Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

Re: Exotic patterns a resume

Postby champagne » Sun Oct 06, 2013 9:59 am

sultan vinegar wrote: I look forward to analysing your files.


The full base was already loaded. I killed to day the old update so the up-to-date base is ph_13_10
I added the zip file ph_13_10_exo containing all data related to exocets and killed the old files

IMO, these files are more dedicated to players wanting to extract some puzzles. They can also be used to compare the results fo other programs trying to identify the "exotic patterns".


sultan vinegar wrote: Can you clarify exactly what patterns are covered by the "extended JE",
as so many have been mentioned in multiple posts in multiple threads that it's hard to keep track of them all.


This is somehow a point where some options are open.
Basically, I wanted to extract puzzles where the JE pattern is missing for some digits, but where the digit per digit condition is there using a general contradiction scheme.

My "JE" identification is "generic" opposed to a "per pattern" in David's approach, so I can have small deviations.
The contradiction process can use different sets of rules.

In my "generic" process, the only constraint is that the targets must use 2 cross lines in the 2 other blocks. This is more than in David's definition


sultan vinegar wrote:
Also, where does DJE fit in these results?


DJE's are included in that statistics. Specific files have been loaded in the "ph_13_10_exo" zip file

I have identified

227111 puzzles having a standard DJE
313 puzzles having a DJE seen in extended mode



sultan vinegar wrote:If it would help, I volunteer to write and maintain an "Ultimate Exocetidae Guide", collecting all the definitions, patterns, extensions, secondary eliminations etc in the one post for easy reference.
Champagne could then periodically copy and paste the post into one of the reserved posts at the very beginning of this thread whenever I update it.
Yes/No/Better Ideas???


As more and more the exocet pattern seems to be the main source for the highest ratings, this makes sense.
We have a good chance to find close patterns and it would be good than younger guys take over that topic.

Regarding the best way to keep something updated in the forum, jasonlion can surely help us, for example changing the ownership of the post 7 in that thread if we don't want to open a new one;
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Re: Exotic patterns a resume

Postby David P Bird » Sun Oct 06, 2013 10:17 am

sultan vinegar wrote:If it would help, I volunteer to write and maintain an "Ultimate Exocetidae Guide", collecting all the definitions, patterns, extensions, secondary eliminations etc in the one post for easy reference.
I've tried to do this, but failed principally because every new start has attracted so many discussions that the purpose of the thread has been defeated. Before you embark on an "Ultimate Exocetidae Guide", I would like to explain what's been behind my attempts.

My work has been dominated by two strong views I hold about the differences between patterns and methods and the acceptability of different methods. For me:
    Patterns must consist of a number of specified elements that should be capable of being identified without following any logic other than counting.
    Methods should only consider two rival cases and the logical streams used should be bi-directional. However they may include inferences resulting from the analysis of known patterns.
These restrictions limit the difficulty of the puzzles that can be solved, but there lies the challenge – to make an assent using only ropes and crampons and without resorting to scaffolding. I would point out that even for those who scorn these disciplines, the findings they've produced for Exocets have benefited their computer solvers considerably, or at least provided an explanation for them.

Champagne, I've got the feeling that some of what you're calling 'Extended Exocets' will be no more than 'Almost Exocets'. As a working definition these are JExocets where one of the specifications is not quite met. We can then produce chains showing that whether the cause of the violation is true or the Exocet is true there are common eliminations. In turn these may then show that one or other case must be true. Depending where the violation is there could then be different classes of these.

We may then get 'False Exocets' which could describe another of your Extended Exocet cases. Here we know the Exocet to be false which therefore limits the possible positions of the base digits in the Exocet band, allowing eliminations to be made as I showed < on the previous page >

Because a) because I don't trust a company that gathered as many passwords and other personal details as they could when making street maps and b) because of the file sizes, I won't be downloading any of your files but will wait for examples to appear on this thread.

[Added] Just as I was posting this you responded. So some bits may be redundant.

David
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Re: Exotic patterns a resume

Postby daj95376 » Mon Oct 07, 2013 4:00 pm

Code: Select all
 eliminations in [band 1] associated with assuming DJE is true
 ### -1234- QExocet   Base = r1c89   Target = r2c3,r3c5==r2c2
 ### -1234- QExocet   Base = r3c12   Target = r1c5,r2c7==r1c6
 *** double QExocet
 +--------------------------------------------------------------------------------+
 |  9       8       5-1234  |  7       1234    124-5   |  6       1234    234     |
 |  7       134-5   1234-5  |  59-124  6       58-124  |  124-8   123489  23489   |
 |  123     134     6       |  1249    134-29  1248    |  78-124  5       789-234 |
 |--------------------------+--------------------------+--------------------------|
 |  4       1567    125     |  3       12      9       |  1278    12678   25678   |
 |  126     169     8       |  1246    5       7       |  3       12469   2469    |
 |  12356   135679  1235    |  8       124     1246    |  1247    124679  245679  |
 |--------------------------+--------------------------+--------------------------|
 |  3568    2       345     |  4569    479     456     |  478     34678   1       |
 |  1368    1346    9       |  1246    7-124   1246    |  5       234678  234678  |
 |  156     1456    7       |  12456   8       3       |  9       246     246     |
 +--------------------------------------------------------------------------------+

David P Bird wrote:Leren, for your tough example
98.7..6..7...6......6....5.4..3.9.....8.573.....8......2......1..9...5....7.839..;975059;GP;13_03;21;1234 ;3;34

I can only find these eliminations using un-branched chains
(9-7)r7c5 = (7-124)r8c5 = DJE - (9)r3c5 = Loop => r7c5 <> 4 (first weak link is conjugate)
(3)r1c5 = (3-9)r3c5 = (9-7) = (7-124)r8r5 = DJE => r1c3 <> 3 (DJE excludes 1234 r1c3)
(4-9)r7c4 = (9-7)r7c5 = (7-124)r8c5 = DJE - (4)r7c468 => r7c4 <> 4 (Spot cells)
(9)r7c4 = (9-7)r7c5 = (7-124)r8c5 = DJE - (124=56)r67c6 => r7c4 <> 5 (Spot cells)

After these I then have to admit defeat and start using derived inferences/branching.

Your first chain can be written as:

Code: Select all
(  9)r3c5 = (9-7)r7c5 = (7-124)r8c5 = DJE - Loop     => r7c5 <> 4

However, since there is a secondary equivalence r3c5==r2c2 for base r1c89. This affords one additional elimination based on your first chain.

Code: Select all
(2-9)r3c5 = (9-7)r7c5 = (7-124)r8c5 = DJE - (29)r3c5 => r3c5 <> 2

This doesn't do anything significant, but it does increase the elimination count for this grid.
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Re: Exotic patterns a resume

Postby sultan vinegar » Tue Oct 08, 2013 2:45 am

DPB, fair points. I'll PM you soon with some thoughts on acceptable methods.

Daj, nice job. I understand your elimination, but I've never seen the QExocet term defined. Is that just the name for an exocet with one of the following secondary equivalences, as shown here?

In a previous post I claimed to not understand the elimations of (3)r1c3 and (35)r2c3. Of course if you get distracted by the ADJE, then you miss the single exocet with AHS and box single extensions: Base = r1c89; Target = r2c3, r3c5/r8c5; AHS (79)c5r378; (3)r1c5 = (3)r3c5, which accounts for the eliminations.
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Re: Exotic patterns a resume

Postby daj95376 » Tue Oct 08, 2013 4:11 am

sultan vinegar wrote:Daj, nice job. I understand your elimination, but I've never seen the QExocet term defined. Is that just the name for an exocet with one of the following secondary equivalences, as shown here?

Sultan,

Essentially, yes. However, sometimes there's a difference in how I'll link a base cell candidate to a single target cell. DPB sometimes objects to my results being called JE/DJE. So, I renamed my results QExocet and qExocet ... the latter not being encountered in awhile.

IIRC, DPB updated his JE/DJE definitions and there is now less distinction between his usage and mine.

Regards, Danny
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Re: Exotic patterns a resume

Postby David P Bird » Tue Oct 08, 2013 1:58 pm

I've managed to look at Leren's tough example again and have to admit I'm not happy with what I wrote before

David P Bird wrote:Leren, for your tough example
98.7..6..7...6......6....5.4..3.9.....8.573.....8......2......1..9...5....7.839..;975059;GP;13_03;21;1234 ;3;34

I can only find these eliminations using un-branched chains
(9-7)r7c5 = (7-124)r8c5 = DJE - (9)r3c5 = Loop => r7c5 <> 4 (first weak link is conjugate)
(3)r1c5 = (3-9)r3c5 = (9-7) = (7-124)r8r5 = DJE => r1c3 <> 3 (DJE excludes 1234 r1c3)
(4-9)r7c4 = (9-7)r7c5 = (7-124)r8c5 = DJE - (4)r7c468 => r7c4 <> 4 (Spot cells)
(9)r7c4 = (9-7)r7c5 = (7-124)r8c5 = DJE - (124=56)r67c6 => r7c4 <> 5 (Spot cells)

After these I then have to admit defeat and start using derived inferences/branching.

The first two chains are fine, but the weak links from the DJE in the other two aren't self explanatory and need to be justified. I believe I mis-copied these from my jottings, and because I can't recreate the missing chain segments, I suspect I was ANDing two logical inferences from the DJE pattern together. (Perhaps that's not a cardinal offence but it's distasteful to me as it's could be taken to be equivalent to branching.)

SV that means I also can't make your (9)r2c4,r3c9 eliminations either.

DAJ I think that SV has hit the nail on the head when he called the elimination of (2)r3c5 when the DJE is true a 'secondary inference".
For anyone that doesn't appreciate the workings they go like this:
If the DJE is true then depending on whether (2) is a member of the base pair in r1c89:
if it is, it must be true in target r2c3 (as it's missing from r2c12) and so false in target r3c5
if it isn't it can't be true in 3c5 anyway.


In all three cases are being evaluated:
a) Spoiler true
b) DJE true with (2) true in r1c89
c) DJE true with (2) false in r1c89
Wearing puritanical hats we could say that that amounts to branching. However, taking a more liberal view, we can say that the elimination is internal to the pattern and therefore should be allowable – if you like, it becomes a sub-pattern. This is unlike some of your other QExocet relaxations where you tag on some amorphic external chain to make the deduction.

All in all, I'm still against secondary inferences that rely on any external conditions, but can accept the internal ones provided they can be notated clearly.

SV, over the years I've struggled to define some hard and fast rules over what's is and isn't acceptable but failed. Wherever the lines are drawn, either some perfectly acceptable method will be ruled out or some blatantly assumptive methods let in! In the early days a general consensus prevailed but that's gone now and it's left up to players to decide for themselves. Provided a player adopts a consistent approach no-one can really object.
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Re: Exotic patterns a resume

Postby daj95376 » Tue Oct 08, 2013 3:41 pm

[Withdrawn: probably not appropriate.]
Last edited by daj95376 on Thu Oct 10, 2013 3:11 am, edited 1 time in total.
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Re: Exotic patterns a resume

Postby ronk » Tue Oct 08, 2013 6:29 pm

David P Bird wrote:98.7..6..7...6......6....5.4..3.9.....8.573.....8......2......1..9...5....7.839..;975059;GP;13_03;21;1234 ;3;34

I can only find these eliminations using un-branched chains
(9-7)r7c5 = (7-124)r8c5 = DJE - (9)r3c5 = Loop => r7c5 <> 4 (first weak link is conjugate)
(3)r1c5 = (3-9)r3c5 = (9-7) = (7-124)r8r5 = DJE => r1c3 <> 3 (DJE excludes 1234 r1c3)
(4-9)r7c4 = (9-7)r7c5 = (7-124)r8c5 = DJE - (4)r7c468 => r7c4 <> 4 (Spot cells)
(9)r7c4 = (9-7)r7c5 = (7-124)r8c5 = DJE - (124=56)r67c6 => r7c4 <> 5 (Spot cells)

Let's back up a little here. Doesn't each AJE in a ADJE need to stand on its own? IOW shouldn't each AJE consideration be legitimate with only one pair of base cells? This is no problem for AJE (1234)r1c89, r2c3, r3c5.

14 Truths = {124C3 123479C5 124C7 1N89}
17 Links = {1234r1 12r4 124r6 4r7 2n3 378n5 124b3}
4 Eliminations --> r12c3<>3, r2c3<>5, r7c5<>4

Hidden Text: Show
Code: Select all
+-------------------------+-----------------------+-------------------------+
| 9      8       5-3(124) | 7      (1234)   1245  | 6        (1234)  (234)  |
| 7      1345    -35(124) | 12459  6        12458 | 8(124)   123489  23489  |
| 123    134     6        | 1249   (12349)  1248  | 78(124)  5       234789 |
+-------------------------+-----------------------+-------------------------+
| 4      1567    5(12)    | 3      (12)     9     | 78(12)   12678   25678  |
| 126    169     8        | 1246   5        7     | 3        12469   2469   |
| 12356  135679  35(12)   | 8      (124)    1246  | 7(124)   124679  245679 |
+-------------------------+-----------------------+-------------------------+
| 3568   2       35(4)    | 4569   (79-4)   456   | 78(4)    34678   1      |
| 1368   1346    9        | 1246   (1247)   1246  | 5        234678  234678 |
| 156    1456    7        | 12456  8        3     | 9        246     246    |
+-------------------------+-----------------------+-------------------------+

Note that the 2nd base pair (1234)r3c12 is not part of the logic.

Note also that the addition of truth 2R2 adds exclusion r3c5<>2. Why? If base r1c89<>2 then target r3c5<>2. If r1c89=2 then r3c5=2 is invalid because r2c12 is void of digit <2> candidates. IOW r3c5=2 and r2c3=2 cannot both be true in the AJE.

Now, has anyone shown the logic details for AJE (1234)r3c12, r1c5, r2c7 without the other AJE in (1234)r1c89, r2c3, r3c5 :?:

FWIW r7c5<>4 is a cannibalistic exclusion which can be made with a smaller pattern.
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Re: Exotic patterns a resume

Postby sultan vinegar » Wed Oct 09, 2013 2:30 am

Code: Select all
(4-9)r7c4 = (9-7)r7c5 = (7-124)r8c5 = DJE - (4)r7c468 => r7c4 <> 4 (Spot cells)
(9)r7c4 = (9-7)r7c5 = (7-124)r8c5 = DJE - (124=56)r67c6 => r7c4 <> 5 (Spot cells)


DPB, for what it's worth, I'm happy with these two chains, and I think that you should be too! Here's my POV:Here, you conclude:
2) When both true base digits are confined to two instances in the S cells, within the 3 cross lines, each digit must occur once in the JE band and twice in the other bands, in the S cells.

So surely the weak inferences: DJE - (4)r7c468 and DJE - (124=56)r67c6 are valid.
Hypothetically, if (7)r8c5 had already been proven true, then you would have no problem in eliminating (4)r7c468 nor (124)r6c6.
So for the weak inference to be valid, any notion of whether or not the DJE is true or not in the current puzzle state doesn't matter. That would be using memory - which you hate! All that needs to be considered is: Is at most one of DJE and (124)r6c6 true? Two cases:
(i) If the DJE is true then (124)r6c6 is false, as noted by you in your definition.
(ii) If the DJE is false, then the state of (124)r6c6 is irrelevant.
All up, at most one is true, so we have a weak inference. What is linked to that weak inference is irrelevant, the weak inference is still valid!

(2-9)r3c5 = (9-7)r7c5 = (7-124)r8c5 = DJE - (29)r3c5 => r3c5 <> 2

In all three cases are being evaluated:
a) Spoiler true
b) DJE true with (2) true in r1c89
c) DJE true with (2) false in r1c89


Again, I think you are using memory, remembering that the spoiler is true. In my view, that is irrelevant. The spoiler is not part of the inference: DJE - (2)r3c5. So there are not three cases, and there is no branching.

Let's back up a little here. Doesn't each AJE in a ADJE need to stand on its own?


Ronk, I agree.
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Re: Exotic patterns a resume

Postby David P Bird » Wed Oct 09, 2013 1:07 pm

Ronk wrote:Let's back up a little here. Doesn't each AJE in a ADJE need to stand on its own? IOW shouldn't each AJE consideration be legitimate with only one pair of base cells? This is no problem for AJE (1234)r1c89, r2c3, r3c5.

I see what you're driving at but don't think that it's a requirement. I actually find DAJ's elimination slightly easier to justify using the double JE than the single one. However your viewpoint could be useful for clearly notating any secondary inferences (see below).

SV, As I proceed through the autumn of my years, I found I'm not so sharp anymore and am liable to miss vital contradictory conditions that make my inferences unsound. I therefore welcome your contributions that keep me on my toes.

Firstly on Leren's puzzle
You wrote:(i) If the DJE is true then (124)r6c6 is false, as noted by you in your definition.

Some time back this was a mistake I made, but the inference between them is strong-only as I explained in the opening para < here >.

Regarding the DJE – (4)r7c468 inference, it needs to show that they can't be true together.
If (4)r7c468 is true, it still allows (4) to be true in r2c3, r6c7, & r8c5 to satisfy the 2 S cells + 1 target cell condition. Therefore the link isn't self sufficient.

This type of approach seems sound to me though:
(124)spoiler:r8c5 = DJE - (4#2)r123c37 = (4)r67c37 - [edited]
but I haven't been able to extend any variation of this theme into anything useful!

Secondly on DAJs (2)r3c5 elimination, in my mental model I consider the opening node to be remembered as that's the one that will make the eventual elimination. As the chain is built we alternately consider the effect of this node being true or false elsewhere in the puzzle, so at anytime the have both end nodes under consideration. Once an inference has been continued from an intermediate node, it's the state of that node that should be forgotten.

The inference DJE - (29)r3c5 is sound but isn't self explanatory. The – (9)r3c5 is fundamental to the pattern, but the – (2)r3c5 follows on from further feature of the sub-pattern that has been spotted, and this needs to be detailed somehow. In dealing with pattern such as URs, ronk developed a type numbering system which handles the different cases very well. The only problems these give me (and therefore I suppose others), is that when these numbers are used in the notations, I can never remember the associated sub-pattern.

JExocets are complicated patterns with a range of basic configurations and secondary inferences (which can also appear in combination). See <here>. Cataloguing them by type number would therefore be quite a daunting task. The sort of approach I would favour would be to notate the chain something like this:
    (2-9)r3c5 = (9-7)r7c5 = (7-124)r8c5 = DJE *- (29)target:r3c5 => r3c5 <> 2
    * As (2) would have to be true in either target r2c3 or base cells r3c12.
This would allow anyone who had some familiarity with the JExocet basics to understand the reason without needing to consult a pattern book.

DPB
Last edited by David P Bird on Thu Oct 10, 2013 10:38 pm, edited 1 time in total.
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Re: Exotic patterns a resume

Postby ronk » Wed Oct 09, 2013 3:39 pm

sultan vinegar wrote:
Code: Select all
(4-9)r7c4 = (9-7)r7c5 = (7-124)r8c5 = DJE - (4)r7c468 => r7c4 <> 4 (Spot cells)
(9)r7c4 = (9-7)r7c5 = (7-124)r8c5 = DJE - (124=56)r67c6 => r7c4 <> 5 (Spot cells)

DPB, for what it's worth, I'm happy with these two chains, and I think that you should be too! Here's my POV:Here, you conclude:
2) When both true base digits are confined to two instances in the S cells, within the 3 cross lines, each digit must occur once in the JE band and twice in the other bands, in the S cells.

So surely the weak inferences: DJE - (4)r7c468 and DJE - (124=56)r67c6 are valid.

[Edit: Original comment withdrawn after seeing daj95376's post.]

sultan vinegar wrote:
I wrote:Let's back up a little here. Doesn't each AJE in a ADJE need to stand on its own?
Ronk, I agree.

After David P Bird's comment and due consideration, I have changed my mind. I guess this means an ADJE could exist without either an inclusive stand-alone JE or AJE. :shock: :?
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Re: Exotic patterns a resume

Postby sultan vinegar » Thu Oct 10, 2013 4:50 am

DPB, I’ll continue this discussion here as I believe it is very pertinent to exotic patterns and their notation, and not off-topic.

My summary of your last post in one sentence: “SV has been fooled by the 2 parallel lines case (II) <here> of the DJE (again)!”

To rectify it, I need to tighten up my notation. The trap with ADJE having multiple potential spoilers is that depending on which of these potential spoilers are true/false, you can get different DJE (as in the three cases <here>). That’s why the link is non-symmetrical in the way it works, because “DJE” by itself can mean different things depending on which side of the link you start.
When I write DJE – (4)r7c468, what I actually mean when I write “DJE” is “DJE 2 parallel lines case (I)”. If I make this adjustment then I believe that the chain is valid. It is now just a question of how to notate that succinctly. Your comment:
JExocets are complicated patterns with a range of basic configurations and secondary inferences (which can also appear in combination). See <here>. Cataloguing them by type number would therefore be quite a daunting task. The sort of approach I would favour would be to notate the chain something like this:
(2-9)r3c5 = (9-7)r7c5 = (7-124)r8c5 = DJE *- (29)target:r3c5 => r3c5 <> 2
* As (2) would have to be true in either target r2c3 or base cells r3c12.
This would allow anyone who had some familiarity with the JExocet basics to understand the reason without needing to consult a pattern book.

Is right on the money. Perhaps listing the covering links (C) along with the base (B) and target (T) cells would clarify this in my case?
Code: Select all
(4-9)r7c4 = (9-7)r7c5 = (7-124)r8c5 = DJE*[B:r1c89,r3c12;T:r1c5,r2c37,r3c5;C:12r46,4r67] – (4)r7c4 => r7c4 <> 4. *Box singles extension used on candidate 3.

But then there are other cases where you don’t care which DJE is true to get the next link in the chain, such as <here>. So what to do???
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Re: Exotic patterns a resume

Postby David P Bird » Thu Oct 10, 2013 10:36 pm

sultan vinegar wrote: Perhaps listing the covering links (C) along with the base (B) and target (T) cells would clarify this in my case?
Code: Select all
(4-9)r7c4 = (9-7)r7c5 = (7-124)r8c5 = DJE*[B:r1c89,r3c12;T:r1c5,r2c37,r3c5;C:12r46,4r67] – (4)r7c4 => r7c4 <> 4. *Box singles extension used on candidate 3.

But then there are other cases where you don’t care which DJE is true to get the next link in the chain, such as <here>. So what to do???

By setting the parameters you have for the DJE, you are only considering the case when r8c357 doesn't hold any (1) (2) or (4). This means this chain therefore proves nothing new.

Your starred comment for (3) aren't really necessary as its partial fish cells can only hold 2 truths anyway. However when the DJE is true, (3) must be true in either target r1c5 or target r3c5, so it couldn't occupy target r2c3. This provides a secondary inference that would need some sort of detailing if it were used.

I'm afraid the only way I see to determine if the DJE must be true or false is to resort to branching and/or forcing chains in the style of DAJ.

BTW I notice I blundered on the chain I gave in my previous reply and have edited it.

DPB
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Re: Exotic patterns a resume

Postby daj95376 » Thu Oct 10, 2013 10:49 pm

__

The current posts make no sense to me. In fact, I withdrew two previous posts because of my confusion. There are references to ADJE, DJE, and even JE that lack cohesion to me. The discussion of semantics on weak links involving a DJE puts the icing on the cake.

The puzzle has one ADJE with only one potential DJE that I can find. The "A" of the ADJE occurs because r8c5 contains candidates {1,2,4}. If these candidates were to be eliminated, then the DJE and its eliminations would remain. What are the eliminations if the DJE is assumed to be true??? Ironically, no one took the time to list them!!!

Code: Select all
 eliminations associated with assuming DJE is true in ADJE
 ### -1234- QExocet   Base = r1c89   Target = r2c3,r3c5==r2c2
 ### -1234- QExocet   Base = r3c12   Target = r1c5,r2c7==r1c6
 *** double QExocet
 +--------------------------------------------------------------------------------+
 |  9       8       5-1234  |  7       1234    124-5   |  6       1234    234     |
 |  7       134-5   1234-5  |  59-124  6       58-124  |  124-8   123489  23489   |
 |  123     134     6       |  1249    134-29  1248    |  78-124  5       789-234 |
 |--------------------------+--------------------------+--------------------------|
 |  4       567-1   125     |  3       12      9       |  1278    678-12  5678-2  |
 |  126     169     8       |  1246    5       7       |  3       12469   2469    |
 |  356-12  35679-1 1235    |  8       124     6-124   |  1247    679-124 5679-24 |
 |--------------------------+--------------------------+--------------------------|
 |  3568    2       345     |  569-4   479     56-4    |  478     3678-4  1       |
 |  1368    1346    9       |  1246    7-124   1246    |  5       234678  234678  |
 |  156     1456    7       |  12456   8       3       |  9       246     246     |
 +--------------------------------------------------------------------------------+

What's of no consequence is the specific JE patterns used for each candidate value to derive the DJE. This qualifies as losing sight of the forest for the trees.

As for the weak link discussions:

    *) if the DJE is true then all of its eliminations occur. Even subsets like -(4)r7c468 and -(124=56)r67c6.

    *) If any eliminations associated with the DJE are assumed true, then it follows that the DJE must be false.

If anything, I was expecting discussions on the r-to-l reading of the strong link (7-124)r8c5 = DJE in DPB's loop. _ :evil: _
daj95376
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Re: Exotic patterns a resume

Postby David P Bird » Fri Oct 11, 2013 12:47 am

daj95376 wrote:As for the weak link discussions:

    *) if the DJE is true then all of its eliminations occur. Even subsets like -(4)r7c468 and -(124=56)r67c6.

    *) If any eliminations associated with the DJE are assumed true, then it follows that the DJE must be false.

If anything, I was expecting discussions on the r-to-l reading of the strong link (7-124)r8c5 = DJE in DPB's loop. _ :evil: _

Your second bullet point doesn't hold with respect to the eliminations in the non JE bands because it's possible for (124)r8c5 and the DJE to be true together. For example if (4)r8c5 and (4)r7c7 were both true the DJE would be forced true as well. If (1)r8c5 and (1)r6c7 were both true it would depend on (1)r4c3 whether the DJE was true or false.

On your final point
Left to right
If (124)r8c5 is false the DJE must be true
If (124)r8c5 is true the DJE may be true
Right to Left
If the DJE is false a base digit must be true in 3 'S' cells which means (124)r8c5 must be true
If the DJE is true (124)r8c5 may be true

So either way we can see they can never both be false and there is strong inference between them.

DPB
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