond to real patterns, this seems rather pointless.
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### Re: JExocet Pattern Defintion

Hi Champagne,
Champagne wrote:
For me the logic of the exocet is requiring a locked candidate in that situation.
The basic for an Exocet are

if any of the base digit must be in the target, then
the target can only contain the base digits
the solution has the same couple of digits in the base and the target.

to extend that rule to a twin exocet, you need the locked candidate.

I'm confident that you and I will agree to the JE requirements in any particular case, and it is the choice of words that is the problem here. I was only considering the requirements for the basic eliminations of non-base digits from the target cells. As we know, the pattern in the primary band carries a number of extra inferences that can be used to advantage in combination with other circumstances.

When twin patterns arise (which have never been discussed here) it's a bonanza. For a start all the fin eliminations for four partial fish can be made, and then there are a bunch of others in the main band. However, the pattern elements needed to make the basic eliminations still remain the same, which together I believe, force the locked digits you mention.

You wrote:this is very easy to do, but requires cycles. The way things are going, I see no reason to change my priorities trying to answer to that question. I prefer to go ahead with investigations in the "potential hardest" area

I accept that, just as writing an illustrated guide to the pattern is low on my priorities (particularly regarding the attitudes towards my contributions in another section of this forum in recent times). I'll be very interested in anything you find.

David
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### Re: JExocet Pattern Defintion

blue wrote:
champagne wrote:
blue wrote:I got a very nice speedup, by solving the puzzle beforehand, and looking only at cases where the base and target pairs, actually contain the same pair of (distinct) digits in the solution.

very good idea.I keep it in mind and will do the same. My first reaction would be "what about twin exocets"

I don't look for twins, specifically. I only find both, when they exist.

I had forgotten that you use the "twin" to refer to the case with an AHS target pair.
I was thinking "double exocet" when I wrote that. Sorry for the confusion.
(It looks like David just made the same mistake that I did).
I wrote something to look for exocets with AHS targets too, but I made it too general (> 2 cells, allowed).
It took a long time to run, and it found a lot more than I had anticipated ... worthless cases with
no eliminations ... and very little in the 2-cell area.
I trashed the code, and I don't really remember what I tried in the way of "speedups".
I would guess that I looked for two target cells that contained the base cell digits, and then
looked at whether forcing one of them, would produce a hidden n-tuple that didn't exist before.
If that's the case, then the one target cell can be extended to a set that includes the 'n' cells from
the "would be" n-tuple. When the positions for the target cells are unrestricted, you'ld probably
also need to make sure that if you extended each cell to an AHS cell set, that the two cell sets
didn't overlap, and (whether it was two AHS or one) that neither set included a base cell.
(Does that sound right ?).

David P Bird wrote:If additionally these two target options contain a locked candidate, I think we then get to the JE+ circumstances you're considering. However, then proof of the eliminations wouldn’t depend on the existence of the locked candidate.

Is that right? If not a diagram would help.

The locked candidate is needed, in the proof.
It's important that after the cells that would contain the AHS digit(s) are counted, only two target cells remain -- one for each base cell value.
Is that enough ? ... I'm not really sure that a diagram would help.

Regards,
Blue.
Last edited by blue on Fri May 17, 2013 11:06 am, edited 1 time in total.
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### Re: JExocet Pattern Defintion

A quick reply as I'm don't have any more time to check in detail right now.

Here I've been using twin Exocets to mean that there are two Exocet signature patterns in the same band with the same base digits. When an AHS makes it impossible to identify which cell in the object cells will hold a base digit I've been calling that the JE+ pattern.

Blue wrote: I wrote something to look for exocets with AHS targets too, but I made it too general (> 2 cells, allowed).
It took a long time to run, and it found a lot more than I had anticipated ... worthless cases with no eliminations ... and very little in the 2-cell area.

That's very interesting! I never found a supporting case but couldn't rule out the theoretical possibility that the AHS would be > 2 cells. Did you ever find one at all? It seems that the definition should concentrate on the AH pair with just a rider that the AHS could be bigger in exceptional circumstances.
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### Re: JExocet Pattern Defintion

Hi David,

David P Bird wrote:
Blue wrote: I wrote something to look for exocets with AHS targets too, but I made it too general (> 2 cells, allowed).
It took a long time to run, and it found a lot more than I had anticipated ... worthless cases with no eliminations ... and very little in the 2-cell area.

That's very interesting! I never found a supporting case but couldn't rule out the theoretical possibility that the AHS would be > 2 cells. Did you ever find one at all? It seems that the definition should concentrate on the AH pair with just a rider that the AHS could be bigger in exceptional circumstances.

I think there were a few, yes.
AHS in a box, rather than a column, may have been more common.
About the definition, (I think) I agree -- maybe even without the rider.

Blue.
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### Re: JExocet Pattern Defintion

blue wrote:I wrote something to look for exocets with AHS targets too, but I made it too general (> 2 cells, allowed).
It took a long time to run, and it found a lot more than I had anticipated ... worthless cases with
no eliminations ... and very little in the 2-cell area.

On my side, it came in a quite different way.

"Platinum Blonde" had been studied for long and was classified on my side as a far parent of the Exocet when "abi" showed that it could be solved exactly as a Jexocet.
the "twin Jexocet" appeared when we tried to understand why. (BTW it has been named twin Jexocet at that time and I try to keep the name )

I never looked for a general search of "twin exocets". Usually, I don't look for patterns that has not shown a high solving potential out of an example.
I only look for the specific twin Jexocet pattern as a side search for Jexocets.

May be another remark for Jexocets. Most of the Jexocets found in the "potential hardest" data base have four digits.
I guess the ratio of Jexocets with 3 digits would grow with puzzles in the grey zone.

"fata morgana", Platinum Blonde".... don't reach the conditions to enter the "potential hardest" data base.

I also studied years ago exocets of 2 digits but found a poor interest in them. A they did not show in potential hardest, I stopped the search.
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### Re: JExocet Pattern Defintion

Hi Blue,

I'm struggling to make sense of the situation you believe isn't covered in the definition of JE+, as I'm getting mixed messages from you.

For the JE+ pattern in one of the boxes we can't say which object cell will become the target, but they both occupy the same cross line (column) out of sight of the base cells (ie two cells).

you wrote:There's a possible variation where rather then considering where it can go in the column, one considers where it can go in the box containing the target pair.

You can't be referring to the two cells that must contain base digits out of the four object cells, as they can't both be in the same box, so you must mean the object pair here.

An object cell pair must be different rows to the base pair and if they can be in different columns we extend the object cells from two to four cells (in the row/column intersections) that can only hold one instance of a base digit. To be distinct from the basic JE pattern, this requires that they must contain either an AH triple plus a given, or an AH quad, ie two remote possibilities.

In addition to this both columns must give equivalent results regarding how many instances of each base digit the partial fish pattern can contain. This has yet to be found for two columns in a stack, but again is another remote possibility.

The prospects of such a pattern existing are therefore the product of two very small possibilities.

If my analysis is right, are you really suggesting that the JE+ definition should cover this, particularly in light of your opinion that searching for a JE+ with an AHS >2 cells is a waste of time?

you wrote:would guess that I looked for two target cells that contained the base cell digits, and then looked at whether forcing one of them, would produce a hidden n-tuple that didn't exist before.
If that's the case, then the one target cell can be extended to a set that includes the 'n' cells from the "would be" n-tuple. When the positions for the target cells are unrestricted, you'ld probably also need to make sure that if you extended each cell to an AHS cell set, that the two cell sets didn't overlap, and (whether it was two AHS or one) that neither set included a base cell.
(Does that sound right ?).

In a word, no

David
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### Re: JExocet Pattern Defintion

Hi David,

David P Bird wrote:I'm struggling to make sense of the situation you believe isn't covered in the definition of JE+, as I'm getting mixed messages from you.

(...)

you wrote:There's a possible variation where rather then considering where it can go in the column, one considers where it can go in the box containing the target pair.

(...)

An object cell pair must be different rows to the base pair and if they can be in different columns we extend the object cells from two to four cells (in the row/column intersections) that can only hold one instance of a base digit. To be distinct from the basic JE pattern, this requires that they must contain either an AH triple plus a given, or an AH quad, ie two remote possibilities.

That's exactly what I was talking about, except that I would call them an AH pair, and AH triple -- counting digits, not cells.
The possiblity may be remote, but that shouldn't matter.

Here is is an example.
It isn't the best -- 6r1c5 is redundant, for example, and without it the

Code: Select all
`+------------------+-------------------+-------------------+| 24    134  5     | 1234    6    7    | 1234  8     9     || 2468  9    1234  | 12348   5    1234 | 7     136   12346 || 2468  78   12347 | 123489  289  1234 | 1234  136   5     |+------------------+-------------------+-------------------+| 1     56   234   | 2468    278  9    | 345   357   348   || 7     56   49    | 1468    3    146  | 1459  2     148   || 249   34   8     | 5       27   124  | 6     1379  134   |+------------------+-------------------+-------------------+| 589   78   79    | 2369    1    2356 | 239   4     236   || 3     2    19    | 69      4    8    | 159   1569  7     || 459   14   6     | 7       29   235  | 8     139   123   |+------------------+-------------------+-------------------+`

The base cells are r1c12, and the fish columns are c347.
r3c7 is a "normal" target cell, and the other target is the "box" AHS for 89 in r23c4+r3c5.
The only elimination is for 2r3c5, and it's kind of a special case, since it doesn't fit the
general description: "non-AHS, non-base-cell digit".

David P Bird wrote:If my analysis is right, are you really suggesting that the JE+ definition should cover this, particularly in light of your opinion that searching for a JE+ with an AHS >2 cells is a waste of time?

Some clarification is in order.

Whether it should be included, isn't for me to decide.
The "AH single in a column" seems easy to explain.
The other cases are a simple extensions of that idea. (But see below).
Maybe the simple JE+ pattern, and a JE++ to cover the more general cases ?
Again, it's (thankfully) not my decision.

For the other kinds of AHS, the example above, with its "odd" elimination, shows that there is an added layer of
complexity, if you want to cover all of the (easily explainable) elimination possibities. Sticking with the "cells in a fish column, in the base band" variety, avoids all of that. Assuming the line-box eliminations have been done at that point, the the "is it a box AHS or a column AHS" question, would be avoided as well (... it's both).

David P Bird wrote:
you wrote:would guess that I looked for two target cells that contained the base cell digits, and then looked at whether forcing one of them, would produce a hidden n-tuple that didn't exist before.
If that's the case, then the one target cell can be extended to a set that includes the 'n' cells from the "would be" n-tuple. When the positions for the target cells are unrestricted, you'ld probably also need to make sure that if you extended each cell to an AHS cell set, that the two cell sets didn't overlap, and (whether it was two AHS or one) that neither set included a base cell.
(Does that sound right ?).

In a word, no

Right. I see that I should at least have added that the hidden n-tuple (and so the AHS), shouldn't include a base digit.
(With that, it would be impossible for the associated AHS to include a base cell).

About the AHS's overlapping ... what ?
If they shared a candidate, then the elimination argument wouldn't work, I think.
If they shared a cell, but not a candidate, then the (suitably modified) "exocet" condition
couldn't be met, since if it was, it would be forcing (N1+1)+(N2+1) distinct number
placements, into fewer then N1+N2+2 cells.
Saying that they don't overlap ... the cell sets in particular ... covers both cases.

What else am I missing ?

Whether I actually used the hidden n-tuple idea, or wrote code to look for AHS's directly, I don't know.
I know I didn't have any pre-existing AHS code around at the time.

Blue.
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### Re: JExocet Pattern Defintion

Blue, I'm pleased you were able to find (or construct?) an example!

I don't know if you're on-line at the moment, but in case you are here's a quick response - which I might edit if a get a flash of inspiration later.

In your grid columns 3, 4, & 7 do provide a qualifying partial fish pattern, but columns 3, 5, & 7 don't.

Now I fail to see how you can be sure that the Almost Hidden Triple isn't (289) in r23c4,r3c5
In other words what I have missed in thinking that there's nothing to stop (2)r3c5 being true? In that case the JE requirements wouldn't be satisfied, and we have no pattern.

(BTW. Note my usage of the AH Triple term – an almost hidden set is N cells containing N-1 locked candidates.)

David
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### Re: JExocet Pattern Defintion

Hi David,

Blue, I'm pleased you were able to find (or construct?) an example!

It was easier to just construct one. It's only SER 8.4.

(BTW. Note my usage of the AH Triple term – an almost hidden set is N cells containing N-1 locked candidates.)

OK -- odd, but OK. I see them as N+1 cells containg N locked candidates.

In your grid columns 3, 4, & 7 do provide a qualifying partial fish pattern, but columns 3, 5, & 7 don't.

Now I fail to see how you can be sure that the Almost Hidden Triple isn't (289) in r23c4,r3c5
In other words what I have missed in thinking that there's nothing to stop (2)r3c5 being true? In that case the JE requirements wouldn't be satisfied, and we have no pattern.

Vocubulary is shifting again. If it's an AHS triple in your terms (3 cells), then it should only have the two digits -- 8 & 9.
It's that if 2r3c5 was true, then the 89 would be forced to r23c4, leaving no room for the base digit that we know must go there (from the partial fish paterns).

Regards,
Blue.
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### Re: JExocet Pattern Defintion

blue wrote:Hi David,
In your grid columns 3, 4, & 7 do provide a qualifying partial fish pattern, but columns 3, 5, & 7 don't.

Now I fail to see how you can be sure that the Almost Hidden Triple isn't (289) in r23c4,r3c5
In other words what I have missed in thinking that there's nothing to stop (2)r3c5 being true? In that case the JE requirements wouldn't be satisfied, and we have no pattern.

Vocubulary is shifting again. If it's an AHS triple in your terms (3 cells), then it should only have the two digits -- 8 & 9.
It's that if 2r3c5 was true, then the 89 would be forced to r23c4, leaving no room for the base digit that we know must go there (from the partial fish paterns).

Regards,
Blue.

Blue, thanks for the quick reply.

Out of the four base candidates only the two that are true in the base cells will be subject to the pattern constraints when everything is resolved. This means that the other ones can occupy r1c4 and also r23c3 so the fish requirements won't apply to them.

David
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