exocet pattern in hardest puzzles

Advanced methods and approaches for solving Sudoku puzzles

Re: bi bi pattern in hardest puzzles

Postby David P Bird » Fri Apr 13, 2012 4:32 pm

champagne, I have desperately tried to find a form of words that would satisfy both of us, you for the programmers and me for the manual solvers.

If programmers are happy to accept your Exocet definition as defining a pattern so be it, but it doesn't qualify as one for a manual solver.

Our problem, as so often in Sudoku, is that each of us has a personal understanding of what our terms mean, and they are all different. That's what's hindered us in trying to develop your ideas further.

I too am getting the impression that this collaboration is getting harder and harder to conduct peacefully.

I'm sorry if anything I've written has given you offence, but I assure you I tried to be constructive throughout the discussion.

DPB
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Re: bi bi pattern in hardest puzzles

Postby champagne » Fri Apr 13, 2012 5:03 pm

David P Bird wrote:champagne, I have desperately tried to find a form of words that would satisfy both of us, you for the programmers and me for the manual solvers.

If programmers are happy to accept your Exocet definition as defining a pattern so be it, but it doesn't qualify as one for a manual solver.

Our problem, as so often in Sudoku, is that each of us has a personal understanding of what our terms mean, and they are all different. That's what's hindered us in trying to develop your ideas further.

I too am getting the impression that this collaboration is getting harder and harder to conduct peacefully.

I'm sorry if anything I've written has given you offence, but I assure you I tried to be constructive throughout the discussion.

DPB


no offence so far, it's just that the non proper and misleading use of the term exocet creates confusion.

use another word for your "start pattern" and you'll see clouds vanishing.

It's not a conflict between computers and human solvers, it's more simply a use of a word with a precise 'logic" content with another content, putting fog in the landscape.

BTW I had a look on the last puzzles I just posted, and I see (as non efficient manual solver) interesting points.

champagne
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Re: bi bi pattern in hardest puzzles

Postby ronk » Fri Apr 13, 2012 11:17 pm

champagne wrote:I now see several puzzles having a property similar to that one
Code: Select all
....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

Can't see the 2nd one. Would you please provide the strong inference sets (truths) for it?

champagne wrote:
Code: Select all
.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

Similar problem here, I only see the normal double exocet (the 1st and 3rd in your list).
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Re: bi bi pattern in hardest puzzles

Postby JC Van Hay » Sat Apr 14, 2012 5:36 am

ronk wrote:
champagne wrote:I now see several puzzles having a property similar to that one
Code: Select all
....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

Can't see the 2nd one. Would you please provide the strong inference sets (truths) for it?

champagne wrote:
Code: Select all
.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

Similar problem here, I only see the normal double exocet (the 1st and 3rd in your list).

Code: Select all
First puzzle

000056080050700003008000000200000900040500007000092060304000001500100400010000070

+------------------------+---------------------------+------------------------+
| 1479   37(29)   12379  | 34(29)    5        6      | 127    8       4(29)   |
| 1469   5        1269   | 7         1248     1489   | 126    1249    3       |
| 14679  37(269)  8      | 34(29)    1234     1349   | 12567  12459   45(269) |
+------------------------+---------------------------+------------------------+
| 2      37(68)   13567  | 34(68)    134678   13478  | 9      1345    45(8)   |
| 1689   4        1369   | 5         1368     138    | 1238   123     7       |
| 178    37(8)    1357   | 34(8)     9        2      | 1358   6       45(8)   |
+------------------------+---------------------------+------------------------+
| 3      7(2689)  4      | (29-68)   2678     5789   | 2568   259     1       |
| 5      7(2689)  7(269) | 1         37(268)  37(89) | 4      -3(29)  (2689)  |
| (689)  1        (269)  | 34(2689)  23468    34589  | 23568  7       5(2689) |
+------------------------+---------------------------+------------------------+

Exocet : base AALS(2689)r9c13, {2689R8 2689C2 2689C4 2689C9 9N13} => -68r7c4, -3r8c8

   On 2 or 6 or 8 or 9 :

   r9c13-r9c49.r78c13=*[SSF(C149)(r8c9=*r7c4)-r8c56=*r8c89]
      
   => r8c9=[r7c4 and r8c8]

   Conclusion : -68r7c4, -3r8c8


Second puzzle

023000009400000100090030040200810004000007800900040002300090001060000000000500000

+---------------------------+---------------------------+-------------------------+
| 1(5678)   2      3        | 1467    (5678)    14568   | (567)   (5678)  9       |
| 4         578    5678     | 2679    -2(5678)  25689   | 1       235678  3(5678) |
| -1(5678)  9      -1(5678) | 12(67)  3         12(568) | 2(567)  4       (5678)  |
+---------------------------+---------------------------+-------------------------+
| 2         357    567      | 8       1         3569    | 35679   35679   4       |
| 1(56)     1345   1456     | 2369    2(56)     7       | 8       13569   3(56)   |
| 9         13578  15678    | 36      4         356     | 3567    13567   2       |
+---------------------------+---------------------------+-------------------------+
| 3         4578   24578    | 2467    9         2468    | 24567   25678   1       |
| 1(578)    6      1245789  | 12347   2(78)     12348   | 234579  235789  3(578)  |
| 1(78)     1478   124789   | 5       2(678)    123468  | 234679  236789  3(678)  |
+---------------------------+---------------------------+-------------------------+

First 2 exocets : base AALS(5678)r1c78, {5678R3 5678C1 5678C5 5678C9 1N78} => -1r3c13, -2r2c5

   On 5 or 6 or 7 or 8 :

   r1c78-r1c15.r23c79=*[SSF(C159)(r3c1=*r2c5)-r3c46=*r3c15]
      
   => r3c1=[r2c5 and r3c3]

   Conclusion : -1r3c13, -2r2c5

+-------------------------+--------------------------+--------------------------+
| 1(5678)  2      3       | 1467    (567-8)  14568   | 567      5678    9       |
| 4        (578)  (5678)  | 2679    2(5678)  25689   | 1        235678  3(5678) |
| 1(5678)  9      1(5678) | 12(67)  3        12(568) | -2(567)  4       (5678)  |
+-------------------------+--------------------------+--------------------------+
| 2        357    567     | 8       1        3569    | 35679    35679   4       |
| 1(56)    1345   1456    | 2369    2(56)    7       | 8        13569   3(56)   |
| 9        13578  15678   | 36      4        356     | 3567     13567   2       |
+-------------------------+--------------------------+--------------------------+
| 3        4578   24578   | 2467    9        2468    | 24567    25678   1       |
| 1(578)   6      1245789 | 12347   2(78)    12348   | 234579   235789  3(578)  |
| 1(78)    1478   124789  | 5       2(678)   123468  | 234679   236789  3(678)  |
+-------------------------+--------------------------+--------------------------+

Second 2 exocets : base AALS(5678)r2c23, {5678R3 5678C1 5678C5 5678C9 2N23} => -8r1c5, -2r3c7

   On 5 or 6 or 7 or 8 :

   r2c23-r1c1.r3c13=*[SSF(C159)(r3c9=*r1c5)-r3c46=*r3c79]
      
   => r3c9=[r1c5 and r3c7]

   Conclusion : -2r3c7, -8r1c5


Note : After that : LC and LS to the end !
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Re: bi bi pattern in hardest puzzles

Postby daj95376 » Sat Apr 14, 2012 7:59 am

[Withdrawn: there is an explanation where the non-JExocet cell's value is forced.]
Last edited by daj95376 on Tue Apr 17, 2012 3:49 pm, edited 1 time in total.
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Re: bi bi pattern in hardest puzzles

Postby ronk » Sat Apr 14, 2012 4:04 pm

David P Bird wrote: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.

People say a picture is worth a thousand words so, by your definition, is the following a "JExocet?" Note that digit 3 appears in only one "cross-line", as you term it, of bands 2 and 3. [edit: Note David P Bird's "cross-lines" might actually be the vertical strong sets, rather than the horizontal weak sets. See diagram here.]

Image

I tried to clear this up earlier when ...
here I quoted and 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.

Since neither champagne nor you corrected me, I assumed my understanding was correct. If you say the above is a "JExocet", then my understanding is incorrect, suggesting your wording of "condition 3" could be improved further.
Last edited by ronk on Tue Apr 17, 2012 9:04 pm, edited 1 time in total.
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Re: bi bi pattern in hardest puzzles

Postby David P Bird » Sat Apr 14, 2012 5:44 pm

ronk wrote:If you say the above is a "JExocet", then my understanding is incorrect, suggesting your wording of "condition 3" could be improved even further.

Your diagram would satisfy the three conditions I gave with or without the (3)r8c7 you show. The elimination of non-members from the target cells doesn't depend on anything further.
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Re: bi bi pattern in hardest puzzles

Postby ronk » Sat Apr 14, 2012 6:18 pm

David P Bird wrote:
ronk wrote:If you say the above is a "JExocet", then my understanding is incorrect, suggesting your wording of "condition 3" could be improved even further.
Your diagram would satisfy the three conditions I gave with or without the (3)r8c7 you show. The elimination of non-members from the target cells doesn't depend on anything further.

So are you going to rephrase "condition 3" so that others won't mis-interpret the word "restricted" like I did, and maybe champagne did too?

BTW since 3r8c7 is neither a member of a Truth or Link in my diagram, it's really not part of the diagram.
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Re: bi bi pattern in hardest puzzles

Postby David P Bird » Sun Apr 15, 2012 1:11 am

ronk wrote:So are you going to rephrase "condition 3" so that others won't mis-interpret the word "restricted" like I did, and maybe champagne did too?

OK that condition has got a loophole but it's not corrected by insisting on a particular interpretation of what "restricted" means which is what misdirected me. This is a rewrite:

3) Outside the JExocet band no member digit should be capable of simultaneously occupying more than two of the cross-line cells
This is satisfied when the all openings for a digit in these external cells can be covered by no more than two lines.

Code: Select all
Examples
 . . \ | \ . . | \ . .      . . O | \ . . | O . .     . . \ | \ . . | O . .   
 . . O | O . . | O . .      . . O | \ . . | O . .     . . O | O . . | O . .   
 . . \ | \ . . | \ . .      . . O | \ . . | O . .     . . \ | \ . . | O . .   
 . . \ | \ . . | \ . .      . . O | \ . . | O . .     . . \ | \ . . | O . .   
 . . O | O . . | O . .      . . O | \ . . | O . .     . . \ | \ . . | O . .   
 . . \ | \ . . | \ . .      . . O | \ . . | O . .     . . \ | \ . . | O . .
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Re: bi bi pattern in hardest puzzles

Postby daj95376 » Sun Apr 15, 2012 5:49 am

Do we have an example of a single Exocet, restricted to a chute, that's not a JExocet?

Code: Select all
 JExocet example pattern for member digit X
 +-----------------------------------+
 |  B  B  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  T  .  .  |  /  .  .  |     base and target cells in band 1
 |  .  .  .  |  /  .  .  |  T  .  .  |
 |-----------+-----------+-----------|
 |  .  .  X  |  X  .  .  |  X  .  .  | <-   cross lines in two bands
 |  .  .  /  |  /  .  .  |  /  .  .  |
 |  .  .  /  |  /  .  .  |  /  .  .  |
 |-----------+-----------+-----------|
 |  .  .  X  |  X  .  .  |  X  .  .  | <-   cross lines in two bands
 |  .  .  /  |  /  .  .  |  /  .  .  |
 |  .  .  /  |  /  .  .  |  /  .  .  |
 +-----------------------------------+
          ^     ^           ^               restricting columns

Code: Select all
 JExocet example pattern for member digit Y
 +-----------------------------------+
 |  B  B  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  T  .  .  |  /  .  .  |      base and target cells in band 1
 |  .  .  .  |  /  .  .  |  T  .  .  |
 |-----------+-----------+-----------|
 |  .  .  /  |  /  .  .  |  /  .  .  |
 |  .  .  Y  |  Y  .  .  |  Y  .  .  | <-   cross lines in one band
 |  .  .  Y  |  Y  .  .  |  Y  .  .  | <-   cross lines in one band
 |-----------+-----------+-----------|
 |  .  .  /  |  /  .  .  |  /  .  .  |
 |  .  .  /  |  /  .  .  |  /  .  .  |
 |  .  .  /  |  /  .  .  |  /  .  .  |
 +-----------------------------------+
          ^     ^           ^               restricting columns

Note: Although my examples shows all six (possible) cells populated in the intersection of the cross lines and the restricting columns, I know of real puzzles where five populated cells are acceptable.
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Re: bi bi pattern in hardest puzzles

Postby David P Bird » Sun Apr 15, 2012 9:02 am

In a JExocet the target cells will hold the same two digits that are true in the base cells.
Provided this is remembered, no great logic is needed to derive the eliminations in this puzzle discussed above.
Code: Select all
....56.8..5.7....3..8......2.....9...4.5....7....92.6.3.4.....15..1..4...1.....7.
 *----------------------*----------------------*----------------------*
 | 1479   2379   12379  | 2349   5      6      | 127    8      249    | 29
 | 1469   5      1269   | 7      1248   1489   | 126    1249   3      | -
 | 14679  23679  8      | 2349   1234   1349   | 12567  12459  24569  | 269
 *----------------------*----------------------*----------------------*
 | 2      368    1356   | 3468   134678 13478  | 9      1345   458    | 68
 | 1689   4      1369   | 5      1368   138    | 1238   123    7      | -
 | 178    378    1357   | 348    9      2      | 1358   6      458    | 78
 *----------------------*----------------------*----------------------*
 | 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  |
 *----------------------*----------------------*----------------------*
          ^               ^                                    ^

(2689)JExocet:r9c13,r7c4,r8c9
Here, as usual, the two true base digits will occur together in 3 mini-lines in tier 3: r9b7, r7b8, & r8b9.
1) As r8c7 can't hold a member candidate, r8c89 must hold two of them allowing (3)r8c8 to be deleted
2) As in r8b9 (6) or (8) can only be true in r8c9, neither can be true in r7c4 which must hold the other true base digit.
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Re: bi bi pattern in hardest puzzles

Postby ronk » Sun Apr 15, 2012 11:21 am

daj95376 wrote: Do we have an example of a single Exocet, restricted to a chute, that's not a JExocet?
Code: Select all
 JExocet example pattern for member digit X
 +-----------------------------------+
 |  B  B  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  T  .  .  |  /  .  .  |     base and target cells in band 1
 |  .  .  .  |  /  .  .  |  T  .  .  |
 |-----------+-----------+-----------|
 |  .  .  X  |  X  .  .  |  X  .  .  | <-   cross lines in two bands
 |  .  .  /  |  /  .  .  |  /  .  .  |
 |  .  .  /  |  /  .  .  |  /  .  .  |
 |-----------+-----------+-----------|
 |  .  .  X  |  X  .  .  |  X  .  .  | <-   cross lines in two bands
 |  .  .  /  |  /  .  .  |  /  .  .  |
 |  .  .  /  |  /  .  .  |  /  .  .  |
 +-----------------------------------+
          ^     ^           ^               restricting columns

Note: Although my examples shows all six (possible) cells populated in the intersection of the cross lines and the restricting columns, I know of real puzzles where five populated cells are acceptable.

As of now, every known "Exocet" is also a "JExocet" except for one out of 11454, one where the base cells share a band with one target cell and a stack with the other.

As to "populated cells", there can be as few as zero when counting only those pattern members required for a deduction (see digit 9 here). I think David P Bird would count them differently.

In the limit, there can be as few as zero populated cells for as many as 3 digits of a 4-digit pattern, in which case the pattern has been reduced to a 3-digit exocet.
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Re: bi bi pattern in hardest puzzles

Postby ronk » Sun Apr 15, 2012 1:43 pm

David P Bird wrote:3) Outside the JExocet band no member digit should be capable of simultaneously occupying more than two of the cross-line cells
This is satisfied when the all openings for a digit in these external cells can be covered by no more than two lines.

Code: Select all
Examples
 . . \ | \ . . | \ . .      . . O | \ . . | O . .     . . \ | \ . . | O . .   
 . . O | O . . | O . .      . . O | \ . . | O . .     . . O | O . . | O . .   
 . . \ | \ . . | \ . .      . . O | \ . . | O . .     . . \ | \ . . | O . .   
 . . \ | \ . . | \ . .      . . O | \ . . | O . .     . . \ | \ . . | O . .   
 . . O | O . . | O . .      . . O | \ . . | O . .     . . \ | \ . . | O . .   
 . . \ | \ . . | \ . .      . . O | \ . . | O . .     . . \ | \ . . | O . .

I know what you're trying to say, but I find those diagrams confusing. If you're going to show only six in the left, why show more than [edit: two] in the others?

Code: Select all
Examples
 . . \ | \ . . | \ . .      . . . | \ . . | . . .     . . \ | \ . . | . . .   
 . . O | O . . | O . .      . . . | \ . . | . . .     . . O | O . . | . . .   
 . . \ | \ . . | \ . .      . . . | \ . . | . . .     . . \ | \ . . | . . .   
 . . \ | \ . . | \ . .      . . . | \ . . | . . .     . . \ | \ . . | . . .   
 . . O | O . . | O . .      . . . | \ . . | . . .     . . \ | \ . . | . . .   
 . . \ | \ . . | \ . .      . . . | \ . . | . . .     . . \ | \ . . | . . .

In the world of cover set logic if, for any exocet pattern digit, there exists 1) a column void of candidates (as in the 2nd diagram above), or 2) less than two rows with less than two candidates (in the three columns as in the 3rd diagram), those candidates becomes irrelevent to the logic set. Either 1) or 2) occurs in 41 of the 42 puzzles listed here.

[edit: rewrite of the paragraph above]
For any "JExocet" pattern digit, if there exists ...
  1. a column void of candidates (as in the 2nd diagram above), or
  2. two columns with candidates in one row only (as in the 3rd diagram above)
... candidates in the remaining columns become "don't care." One of the two cases occurs in 41 of the 42 puzzles listed here.

The short of it is that you and I look at patterns differently, and so it's easy for us to misinterpret each other's results, especially when there are vocabulary differneces too.

David P Bird wrote:(2689)JExocet:r9c13,r7c4,r8c9
Here, as usual, the two true base digits will occur together in 3 mini-lines in tier 3: r9b7, r7b8, & r8b9.
1) As r8c7 can't hold a member candidate, r8c89 must hold two of them allowing (3)r8c8 to be deleted
2) As in r8b9 (6) or (8) can only be true in r8c9, neither can be true in r7c4 which must hold the other true base digit.

Does that mean you don't consider base r9c13 and target r8c89 to be an "Exocet" either? As you might guess from my post here, I don't.
Last edited by ronk on Sun Apr 15, 2012 9:22 pm, edited 1 time in total.
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Re: bi bi pattern in hardest puzzles

Postby tarek » Sun Apr 15, 2012 3:42 pm

ronk wrote:As of now, every known "Exocet" is also a "JExocet" except for one out of 11454, one where the base cells share a band with one target cell and a stack .

I'm following your discussion when I have time, I must confess to using extended fish logic to understand the chain of thoughts here. Your base/cover discussions remind me of our discussions in the ultimate fish guide. I'm sure your generalised fish definitions could allow Autocannibalism when target eliminations are in more covers than bases.
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Re: bi bi pattern in hardest puzzles

Postby daj95376 » Sun Apr 15, 2012 4:26 pm

ronk wrote:As of now, every known "Exocet" is also a "JExocet" except for one out of 11454, one where the base cells share a band with one target cell and a stack with the other.

As to "populated cells", there can be as few as zero when counting only those pattern members required for a deduction (see digit 9 here). I think David P Bird would count them differently.

In the limit, there can be as few as zero populated cells for as many as 3 digits of a 4-digit pattern, in which case the pattern has been reduced to a 3-digit exocet.

Yes, puzzle "1952" is the known exception to an Exocet in a single chute. However, puzzle "14808" is a Double Exocet instead of a single Exocet. I'll keep an eye out for a single Exocet in a single chute where there are fewer than five occupied cells in the cross lines intersected with the restricting lines. Thanks for the info!
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