exocet pattern in hardest puzzles

Advanced methods and approaches for solving Sudoku puzzles

Re: bi bi pattern in hardest puzzles

Postby ronk » Thu Apr 12, 2012 12:37 pm

champagne wrote:When I run the test on the file of my database, where no restriction was applied except that the target must have the full set of digits, I find all exocets but 1.

This means that in my data base, no exocet with all digits in each target has both targets in the same row/column.

You ran the test on the 30,000+ puzzles? And lost one? Is this the same as the 1 (of 5) leftover here?

By "the target must have the full set of digits", you mean in the union of candidates of the two target cells, right?
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Re: bi bi pattern in hardest puzzles

Postby champagne » Thu Apr 12, 2012 1:09 pm

ronk wrote:
champagne wrote:When I run the test on the file of my database, where no restriction was applied except that the target must have the full set of digits, I find all exocets but 1.

This means that in my data base, no exocet with all digits in each target has both targets in the same row/column.

You ran the test on the 30,000+ puzzles? And lost one? Is this the same as the 1 (of 5) leftover here?

By "the target must have the full set of digits", you mean in the union of candidates of the two target cells, right?


The first test was run on the file "03 E Exocet seen" to try to answer to the first question of David how many of these exocet have the "jexocet" pattern.
Having added the filter for Exocets with special conditions, only one was excluded.
Code: Select all
  special conditions :
   . one target forced to one of the digits
   . exclusive or for one digit in the 2 targets

In my old program, Each of the target cells must have the four digits.
In the new version, only, as you write, union of the 2 targets must have it.

So I ran a new test on the entire file with the new version and got the final ration of 79...% of puzzles having an "jexocet plus special conditions"

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Re: bi bi pattern in hardest puzzles

Postby ronk » Thu Apr 12, 2012 1:58 pm

David P Bird wrote:3) In the array of 18 cross-line cells each base candidate must be restricted to two lines in at least one vertical or horizontal directions.

champagne, I understand this 3rd condition means exactly two lines, not two lines or less. IOW the "JExocet" excludes degenerate varieties. That's why David P Bird expects the count to "fall" considerably. AFAICS that's not what you ran.
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Re: bi bi pattern in hardest puzzles

Postby champagne » Thu Apr 12, 2012 3:06 pm

ronk wrote:
David P Bird wrote:3) In the array of 18 cross-line cells each base candidate must be restricted to two lines in at least one vertical or horizontal directions.

champagne, I understand this 3rd condition means exactly two lines, not two lines or less. IOW the "JExocet" excludes degenerate varieties. That's why David P Bird expects the count to "fall" considerably. AFAICS that's not what you ran.


You have a good idea of what I got with the first run.

a little more than 40 puzzles were excluded. (the list is somewhere above)

Introducing a filter to include "targets in an exclusive or condition", this fell to 5.
4 out of these five had one target forced (and a twin exocet pattern) but were still of the family
1 was out of the scope.

this is a test run on a 20 000 puzzles file having an identified exocet pattern seen by my old program.

I understand it's hard to believe, but facts are there for days, the "jexocet" pattern covers nearly all the known field of "potential hardest" puzzles.

I have no sample file to run tests in other areas.


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Re: bi bi pattern in hardest puzzles

Postby David P Bird » Fri Apr 13, 2012 9:56 am

champagne, thanks for your response. It's clear there have been translation issues though.

To summarise things as I now see them: you ran a file of 11454 having the Exocet pattern against the new search routine
After correcting one line of your code you found 5 of them were rejected.

We then found the condition 3 had omitted the case when a base digit was restricted to two cross-lines.
When that was corrected 4 of the 5 were accepted but one was still rejected.

Which one was that? I may be wrong but they all seem acceptable to me!

What I didn't know was that when that list of 11454 was produced the check for target cells allowed them to see each other, but you never found one case where they did.

I believe that answers my question <here> when I asked if you had ever found one as I thought they were probably impossible. (From Braid Analysis which looks at the patterns of repeating pairs in the mini-lines a band.)

My conjecture therefore is probably true, and maybe we can drop the case where the two targets see each other.

This encourages me to look for a proof of that.

Now are all one-band Exocets also JExocets? I think the answer is yes provided they produce exclusions!

I've seen quite a few puzzles where there are two Exocet matches for the 4 base and target cells, but only one provides exclusions. Each time that is the one that complies with condition 3.
Example: .2.45....4....92....6.2............83...9.5...7...3.1.5..9..3...8......6..1....7.;66;elev;24;2BN F1F3

In the past you've reported cases where the you found Exocet exclusions with split target cells. But these could not have been in your file of 11454 puzzles!

So there are 3 types of Exocet: 1:One-band Exocets, 2:Split Exocets, and 3:JExocets

Perhaps it's time to consider which one of these is the default case and which one(s) need additional descriptions.

Please correct me if I've got any of this wrong.

I'm sure there are still points I've missed and will have to come back to later, but at the moment these seem to be the important ones.
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Re: bi bi pattern in hardest puzzles

Postby ronk » Fri Apr 13, 2012 11:14 am

David P Bird wrote:I've seen quite a few puzzles where there are two Exocet matches for the 4 base and target cells, but only one provides exclusions. Each time that is the one that complies with condition 3.
Example: .2.45....4....92....6.2............83...9.5...7...3.1.5..9..3...8......6..1....7.;66;elev;24;2BN F1F3

I find only one in this puzzle, with the base set at r13c6=1578. Where do you see a 2nd?
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Re: bi bi pattern in hardest puzzles

Postby champagne » Fri Apr 13, 2012 11:24 am

David P Bird wrote:champagne, ...


Please correct me if I've got any of this wrong.

I'm sure there are still points I've missed and will have to come back to later, but at the moment these seem to be the important ones.


David,

I am somehow confused, but i believe that again this is due to the fact that the simple conclusion is hard to accept.

If we accept as "jexocets" the 2 extensions

. one digit forced in exclusive or in the 2 targets when valid in the base
. one digit forced in one of the target when valid in the base

then

all known exocets based on 2 cells in a mini row located in a band are "jexocets"

Only one found exocet is not a located in a band

...4....94....923..8..2...4..6..3...8..59...2.......7.3..9....5..8..21...1...5...;1952;11.20;11.20;10.40;elev;1806;24
base r13c6 targets r2c9 r7c5

I have no example of an exocet producing no direct elimination, but surely, it can exist.

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Re: bi bi pattern in hardest puzzles

Postby champagne » Fri Apr 13, 2012 11:40 am

ronk wrote:
David P Bird wrote:I've seen quite a few puzzles where there are two Exocet matches for the 4 base and target cells, but only one provides exclusions. Each time that is the one that complies with condition 3.
Example: .2.45....4....92....6.2............83...9.5...7...3.1.5..9..3...8......6..1....7.;66;elev;24;2BN F1F3

I find only one in this puzzle, with the base set at r13c6=1578. Where do you see a 2nd?


same remark as ronk
my solver, as shown in the puzzle line, has seen only one exocet

But this could be the source of confusion.

the word exocet is reserved to a pattern having all the qualities of an exocet.
I suspect david call "exocet" a pattern that could be one if the condition 3 was satisfied
in that puzzle, band 1 has such a pattern. It's not an exocet (base r3c46)

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Re: bi bi pattern in hardest puzzles

Postby ronk » Fri Apr 13, 2012 12:40 pm

champagne, how difficult would it be to research 5-digit exocets with your program?

In the illustration below, two optional candidates for each digit have been removed (in bands 2 & 3 only) from vertices of the conditional almost-swordfish. Removal of more would result in a pattern reduction (degeneration) to an almost-x-wing, skyscraper, or hidden single, each being conditional upon the ultimate placements in base cells r1c12. Optional candidates in the base and target cells are not addressed.

____ Image

Code: Select all
+---------------------------------+--------------------+----------------------------+
| (12345)    (12345)  6789(12345) | .  6789(12345)   . | 6789(12345)   .  123456789 |
| .          .        6789(12345) | .  6789          . | -6789(12345)  .  123456789 |
| 123456789  .        6789(12345) | .  -6789(12345)  . | 6789          .  123456789 |
+---------------------------------+--------------------+----------------------------+
| .          .        6789(14)    | .  6789(14)      . | 6789          .  123456789 |
| .          .        6789        | .  6789(2)       . | 6789(2)       .  123456789 |
| .          .        6789(35)    | .  6789(5)       . | 6789(3)       .  123456789 |
+---------------------------------+--------------------+----------------------------+
| .          .        6789(2)     | .  6789(1)       . | 6789(12)      .  123456789 |
| .          .        6789(3)     | .  6789(35)      . | 6789(5)       .  123456789 |
| .          .        6789(4)     | .  6789          . | 6789(4)       .  123456789 |
+---------------------------------+--------------------+----------------------------+

     17 Truths = {12345C3 12345C5 12345C7 1N12}
     22 Links = {12345r1 14r4 2r5 35r6 12r7 35r8 4r9 3n5 2n7 12345b1}

[edit: replace lost image]
Last edited by ronk on Sat Apr 14, 2012 2:25 pm, edited 1 time in total.
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Re: bi bi pattern in hardest puzzles

Postby champagne » Fri Apr 13, 2012 1:56 pm

ronk wrote:champagne, how difficult would it be to research 5-digit exocets with your program?

In the illustration below, two optional candidates for each digit have been removed (in bands 2 & 3 only) from vertices of the conditional almost-swordfish. Removal of more would result in a pattern reduction (degeneration) to an almost-x-wing, skyscraper, or hidden single, each being conditional upon the ultimate placements in base cells r1c12. Optional candidates in the base and target cells are not addressed.



In theory I have to change 1 or 2 lines of code.

I did it on the code complying to david's constraints without success (no puzzles found in the file "03NN)".
On the code having the minimum of constraints, I have first to switch from
"each cell of the target has all digits"
to
"union of cells of the target have all digits

As I switch off my computer for several days this afternoon, answer can be next week.

I would not bet a lot on our chances to find one.

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Re: bi bi pattern in hardest puzzles

Postby David P Bird » Fri Apr 13, 2012 2:18 pm

champagne, ronk

The crucial difference for me is that I would class Exocet as a method and JExocet as a pattern.

To justify the eliminations produced by a method, a notation or diagram of the inferences being used is needed. In contrast to justify the eliminations produced by a proven pattern it's only necessary to identify where that pattern can be found.

champagne, No one is going to doubt a proven computer program's results, but if they are just stated with an incomplete explanation they have limited use.

If the signature pattern (2 base cells and 2 target cells with companion empty cells) is recognised, your computer will attempt the rest of the Exocet method. If that succeeds you then call it as an Exocet but if it fails it's not. I can see the logic in that but it's strange to me.

So let me rephrase to avoid this issue: So far all one band Exocets that have been fiund are covered by an JExocet pattern.

There may be future exceptions though. For example, the JExocet pattern may only be made when a member digit has been eliminated in one of the cross-line cells. We may then find the eliminations can be proved either by using brute force or more elegantly by finding that elimination.

Exploring other ways a pattern could be considered an Almost JExocet could also be fruitful but as I've said before the chances of finding them are not very good.

BTW The example I provided had two Exocet signature patterns only one of which led to eliminations. I thought that was clear from the description I gave.
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Re: bi bi pattern in hardest puzzles

Postby ronk » Fri Apr 13, 2012 2:53 pm

David P Bird wrote:So let me rephrase to avoid this issue: So far all one band Exocets that have been fiund are covered by an JExocet pattern.
There may be future exceptions though.

There seems to be some confusion about whether your "JExocet" requires the rarely-quoted "condition 3" to be true or not. I am under the impression that it does. If that impression is true, we already know of the 42-1=41 exocet puzzles where the JExocet doesn't apply.

David P Bird wrote:The example I provided had two Exocet signature patterns only one of which led to eliminations. I thought that was clear from the description I gave.

A required signature, or marker, for a pattern does not a pattern make.
Last edited by ronk on Fri Apr 13, 2012 3:05 pm, edited 1 time in total.
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Re: bi bi pattern in hardest puzzles

Postby champagne » Fri Apr 13, 2012 2:59 pm

David P Bird wrote:If the signature pattern (2 base cells and 2 target cells with companion empty cells) is recognised, your computer will attempt the rest of the Exocet method. If that succeeds you then call it as an Exocet but if it fails it's not. I can see the logic in that but it's strange to me.


David, I think that this is one key sentence.

The exocet has been defined based on some logic properties.

Your "signature pattern" is not at all a "signature for an exocet".

In your mind, it is, and 2 lines later, you jump on it.

An exocet is an exocet that's it. Refer to the definition.

Whether all exocets found by a computer can be found by a player is another question (of importance).

I am afraid that if you can not clarify that point cooperation will be much tougher.

I just rewrite (once more) the logic of an exocet in the wider definition

Code: Select all
Considering  a base having 'd' free digits and
 n cells
 p locked digits
such as n-p=2   (we are considering a subset where p=0 and cells are in a mini row) 

If we can find a target of 2 cells such that,
for each of the 'd' digits
   if the digit is valid in the base then one cell of the target  contains the digit
we can conclude the folllowing
the target can not contain other digits
the pair of digits solution of the base is the pair of digits solution of the target.

Such a pattern is named an Exocet.


This is pure logic, and many many patterns can fit with that logic.
A pattern that has chances to fit with the constraints can not be called an exocet as long as it has not be proven that it is one;


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Re: bi bi pattern in hardest puzzles

Postby champagne » Fri Apr 13, 2012 3:15 pm

It seems that we are far from having covered the potential of exocets.

Trying to answer to Ronk's question, I first, as written earlier, change the general code to erase the false constraints to have all digits in both targets.

I now see several puzzles having a property similar to that one

Code: Select all
61;elev;31;2BN A9C9
....56.8..5.7....3..8......2.....9...4.5....7....92.6.3.4.....15..1..4...1.....7.
-> r9c1 r9c3 r7c4 r8c9 
-> r9c1 r9c3 r8c8 r8c9

A     B     C     |D      E      F     |G     H     I     
1479  2379  12379 |2349   5      6     |127   8     249   
1469  5     1269  |7      1248   1489  |126   1249  3     
14679 23679 8     |2349   1234   1349  |12567 12459 24569
---------------------------------------------------------
2     3678  13567 |3468   134678 13478 |9     1345  458   
1689  4     1369  |5      1368   138   |1238  123   7     
178   378   1357  |348    9      2     |1358  6     458   
---------------------------------------------------------
3     26789 4     |2689   2678   5789  |2568  259   1     
5     26789 2679  |1      23678  3789  |4     239   2689 
689   1     269   |234689 23468  34589 |23568 7     25689

The second exocet reinforces strongly the power of the first one.

It seems that such situation comes in 10 to 20% of the sample (puzzles having an exocet)

This is a fresh result, but I am confident that the second exocet is there.

I have also seen puzzles with four exocets as that one

Code: Select all
264;elev;266;2BN G1H1;2BN B2C2
.23.....94.....1...9..3..4.2..81...4.....78..9...4...23...9...1.6..........5.....
-> r1c7 r1c8 r2c5 r3c1 
-> r1c7 r1c8 r3c1 r3c3 
-> r2c2 r2c3 r1c5 r3c9 
-> r2c2 r2c3 r3c7 r3c9

A     B     C       |D     E     F      |G      H      I     
15678 2     3       |1467  5678  14568  |567    5678   9     
4     578   5678    |2679  25678 25689  |1      235678 35678
15678 9     15678   |1267  3     12568  |2567   4      5678 
------------------------------------------------------------
2     357   567     |8     1     3569   |35679  35679  4     
156   1345  1456    |2369  256   7      |8      13569  356   
9     13578 15678   |36    4     356    |3567   13567  2     
------------------------------------------------------------
3     4578  24578   |2467  9     2468   |24567  25678  1     
1578  6     1245789 |12347 278   12348  |234579 235789 3578 
178   1478  124789  |5     2678  123468 |234679 236789 3678 

subject as usual to deeper investigations

champagne

[ronk-moderator edit: added puzzle identifiers]
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Re: bi bi pattern in hardest puzzles

Postby David P Bird » Fri Apr 13, 2012 4:13 pm

ronk wrote:There seems to be some confusion about whether your "JExocet" requires the rarely-quoted "condition 3" to be true or not. I am under the impression that it does. If that impression is true, we already know of the 42-1=41 Exocet puzzles where the JExocet doesn't apply.

I coined JExocet for the first time two days ago <here> because it needed to be distinguished from champagne's broader definition of Exocet, and I chose that name to try to show that it was borne out of his work.

The following day <here> I made it crystal clear that the pattern needed to fulfil all three conditions.

As you were the one that pointed out that the first version of condition 3 missed some cases and that my use of the Swordfish concept was confusing, I'm surprised that you don't recall that I produced version 2 of condition 3) to cover the omission which avoided any reference to Swordfish.

Under these circumstances I'm sorry but I take your wording 'rarely-quoted "condition 3"' to be somewhat derogatory and inflammatory.

ronk wrote:A required signature, or marker, for a pattern does not a pattern make.

Now we are in agreement. The locations of only the base and target cells are insufficient to identify the rest of the pattern elements used in Exocet eliminations. For JExocet they are, as the locations of the 18 cross-line cells are stipulated in reference to these cells.
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