JExocet Pattern Definition

Advanced methods and approaches for solving Sudoku puzzles

Re: JExocet Pattern Defintion

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.
denis_berthier
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Re: JExocet Pattern Defintion

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!
David P Bird
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Re: JExocet Pattern Defintion

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.
David P Bird
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Re: JExocet Pattern Defintion

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!

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.
denis_berthier
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Re: JExocet Pattern Defintion

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.
David P Bird
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Re: JExocet Pattern Defintion

denis_berthier wrote:In my view of Jk-Exocet, the S-cells are the most important part (I'll explain this in a further post).

Since strong inference sets "make the sudoku world go around", this shouldn't be a surprise to any participants in this thread. See Allan Barker's 2nd graphic in his 2009 post here.

As to your fish comment, I believe swordfish and x-wings have been mentioned in conjunction with JExocets several times in the past.
ronk
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Re: JExocet Pattern Defintion

ronk wrote:
denis_berthier wrote:In my view of Jk-Exocet, the S-cells are the most important part (I'll explain this in a further post).

Since strong inference sets "make the sudoku world go around", this shouldn't be a surprise to any participants in this thread.

As there are 3k + 6 CSP-variables / 2D-cells /sis involved in the pattern, I can't see how your remark can be relevant to my saying that the 3k ones associated with the S cells and Base Digits are the important ones.

Moreover, what I say can't be so obvious, as:
- it is totally opposite to champagne's view according to which the core of the pattern consists of the base and target cells;
- David's "mental model" was based on the JE band.
denis_berthier
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Re: JExocet Pattern Defintion

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!

As long as this has come up, I should mention that there's no reason to restrict the target cells to the base cell band.
Here's an alternate proposal for the (core of the) pattern definition:

Code: Select all
`*-------*-------*-------*| B B . | . . . | . . . |  B = base cells| . . . | S . . | S . . |  S = fish column cells| . . . | S . . | S . . |*-------*-------*-------*| . . S | S . . | S . . |  T : two S cells are designated as target cells| . . S | S . . | S . . || . . S | S . . | S . . |*-------*-------*-------*| . . S | S . . | S . . |  Requirement: for each base digit, the candidates| . . S | S . . | S . . |  in the S cells are restricted to two rows and the| . . S | S . . | S . . |  target cells*-------*-------*-------*`

Here's an example from champagne's "potential hardest" list.

Code: Select all
`#9004 GP;H244798.7.......7.6.9....6.5....4......3..9...2..1...6..5..1.......4.3.....2...98..7..+---------------------+-----------------------+--------------------+| 9      8      12345 | 7      1234(B) 134(B) | 12346  1456  2356  || 235    1245   7     | 1234   6       1348   | 9      1458  2358  || 23     124    6     | 12349  5       13489  | 1234-8 1478  2378  |+---------------------+-----------------------+--------------------+| 4      12567  1258  | 159    1789    1579   | 268    3     26789 || 35678  9      358   | 345    3478    2      | 468    4678  1     || 2378   127    123-8 | 6      134789  13479  | 5      4789  2789  |+---------------------+-----------------------+--------------------+| 1      2567   258   | 2359   2379    35679  | 368    5689  4     || 5678   3      458   | 1459   1479    145679 | 168    2     5689  || 256    2456   9     | 8      1234    13456  | 7      156   356   |+---------------------+-----------------------+--------------------+                S       S                       SBase cells: r1c56S columns: c347Target cells: r3c7, r6c3XSudo output:   14 Truths = {1234C3 1234C4 1234C7 1N56}   18 Links = {1234r1 12r4 34r5 23r7 14r8 6n3 3n7 1234b2}   2 Eliminations --> r3c7<>8, r6c3<>8  `

Regards,
Blue.
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Re: JExocet Pattern Defintion

blue wrote:Here's an alternate proposal for the (core of the) pattern definition:

Code: Select all
`*-------*-------*-------*| B B . | . . . | . . . |  B = base cells| . . . | S . . | S . . |  S = fish column cells| . . . | S . . | S . . |*-------*-------*-------*| . . S | S . . | S . . |  T : two S cells are designated as target cells| . . S | S . . | S . . || . . S | S . . | S . . |*-------*-------*-------*| . . S | S . . | S . . |  Requirement: for each base digit, the candidates| . . S | S . . | S . . |  in the S cells are restricted to two rows and the| . . S | S . . | S . . |  target cells*-------*-------*-------*`

Excellent, this discards all the unnecessary conditions.
denis_berthier
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Re: JExocet Pattern Defintion

denis_berthier wrote:
Moreover, what I say can't be so obvious, as:
- it is totally opposite to champagne's view according to which the core of the pattern consists of the base and target cells;
- David's "mental model" was based on the JE band.

The exocet problematic in my view is very simple

The exocet as such is reduced to the base and the target(s).The common properties to any exocet are clear.

A key issue is "how do you establish the exocet proof".

Here, the JE exocet play a key role just because it is by far the most common exocet.

A third issue is on the solving side. Is there for that specific exocet pattern some solving shorts. Usually, such shorts are tightly linked to the "proof pattern".

The "abi loop" belongs to that third group.

The only common property for any exocet is the link between the base and the target.
champagne
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Re: JExocet Pattern Defintion

blue wrote:98.7.......7.6.9....6.5....4......3..9...2..1...6..5..1.......4.3.....2...98..7..

Base cells: r1c56
S columns: c347
Target cells: r3c7, r6c3

Hi blue,

Interesting example,

I had in mind one example of exocet with the target outside the band, It was not that one; either my memory is weak or you made a deeper search.
champagne
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Re: JExocet Pattern Defintion

Hi champagne,

champagne wrote:I had in mind one example of exocet with the target outside the band, It was not that one; either my memory is weak or you made a deeper search.

#1952 elev;1806 -- base: r13c6, targets: r2c9 r7c5
...4....94....923..8..2...4..6..3...8..59...2.......7.3..9....5..8..21...1...5...

Yes, I always wondered how you knew of that one, but not the others.

Regards,
Blue.
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Re: JExocet Pattern Defintion

Hi Blue,

blue wrote:Here's an alternate proposal for the (core of the) pattern definition:
Code: Select all
`*-------*-------*-------*| B B . | . . . | . . . |  B = base cells| . . . | S . . | S . . |  S = fish column cells| . . . | S . . | S . . |*-------*-------*-------*| . . S | S . . | S . . |  T : two S cells are designated as target cells| . . S | S . . | S . . || . . S | S . . | S . . |*-------*-------*-------*| . . S | S . . | S . . |  Requirement: for each base digit, the candidates| . . S | S . . | S . . |  in the S cells are restricted to two rows and the| . . S | S . . | S . . |  target cells*-------*-------*-------*`

Congratulations, very good work, but it results in potentially driving a horse and cart through this thread!

The dilemma it poses is that "recognisable pattern" once again. Restricting the base digits to absent givens in the band, makes looking for the signature pattern quite quick and knowing that the other two S lines must pass through targets in the same band makes the subsequent checks reasonably quick too. The potential returns for an advanced player conducting a JE search aren't just a few eliminations in two cells, but also various inferences that can be combined with other patterns. For your version I believe that mainly it will just be the eliminations on offer for a far bigger search effort. (This would also justify Denis' point regarding only counting the patterns that provide eliminations in any survey.)

The choice of the name "Junior Exocet" was fortuitous, because that leaves the door open to call your extended version "Advanced Exocet". However, it should be possible to allow the two targets in JExocet to be in the same box as per Denis' findings.

That's the way I would currently favour going, but I wait for other opinions.

David
David P Bird
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Re: JExocet Pattern Defintion

David P Bird Wrote:
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>    |  *----------------------*----------------------*----------------------*`

I think I can see another JE based elimination in this PM.

If r1c9 = 4 (a non-base digit) then a JE secondary equivalence r1c8==r2c4 would apply so r1c8 = 2 or 3;
If r1c9 <> 4 then r1c8 = 4;

Either way r1c8 <> 6

Leren
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Re: JExocet Pattern Defintion

Hi David,

I don't know if you noticed, but the example that I showed, has only one clue cell out of place -- a "would be" clue at r6c3, moved to r2c3. The base cell band is still deviod of base digit clues, and the 2 clues each for the base digits, are where they usually are.

I agree that there probably isn't much to be gained beyond the standard eliminations.

I wonder how that type of layout might fare in the "abi loop" game, though ?
I see that for the example puzzle, 4r1c5 can be eliminated (using UR considerations).
[ No time to look deeper, at the moment. ]

Regards,
Blue.
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