JExocet Pattern Definition

Advanced methods and approaches for solving Sudoku puzzles

Re: JExocet Pattern Defintion

Postby David P Bird » Wed May 29, 2013 8:18 pm

Hi Champagne,

Thanks for your JExocet/SK Loop combinations, and outlining your indicators for ABI loops.

The first of your JE3/SK combinations is a JE4 though.
98.7.......6.5.........69..4...3..2..1......4..76..8..3.......1.2.....3...89..7..
However in it I'm able to eliminate a base digit from both target cells using short chains and hence to eliminate it from the base cells too which cracks it.
So, already I've found a new line of attack (well, at least for me). The eliminations are justified by considering that the partial fish for the digit can only hold two truths and so the third truth in the JE band must now see the base cells.

David
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Re: JExocet Pattern Defintion

Postby daj95376 » Wed May 29, 2013 9:14 pm

David, did you even reduce the puzzle through Hidden Singles??? If you had, you would have gotten ...

Code: Select all
 *-----------*
 |98.|7..|...|
 |..6|.5.|...|
 |...|..6|9..|
 |---+---+---|
 |4..|.3.|.2.|
 |.1.|...|..4|
 |..7|6..|8..|
 |---+---+---|
 |3..|...|..1|
 |.2.|...|.3.|
 |..8|9..|7..|
 *-----------*

 *-----------------------------------------------------------------------------*
 | 9       8       12345   | 7      B124    B124     | 123456  1456    2356    |
 | 127     347    Q6       | 12348   5       9       |R1234    1478    2378    |
 | 1257    3457   Q12345   | 12348   1248    6       |R9       14578   23578   |
 |-------------------------+-------------------------+-------------------------|
 | 4       6       59      | 158     3       1578    | 15      2       579     |
 | 8       1       2359    | 25      279     257     | 356     5679    4       |
 | 25      359     7       | 6       1249    1245    | 8       159     359     |
 |-------------------------+-------------------------+-------------------------|
 | 3       4579    459     | 2458    24678   24578   | 2456    45689   1       |
 | 1567    2       1459    | 1458    14678   14578   | 456     3       5689    |
 | 156     45      8       | 9       1246    3       | 7       456     256     |
 *-----------------------------------------------------------------------------*

 ### -124- QExocet   Base = r1c56   Target = r2c7,r3c3

It's my understanding that Denis is using SSTS as a precursor to looking for JExocets. I use basics as a precursor.
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Re: JExocet Pattern Defintion

Postby David P Bird » Wed May 29, 2013 10:18 pm

daj, I've got into the habit of checking for SK loops and JEs before making any eliminations at all when they're easier to spot. I now see that that Champagne is checking them after eliminating singles, pairs and triples plus Xwings & Swordfish, so gets a different count of the base digits. I'll switch to his method as I guess it's better - eg in this case I don't need to check the partial fish for (3).
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Re: JExocet Pattern Defintion

Postby daj95376 » Wed May 29, 2013 10:28 pm

David P Bird wrote:daj, I've got into the habit of checking for SK loops and JEs before making any eliminations at all when they're easier to spot. I now see that that Champagne is checking them after eliminating singles, pairs and triples plus Xwings & Swordfish, so gets a different count of the base digits. I'll switch to his method as I guess it's better - eg in this case I don't need to check the partial fish for (3).

David,

IIRC, ronk and I convinced champagne that it didn't make sense to start looking for a complex pattern when basics and some "simple" advanced steps were present to reduce the complexity of the grid. Otherwise, you could have a puzzle that's solvable with Singles and people are discussing SK-Loops that might be present in the original grid. I think it would be a wise idea to obtains a consensus of the steps to be used prior to searching for an advanced solving technique.
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Re: JExocet Pattern Defintion

Postby denis_berthier » Thu May 30, 2013 2:26 am

daj95376 wrote:
denis_berthier wrote:BTW, I can say that the core of the pattern isn't the base and target cells but the constraints in the S columns, as David suggested.

Here's my current perspective on quasi-basic JExocets:
*) Select base and target cells to test [...]


Mine is opposite:
- select S-columns,
- see, digit after digit, which digits satisfy the conditions (the advantage is, you don't have to consider a whole set of digits before you find any restrictions)
- once you have this part, the rest amounts to obvious checks
Last edited by denis_berthier on Thu May 30, 2013 5:11 am, edited 1 time in total.
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Re: JExocet Pattern Defintion

Postby denis_berthier » Thu May 30, 2013 2:35 am

daj95376 wrote:It's my understanding that Denis is using SSTS as a precursor to looking for JExocets. I use basics as a precursor.

daj95376 wrote:
David P Bird wrote:daj, I've got into the habit of checking for SK loops and JEs before making any eliminations at all when they're easier to spot. I now see that that Champagne is checking them after eliminating singles, pairs and triples plus Xwings & Swordfish, so gets a different count of the base digits. I'll switch to his method as I guess it's better - eg in this case I don't need to check the partial fish for (3).

IIRC, ronk and I convinced champagne that it didn't make sense to start looking for a complex pattern when basics and some "simple" advanced steps were present to reduce the complexity of the grid. Otherwise, you could have a puzzle that's solvable with Singles and people are discussing SK-Loops that might be present in the original grid. I think it would be a wise idea to obtains a consensus of the steps to be used prior to searching for an advanced solving technique.

SSTS is a strict minimum, for both sk-loops and JExocets
I don't see why quads (Naked, Hidden and Super-Hidden), that are much simpler than both, shouldn't be searched for before them. Some sets of quads could be counted as (very degenerated) sk-loops.
As for JEs, now that I've coded the basic cases, I see better where it should be classified in my hierarchy. No time to say more now.
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Re: JExocet Pattern Defintion

Postby champagne » Thu May 30, 2013 5:35 am

daj95376 wrote:
David P Bird wrote:daj, I've got into the habit of checking for SK loops and JEs before making any eliminations at all when they're easier to spot. I now see that that Champagne is checking them after eliminating singles, pairs and triples plus Xwings & Swordfish, so gets a different count of the base digits. I'll switch to his method as I guess it's better - eg in this case I don't need to check the partial fish for (3).

David,

IIRC, ronk and I convinced champagne that it didn't make sense to start looking for a complex pattern when basics and some "simple" advanced steps were present to reduce the complexity of the grid. Otherwise, you could have a puzzle that's solvable with Singles and people are discussing SK-Loops that might be present in the original grid. I think it would be a wise idea to obtains a consensus of the steps to be used prior to searching for an advanced solving technique.


Hi all,

I would just make a difference between a research work and the solving process.

EDIT

IMO, each player/solver should be free to start the search at any moment. Each one has its own "rules".

The consensus for a common basis for research work helps, but each one should feel free to explore new areas. Blue brought new families of exocets exploring the AHS in box.

Having a separate process for the research, I have no problem to rally a common position.

In the solving process, on my side, the search for "exotic patterns" starts after all basic moves have been tried (including XYWings and XYZWings) and is done once.

This explains that I lost some of the "JE3 SK loop" of the sample.

Trying to look for frequency of a pattern, it would be possible to use any other rule. Sometimes, elimination of singles is necessary to see the exotic pattern, sometimes it destroys it (in puzzles with relatively low ratings).

I took a standard in the middle of the ford. I apply basic moves limited to triplet and Swordfish before the search of any exotic pattern.
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Re: JExocet Pattern Defintion

Postby David P Bird » Thu May 30, 2013 7:26 am

I consider that both the SK loop and JE patterns are dominated by the positions of the givens. That's why I've been checking for them first – before any other cells are solved to muddy the waters. However, when I did some work on Avoidable Patterns, I modified my spreadsheet to use <N> to mark the givens in my PM grid, so I can now run my checks at any time.

My checking method would be wrong if a new JE or SK pattern could be created by solving cells using simple methods, but I believe the chances of that ever happening are very remote.
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Re: JExocet Pattern Defintion

Postby ronk » Thu May 30, 2013 1:41 pm

David P Bird wrote:I consider that both the SK loop and JE patterns are dominated by the positions of the givens.

As do I, and I'm surprised no one has posted "rules" for this approach. After absolutely zero response in a thread I started on this topic last fall, I deleted the thread.
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Re: JExocet Pattern Defintion

Postby champagne » Fri May 31, 2013 8:49 am

I have finished the generation phase for my sample starting from the file of potential hardest.
I summarized the preliminary results here above.

A second post will come with a deeper exocet analysis

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Re: JExocet Pattern Defintion

Postby denis_berthier » Fri May 31, 2013 9:14 am

Hi David,

In your first post, you write

David P Bird wrote:
Code: Select all
  *-------*-------*-------*
  | B B . | . . . | . . . |  B = Base Cells 
  | . . . | Q . . | R . . |   
  | . . . | Q . . | R . . |  Q = 1st Object Pair
  *-------*-------*-------*  R = 2nd Object Pair
  | . . S | S . . | S . . |       
  | . . S | S . . | S . . |  S = Cross-line Cells     
  | . . S | S . . | S . . |   
  *-------*-------*-------*  . = Any candidates
  | . . S | S . . | S . . | 
  | . . S | S . . | S . . |     
  | . . S | S . . | S . . |   
  *-------*-------*-------*

The different cell pairs occur in different boxes in the same band (the JE band).


I can't see why the Q and R pairs should be in different blocks/boxes. Indeed, my proof works without this assumption.
I think the right condition is:
The two Object Cell Pairs (Q and R) occur in the same band as the Base Cell Pair (B) (the JE band) but not in the same block/box.
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Re: JExocet Pattern Defintion

Postby David P Bird » Fri May 31, 2013 9:42 am

denis_berthier wrote:Hi David,

I can't see why the Q and R pairs should be in different blocks/boxes. Indeed, my proof works without this assumption.
I think the right condition is:
The two Object Cell Pairs (Q and R) occur in the same band as the Base Cell Pair (B) (the JE band) but not in the same block/box.

Wow! I've been working with a pair of blinkers on! I've been considering that the Braid Analysis constraints always had an important part to play in the pattern (although expressing them in Braiding terms has never been needed).

With the targets in the same box, these constraints go and are replaced by the more restrictive box ones, so I guess these cases will occur far less frequently.

Just as I was beginning to think I could see light at the end of the tunnel!
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Re: JExocet Pattern Defintion

Postby David P Bird » Fri May 31, 2013 10:09 am

After Champagne's post I suppose I should post some interim findings based on only a few JE3+SK puzzles

So far the 3 base digits always occur as givens in the 4 SK Loop boxes, with a 4th given that's resolvable to two conjugate configurations. Using that digit as a way to navigate around the boxes then always provides a simple way to solve the puzzle, but usually needs a few steps.

Some nice shortcuts using the JE inferences are sometimes available though as here:

98.7.....6.....5....5.4..7..7..3...2..94..6.......1.8...65..4......8..1......2..3 JE3+SK #006
After basic and SK loop eliminations
Code: Select all
 *----------------------*----------------------*----------------------*
 | <9>    <8>    123    | <7>    56-12  5-3    | #123   2346   14     |
 | <6>    4      7      | #123-8 129    389    | <5>    239    189    |
 | #123   #123   <5>    | 1238   <4>    69     | 1238   <7>    69     |
 *----------------------*----------------------*----------------------*
 | 1458   <7>    148    | 689    <3>    569    | 19     459    <2>    |
 | 1238   123    <9>    | <4>    257    578    | <6>    35     157    |
 | 2345   6      234    | 29     579    <1>    | 379    <8>    4579   |
 *----------------------*----------------------*----------------------*
 | 1238   123    <6>    | <5>    179    379    | <4>    29     789    |
 | 237    59     23     | 369    <8>    4      | 279    <1>    56     |
 | 1478   59     148    | 19     679    <2>    | 789    56     <3>    |
 *----------------------*----------------------*----------------------*

(123)JE3:r3c12,r1c7,r2c4 => r2c4 <> 8
(x)r1c3 = (x)r3c12 – (x)r3c47 =[JE]= (x)r1c7,r2c4 => r1c5 <> 12, r1c6 <> 3
sste

ie either a digits is in r1c3 or the base cells and hence one of the two targets, so can be eliminated from cells seen by the targets & r1c3.

The term "basic eliminations" has never been properly defined AFAIK but here means tuples up to size 3, box/line eliminations & simple fish of any size.
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Re: JExocet Pattern Defintion

Postby denis_berthier » Fri May 31, 2013 10:41 am

David P Bird wrote:
denis_berthier wrote:Hi David,
I can't see why the Q and R pairs should be in different blocks/boxes. Indeed, my proof works without this assumption.
I think the right condition is:
The two Object Cell Pairs (Q and R) occur in the same band as the Base Cell Pair (B) (the JE band) but not in the same block/box.

Wow! I've been working with a pair of blinkers on! I've been considering that the Braid Analysis constraints always had an important part to play in the pattern (although expressing them in Braiding terms has never been needed).
With the targets in the same box, these constraints go and are replaced by the more restrictive box ones, so I guess these cases will occur far less frequently.
Just as I was beginning to think I could see light at the end of the tunnel!


Indeed, I thought you had kept this condition inadvertently.
BTW, in the SudoRules implementation, I don't have this Q block <> R block condition.

In my view of Jk-Exocet, the S-cells are the most important part (I'll explain this in a further post). I thought this was also your view of it.
For the standard Jk-Exocet (S-columns covered by 2 rows for each base digit, or conversely - no covering blocks), the conditions on the S-cells are fish-like and adding a Q block <> R block condition seems queer.

Another point (related to the fish-view): in the non-standard case, when blocks, instead of only rows, are allowed to cover S-cells, we could speak of a Franken Jk-Exocet.
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Re: JExocet Pattern Defintion

Postby David P Bird » Fri May 31, 2013 11:44 am

Denis Berthier wrote: Indeed, I thought you had kept this condition inadvertently.
BTW, in the SudoRules implementation, I don't have this Q block <> R block condition.

In my view of Jk-Exocet, the S-cells are the most important part (I'll explain this in a further post). I thought this was also your view of it.
For the standard Jk-Exocet (S-columns covered by 2 rows for each base digit, or conversely - no covering blocks), the conditions on the S-cells are fish-like and adding a Q block <> R block condition seems queer.

Another point (related to the fish-view): in the non-standard case, when blocks, instead of only rows, are allowed to cover S-cells, we could speak of a Franken Jk-Exocet.

Up to now my mental model has been a Braid pattern in the JE band with an overlapping sort of Franken Swordfish in the cross lines. From my limited practical experience with them based on the hardest puzzles sub-set, I've found the fish fin cell inferences less useful than those in the JE band – but remember, I won't use nets in my solving methods unless they're contained in recognisable patterns.

In < this post > I coined the term Partial Fish to describe the S cells in the JE pattern, but deliberately didn't specify that their lines should be in different bands. I was therefore on the threshold of widening the concept as you've just done. Therefore our thinking isn't that far apart except that we are rather like < Jack Spratt and his wife > regarding the methods we find palatable.
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