Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

Re: Exotic patterns a resume

Postby JC Van Hay » Thu Mar 27, 2014 9:38 pm

RichardGoodrich wrote:In SK loops does SK stand for Steve Kurzhal or something else?

Yes, Stephen/Steve Kurzhals
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Re: Exotic patterns a resume

Postby daj95376 » Tue Sep 02, 2014 5:00 am

champagne wrote:Your ratio is in line with my own statistics.

Comparing results in detail would require a precise definition of what is done as basic moves before the Exocet pattern is searched.

My solver tests many techniques before searching for a QExocet. AFAIK, in your collection of hardest puzzles, only very basic moves are found before searching for a QExocet.

In that file, most of the Exocets appear at the very beginning, but some come later.

I should update the file in the near future and restart my own check of the file for exocets and other exotic patterns.
Could you remind us in that thread the best definition of your Qexocet properties.

In the next update,additions will be mainly, but not only in the 24 clues area.
I am now restarting the search in the 25 clues area where I did not work a lot in the past.

QExocet was originally intended to be my solver's implementation of JExocet. However, DPB didn't agree with my logic. So, I renamed it QExocet. In addition, I recently upgraded QExocet to use a templates search for linking a base cell candidate to the target cell pairs. Normally, this can be replicated manually with little effort.

The following description is based on the assumption that the reader is familiar with the general properties of an Exocet/JExocet. I'm not going to provide a rigorous definition.

Code: Select all
    QExocet chute in [band 1]
    *-------*-------*-------*
    | B B . | . . . | . . . |  B = Base Cells
    | . . . | Q . . | R . . |
    | . . . | Q . . | R . . |  Q = 1st Target Pair
    *-------*-------*-------*  R = 2nd Target Pair
    | . . . | . . . | . . . |
    | . . . | . . . | . . . |  . = Any candidates
    | . . . | . . . | . . . |
    *-------*-------*-------*
    | . . . | . . . | . . . |
    | . . . | . . . | . . . |
    | . . . | . . . | . . . |
    *-------*-------*-------*

Conditions:

1) The base/target/secondary cells all reside within a single chute -- band/stack.

2) The BB/QQ/RR cells are in different boxes of the chute and aligned in mini-lines as presented in the example diagram above.

3) The base cells are limited to 3/4 candidates in each cell, and a total of 3/4 values between them.

4) For every candidate in a base cell, an assumption of it being true must lead, through single-digit logic, to it being true in at least one of the QQ/RR target pairs.

5) Normally, only one Q-cell and one R-cell will contain candidates from the base cells. This isn't a requirement, but it eases justifying eliminations. An exception usually occurs when there is a strong link within a QQ and/or RR pair for some value -- which may be a candidate in the base cells. Another exception is when a Q-cell and/or R-cell is already solved for a candidate value in the base cells.

I will not attempt to describe all of the associated relationships possible. (secondary equivalences is one example)


ADDENDUM:

This grid contains the more common exceptions that I mentioned in (5) above. There is a strong link on <1> in r12c5, and r1c8 is solved for <2>. Both values are candidates in the base cells.

Code: Select all
 +-----------------------------------------------------------------------+
 |  5      1389   1349   |  34679 R13467  4679   |  34678 Q2      13678  |
 |  1489   6      12349  |  34579 R12347  4579   |  34578 Q1345   13578  |
 | B124   B123    7      |  3456   8      2456   |  9      13456  1356   |
 |-----------------------+-----------------------+-----------------------|
 |  1249   129    6      |  3479   5      479    |  37     8      137    |
 |  48     7      45     |  3468   346    1      |  2      356    9      |
 |  3      1589   159    |  2      67     6789   |  567    156    4      |
 |-----------------------+-----------------------+-----------------------|
 |  69     359    359    |  1      467    45678  |  34568  34569  2      |
 |  7      4      259    |  568    26     3      |  1      569    568    |
 |  126    1235   8      |  456    9      2456   |  3456   7      356    |
 +-----------------------------------------------------------------------+
 # 149 eliminations remain

 ### -1234- qExocet   Base = r3c12   Target = r2c8,r2c5   aligned

 obvious eliminations:   -6r1c5, -7r12c5, -5r2c8

_
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Re: Exotic patterns a resume

Postby champagne » Tue Sep 02, 2014 12:16 pm

daj95376 wrote:QExocet was originally intended to be my solver's implementation of JExocet. However, DPB didn't agree with my logic. So, I renamed it QExocet. In addition, I recently upgraded QExocet to use a templates search for linking a base cell candidate to the target cell pairs. Normally, this can be replicated manually with little effort.

The following description is based on the assumption that the reader is familiar with the general properties of an Exocet/JExocet. I'm not going to provide a rigorous definition.

Code: Select all
    QExocet chute in [band 1]
    *-------*-------*-------*
    | B B . | . . . | . . . |  B = Base Cells
    | . . . | Q . . | R . . |
    | . . . | Q . . | R . . |  Q = 1st Target Pair
    *-------*-------*-------*  R = 2nd Target Pair
 
    *-------*-------*-------*

Conditions:

4) For every candidate in a base cell, an assumption of it being true must lead, through single-digit logic, to it being true in at least one of the QQ/RR target pairs.

5) Normally, only one Q-cell and one R-cell will contain candidates from the base cells. This isn't a requirement, but it eases justifying eliminations. An exception usually occurs when there is a strong link within a QQ and/or RR pair for some value -- which may be a candidate in the base cells. Another exception is when a Q-cell and/or R-cell is already solved for a candidate value in the base cells.


_


Hi Danny,

As such, the rule 4) does not guarantee that you have an Exocet logic.

Instead, if in QQ or RR you have a locked candidate not in the base, then, you are in the Exocet logic (You can even have the "blue extension" with more cells and more locked candidates).

I do not recognize a given, but if you have a given in QQ for example, it would still be an exocet if each of the other candidates of the base require RR (one cell or 2 cells with an extra candidate locked).

So IMO your example is another multi fish and additional conditions are required to have it working properly. (I am sure it works in that case).
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Re: Exotic patterns a resume

Postby daj95376 » Wed Sep 03, 2014 5:06 am

Okay, I accept that it's not an Exocet/JExocet pattern. However, the pattern seems simpler than a Multi-Fish.

Code: Select all
 Base Cells Scenario <1x> where x=2,3,4
 +-----------------------------------+
 |  .  .  .  |  .  1  .  |  .  .  .  |
 |  .  .  .  |  .  x  .  |  .  1  .  |  <-  Target Cells = r2c58
 | 1x 1x  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+


 Base Cells Scenario <2x> where x=3,4
 +-----------------------------------+
 |  .  .  .  |  .  1  .  |  .  .  .  |
 |  .  .  .  |  .  2  .  |  .  x  .  |  <-  Target Cells = r2c58
 | 2x 2x  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+


 Base Cells Scenario <34> (a)
 +-----------------------------------+
 |  .  .  .  |  .  1  .  |  .  .  .  |
 |  .  .  .  |  . 34  .  |  . 34  .  |  <-  Target Cells = r2c58
 |  4  3  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+


 Base Cells Scenario <34> (b)
 +-----------------------------------+
 |  .  .  .  |  . 34  .  |  .  .  .  |
 |  .  .  .  |  .  1  .  |  . 34  .  |  <-  Target Cells = r1c5,r2c8
 |  4  3  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+

_
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Re: Exotic patterns a resume

Postby champagne » Wed Sep 03, 2014 6:41 am

daj95376 wrote:Okay, I accept that it's not an Exocet/JExocet pattern. However, the pattern seems simpler than a Multi-Fish.

Code: Select all
 Base Cells Scenario <1x> where x=2,3,4
 +-----------------------------------+
 |  .  .  .  |  .  1  .  |  .  .  .  |
 |  .  .  .  |  .  x  .  |  .  1  .  |  <-  Target Cells = r2c58
 | 1x 1x  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+


 Base Cells Scenario <2x> where x=3,4
 +-----------------------------------+
 |  .  .  .  |  .  1  .  |  .  .  .  |
 |  .  .  .  |  .  2  .  |  .  x  .  |  <-  Target Cells = r2c58
 | 2x 2x  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+


 Base Cells Scenario <34> (a)
 +-----------------------------------+
 |  .  .  .  |  .  1  .  |  .  .  .  |
 |  .  .  .  |  . 34  .  |  . 34  .  |  <-  Target Cells = r2c58
 |  4  3  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+


 Base Cells Scenario <34> (b)
 +-----------------------------------+
 |  .  .  .  |  . 34  .  |  .  .  .  |
 |  .  .  .  |  .  1  .  |  . 34  .  |  <-  Target Cells = r1c5,r2c8
 |  4  3  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+

_


My question would be more what are the key properties for that new animal or a family of that kind.

Your (very clear) diagram push in something as

a) a 3 cells target
b) one potential digit of the base occupies always one cell of the target, 2 if it belongs to the base
c) other digits of the base must occupy the target.

It could work as well with four cells and another digit locked in the RR part of your diagram.

Another quality of a pattern is how often it can be found. Do you have an idea for that one ?
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Re: Exotic patterns a resume

Postby daj95376 » Wed Sep 03, 2014 11:01 pm

[Withdrawn: checking for anomalies in current logic.]

_
Last edited by daj95376 on Thu Sep 04, 2014 10:49 pm, edited 2 times in total.
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Re: Exotic patterns a resume

Postby champagne » Thu Sep 04, 2014 7:25 am

daj95376 wrote:My solver treats the QQ/RR target cell pairs as just that ... pairs. The contents of each pair is examined. If a solved cell is present in a pair, then that cell is dropped from consideration ... no matter what its value. If a locked candidate is present in a cell pair, then both cells in the pair are treated as a unit ... no matter what its value. This means that my solver may use 2-4 total target cells when linking to the base cell candidates.

As for the frequency of a locked candidate in a target cell pair, my solver found 5,278 puzzles, with at least one occurrence, in your PH14_04 file.

_


basically, we are doing similar things, except that I ignore locked candidates if the digit belongs to the base.

I worked out the same file as you for the search of JExocets, but I have problems to match your results.

Depending on the preliminary eliminations, The number puzzles with a "JExocet" pattern vary (but I am below your 1 003 626 puzzles)
Same and even worth for the locked candidates.

Processing the file with no preliminary elimination, I got 4925 puzzles with a locked candidate, not too far from your own figure.

An interesting point would be to check in your file the puzzles where the digit locked belongs to the base. One possible reason to have them all valid would be that your overall processing clear all suspicious cases.

BTW, supposing the wording describing the key properties of your example is OK, it has the same rights to be called an Exocet as the extension to a locked candidate.

One day, we should make a deep match of our processes.
I'll post in the next update of my files all my results on exotic properties. This could be a start.
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Re: Exotic patterns a resume

Postby champagne » Thu Sep 11, 2014 11:00 am

I just loaded in my "google drive space" with the name ph_1409_exocets.zip the results of my analysis of the last update of the data base for the exocets

the link to that storage place is here


The file contains 1 529 600 puzzles but some duplicated puzzles have been seen and cleaned. The file studied has 1 529 417 puzzles.


The search has been done in exclusive mode (all puzzles selected are cleared in later search).

Three main steps have been considered

a) puzzles having a JE pattern (as of my code, with possible small deviations to David's definition)
b) puzzles having no JE pattern, but a band exocet
c) puzzles having no band exocet but another exocet pattern.

In each step, 2 runs have been done:

1) The classical exocet where the contradiction appears within a single floor
2) an extended exocet where the contradiction requires a full expansion of the "true" in the base


The target is always a 2 cells target, except in JE mode where one or more "platinum blonde" mode is authorized (2 cells in a crossing line with a locked digit not belonging to the base).

There is still some room for other definitions of the target, some of them already described as

- more cells with more locked digits (described by blue)
- locked digit belonging to the base with more constraints (described by daj95376)

For sure, many other patterns will come later.

The set of rules used in "extended mode" is the following :

the base is set to true for the digit
the target is set to false for the digit
contradiction is looked for using so far basic rules plus embedded pair triplets ... Xwing swordfish .. and all kinds of X chains

The results for the extended mode can vary a lot depending on the set of rules applied.

The count

998226 JE
181764 JE in extended mode (should receive another name, not recognised as JE's by david)
74817 Band exocet not JE
15878 Band exocet in extended mode
137 other exocets
1007 other exocets in extended mode

1 271 829 in total in a file of 1 529 417 puzzles, more than 83% of the puzzles have an exocet pattern

279 043 puzzles have a double exocet

A separate file for each of these group has been printed. Only the 2 first exocet pattern have been printed in the files, but the total count is given

In each file, the data are the following
- official 81 clue pattern for the puzzle
- sequence number in the data base
- identification 'family code and id code)
- number of exocet detected
- first exocet
- second exocet
'"D" if a double exocet has been seen (only valid for JE's
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is this a new kind of JExocet

Postby champagne » Sat Sep 27, 2014 8:39 am

here a puzzle from the data base of potential hardests

Code: Select all
........1....12..3...3.4.5...1.2..4..4...6..57......6..3.6..5..1.6.8....9..2...1.;248008;dob;12_12_03;11.50

234568 256789 2345789 |5789   5679 5789  |246789  2789 B 1     
4568   56789  45789   |5789   1    2     |46789   789  B 3     
268    1      2789    |3      679  4     |26789   5      26789
-----------------------------------------------------------
3568   5689   1       |5789   2    35789 |3789    4      789   
238    4      2389    |1789T  379  6     |123789T 23789  5     
7      2589   23589   |14589  3459 3589  |12389   6      289   
-----------------------------------------------------------
248    3      2478    |6      479  1     |5       2789   24789 t
1      257    6       |4579   8    3579  |2379    2379   2479 
9      578    4578    |2      3457 357   |3678    1      4678 


r1c8 r2c8 r5c4 r5c7 r7c9


My code did not look so far for such an exocet pattern. May be blue's code already catch it.

This is very similar to a JE pattern with a locked digit, but here the second cell (r5c4 for the locked digit '1') is outside the band.

This is the first puzzle I got in a general search of exocets with one locked digit
Last edited by champagne on Sat Sep 27, 2014 5:05 pm, edited 1 time in total.
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Re: Exotic patterns a resume

Postby champagne » Sat Sep 27, 2014 3:48 pm

Anotherr example where the solver has seen 8 exocets with locked digits
Code: Select all
........1.....2..3..4.5..6....5.7.3...3...7...5..3.6.4..5.6..7..8.9.....19..7..4.;782521;DOB;13_01;10.8
PM at the start of the search
235689 2367 2689  |34678 489   34689 |24589 2589  1   
5689   167  1689  |467   1489  2     |4589  589   3   
2389   123  4     |138   5     1389  |289   6     7   
------------------------------------------------------
24689  1246 12689 |5     12489 7     |1289  3     289 
2489   124  3     |12468 12489 14689 |7     12589 2589
2789   5    12789 |128   3     189   |6     1289  4   
------------------------------------------------------
234    234  5     |12348 6     1348  |12389 7     289 
23467  8    267   |9     124   1345  |1235  125   256 
1      9    26    |238   7     358   |2358  4     2568

r4c7r4c9 r6c1r6c3 r1c8
r4c7r4c9 r6c1r6c3 r6c4
r4c7r4c9 r6c1r6c3 r8c5
r4c7r4c9 r6c1r6c3 r9c3r9c9

r6c4r6c6 r5c8r5c9 r1c8
r6c4r6c6 r5c8r5c9 r8c5
r6c4r6c6 r5c8r5c9 r9c3r9c9

r1c5r2c5 r5c4r5c6 r5c8r5c9


this is after several eliminations including dynamic chain contradictions (serate mode) for 1r2c4 8r2c4.
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Re: is this a new kinf of JExocet

Postby daj95376 » Sat Sep 27, 2014 4:26 pm

[Withdrawn: invalid scenario.]

_
Last edited by daj95376 on Sun Sep 28, 2014 2:50 am, edited 1 time in total.
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Re: is this a new kinf of JExocet

Postby champagne » Sat Sep 27, 2014 5:04 pm

daj95376 wrote:
One observation.

If r5c4=1 and r5c7=3, then it seems to me that both candidates from r12c8 will be forced into r7c9.

_


Just applying the exocet property we have

r5c7 <3>
r7c9 <4>

I did not look for more

The second puzzle with 8 exocets is likely open to side effects

Best Regards
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Re: is this a new kind of JExocet

Postby blue » Sat Sep 27, 2014 8:56 pm

champagne wrote:My code did not look so far for such an exocet pattern. May be blue's code already catch it.

It does, but it's nice to see someone else finding them too.

For the 2nd puzzle with 8 exocets, my code gets more or less the same results.
For the cases where you have "r9c3r9c9" as a target (with a locked <6>) it just has r9c3.

Code: Select all
r4c7r4c9 r6c1r6c3 r1c8      -->  (1289) r4c79 r1c8 ahs:7r6
r4c7r4c9 r6c1r6c3 r6c4      -->  (1289) r4c79 ahs:7r6 r6c4
r4c7r4c9 r6c1r6c3 r8c5      -->  (1289) r4c79 ahs:7r6 r8c5
r4c7r4c9 r6c1r6c3 r9c3r9c9  -->  (1289) r4c79 ahs:7r6 r9c3 (*)

r6c4r6c6 r5c8r5c9 r1c8      -->  (1289) r6c46 r1c8 ahs:5r5
r6c4r6c6 r5c8r5c9 r8c5      -->  (1289) r6c46 ahs:5r5 r8c5
r6c4r6c6 r5c8r5c9 r9c3r9c9  -->  (1289) r6c46 ahs:5r5 r9c3 (*)

r1c5r2c5 r5c4r5c6 r5c8r5c9  -->  (1489) r12c5 ahs:6r5 ahs:5r5

Going that way for those cases, <6> is eliminated from r9c3 via the exocet logic, and subsequenty forced to r9c9.

I haven't checked the code, but I think I find the ones that you do too, and then filter them out, as cases where an AHS targets is a superset of a smaller target. I also look for cases with 2+ locked digits (in 3+ cells), and that kind of situation probably came up often enough to add the filter.
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Re: is this a new kind of JExocet

Postby champagne » Sun Sep 28, 2014 5:51 am

blue wrote:It does, but it's nice to see someone else finding them too.
For the 2nd puzzle with 8 exocets, my code gets more or less the same results.
For the cases where you have "r9c3r9c9" as a target (with a locked <6>) it just has r9c3.

I haven't checked the code, but I think I find the ones that you do too, and then filter them out, as cases where an AHS targets is a superset of a smaller target. I also look for cases with 2+ locked digits (in 3+ cells), and that kind of situation probably came up often enough to add the filter.


It's ok for your remark. I was drafting the search for 2 locked digits and I was thinking of a process filtering such cases.

In fact this also means that the current process for one locked digit gives the priority to the pair, another anomaly.

The amazing fact is that with all these patterns, the exocet is there in about 85% of the current data base of potential hardest.
Do you have a count of the puzzles in that data base where the first occurrence of an exocet has a 2+ locked digit

PS: using the pm per digit, it remains relatively easy to detect such exocets compared to the horrible chain nets than you can use instead.
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Re: Exotic patterns a resume

Postby daj95376 » Mon Sep 29, 2014 9:36 am

If the following is redundant or the timing is inappropriate, please send me a private message and I'll delete this posting.


I'm always impressed with the simplicity of the JExocet pattern. However, a less common cousin of the JExocet also exists. Here is a puzzle from champagne's collection that contains a JExocet and its cousin.

Code: Select all
98.7..6..5...98.4...7.6....3.......2..8..94....5..79....6..47.....5.........8..1.

 +--------------------------------------------------------------------------------+
 |  9       8       1234    |  7       12345   1235    |  6       235     135     |
 |  5       6       123     |  123     9       8       |  123     4       7       |
 |  124     1234    7       |  1234    6       1235    |  12358   23589   13589   |
 |--------------------------+--------------------------+--------------------------|
 |  3       1479    149     |  1468    145     156     |  158     5678    2       |
 |  1267    127     8       |  1236    1235    9       |  4       3567    1356    |
 |  1246    124     5       |  123468  1234    7       |  9       368     1368    |
 |--------------------------+--------------------------+--------------------------|
 |  128     12359   6       |  1239    123     4       |  7       23589   3589    |
 |  1248    12349   12349   |  5       7       1236    |  238     23689   34689   |
 |  247     234579  2349    |  2369    8       236     |  235     1       34569   |
 +--------------------------------------------------------------------------------+
 # 158 eliminations remain

Here is the JExocet:

Code: Select all
 r1c89 = 1  ->  2x finned Swordfish c367\r48 + r2|r3  =>   (1)r2c3 = (1)r3c6   (SL)
 r1c89 = 2  ->  2x finned Swordfish c367\r89 + r2|r3  =>   (2)r2c3 = (2)r3c6   (SL)
 r1c89 = 3  ->  2x finned Swordfish c367\r89 + r2|r3  =>   (3)r2c3 = (3)r3c6   (SL)

 r1c89 = 5  -> - (5)r1c56 = (5)r3c6   (forced)

 ### -1235- JExocet   Base = r1c89   Target = r2c3==r3c4,r3c6

Here is the cousin:

Code: Select all
 r3c12 = 1  ->  finned Swordfish c367\r481 fc=r2c7  ->  -1r1c9   =>  =1r2c7   (forced)
 r3c12 = 2  ->  finned Swordfish c367\r891 fc=r2c7  ->  -2r1c8   =>  =2r2c7   (forced)
 r3c12 = 3  ->  finned Swordfish c367\r891 fc=r2c7  ->  -3r1c89  =>  =3r2c7   (forced)

 r3c12 = 4  ->  - (4)r1c3 = (4)r1c5   (forced)

 ### -1234-  Exocet   Base = r3c12   Target = r2c7==r1c6,r1c5

In the JExocet, we have target cell r3c6=5 and target cell (r2c3==r3c4)=<123>.

In the cousin, we have target cell r1c5=4 and target cell (r2c7==r1c6)=<123>.
daj95376
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