exocet pattern in hardest puzzles

Advanced methods and approaches for solving Sudoku puzzles

Re: bi bi pattern in hardest puzzles

Postby daj95376 » Wed May 09, 2012 4:29 pm

ronk wrote:I'm not aware of "target cells in a single mini-unit", other than (sometimes) the dependent target cells of an exocet double. If that's not what you're referring to, please post an example or two.

How about one puzzle with two examples in it. A two-fer!!!

Code: Select all
1.34............36.8..2.4............7..4.5.....6.1..8..2.9...4.9.....5.8....79..

;3049;elev;1436;2;4

;r8c1 r8c3 r7c7 r7c8   target cells in [r7] intersecting [b9]
;r9c8 r9c9 r8c4 r8c5   target cells in [r8] intersecting [b8]

   c4b8  Locked Candidate 1              <> 2    r45c4

 +--------------------------------------------------------------------------------+
 |  1       256     3       |  4       5678    5689    |  278     2789    2579    |
 |  24579   245     4579    |  15789   1578    589     |  1278    3       6       |
 |  5679    8       5679    |  13579   2       3569    |  4       179     1579    |
 |--------------------------+--------------------------+--------------------------|
 |  234569  123456  145689  |  35789   3578    23589   |  12367   124679  12379   |
 |  2369    7       1689    |  389     4       2389    |  5       1269    1239    |
 |  23459   2345    459     |  6       357     1       |  237     2479    8       |
 |--------------------------+--------------------------+--------------------------|
 |  3567    1356    2       |  1358    9       3568    |  13678   1678    4       |
 |  367     9       167     |  1238    1368    4       |  123678  5       1237    |
 |  8       13456   1456    |  1235    1356    7       |  9       126     123     |
 +--------------------------------------------------------------------------------+
 # 181 eliminations remain
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Re: bi bi pattern in hardest puzzles

Postby ronk » Thu May 10, 2012 2:00 pm

daj95376 wrote:How about one puzzle with two examples in it. A two-fer!!!

1.34............36.8..2.4............7..4.5.....6.1..8..2.9...4.9.....5.8....79..

;3049;elev;1436;2;4

;r8c1 r8c3 r7c7 r7c8 target cells in [r7] intersecting [b9]

Thanks. For 24000+ exocets we've had swordfish, including degenerate versions thereof, with defining line-sets (aka truths, base sets, strong inference sets) in lines perpendicular to the lines containing the base cells. Now we apparently have a few jellyfish with defining line-sets parallel to the line through the base cells. I know they meet champagne's definition of an exocet, but the logic may be very different than for the 24000+.

____Image
Code: Select all
     15 Truths = {1R3579 3R3579 6R3579 7R7 8N13}
     21 Links = {1c3489 3c1469 6c1368 7n78 1367b7 136b8}

daj95376, in an earlier post you wrote "mini-units" instead of "mini-lines." Does that mean you are aware of some with target cells in a box, but not in a [single] row or column?
Last edited by ronk on Thu May 10, 2012 4:30 pm, edited 1 time in total.
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Re: bi bi pattern in hardest puzzles

Postby daj95376 » Fri May 11, 2012 1:00 am

ronk wrote:daj95376, in an earlier post you wrote "mini-units" instead of "mini-lines." Does that mean you are aware of some with target cells in a box, but not in a [single] row or column?

I use mini-unit for the 3-cell intersection of a line and a box. According to Sudopedia, there's mini-col as an alternative to boxcol, and there's mini-row as an alternative to boxrow, but the use of box-line and line-box seem to be associated with Locked Candidates. I don't know where I first saw mini-unit used, but I just started repeating it because I've always favored the use of unit over house to generalize box/column/row.

As for the puzzle under discussion, I find it interesting that XSUDO found the same eliminations that my template solver found after resolving 1422 combinations of templates. Logic that I wouldn't recommend for the manual solver.

Hidden Text: Show
Code: Select all
1.34............36.8..2.4............7..4.5.....6.1..8..2.9...4.9.....5.8....79..

_        Hidden Single                   =  4    r8c6

   c4b8  Locked Candidate 1              <> 2    r45c4

 +--------------------------------------------------------------------------------+
 |  1       256     3       |  4       5678    5689    |  278     2789    2579    |
 |  24579   245     4579    |  15789   1578    589     |  1278    3       6       |
 |  5679    8       5679    |  13579   2       3569    |  4       179     1579    |
 |--------------------------+--------------------------+--------------------------|
 |  234569  123456  145689  |  35789   3578    23589   |  12367   124679  12379   |
 |  2369    7       1689    |  389     4       2389    |  5       1269    1239    |
 |  23459   2345    459     |  6       357     1       |  237     2479    8       |
 |--------------------------+--------------------------+--------------------------|
 |  3567    1356    2       |  1358    9       3568    |  13678   1678    4       |
 |  367     9       167     |  1238    1368    4       |  123678  5       1237    |
 |  8       13456   1456    |  1235    1356    7       |  9       126     123     |
 +--------------------------------------------------------------------------------+
 # 181 eliminations remain

 Templates: 49 54 60 8 108 33 52 25 60

 for '1' = { r1c1,r2c4,r3c9,r4c3,r5c8,r6c6,r7c7,r8c5,r9c2 }, non-productive
 for '1' = { r1c1,r2c5,r3c8,r4c7,r5c3,r6c6,r7c2,r8c4,r9c9 }, non-productive
 for '1' = { r1c1,r2c5,r3c9,r4c7,r5c3,r6c6,r7c8,r8c4,r9c2 }, non-productive
 for '3' = { r1c3,r2c8,r3c6,r4c5,r5c1,r6c7,r7c2,r8c9,r9c4 }, non-productive
 for '3' = { r1c3,r2c8,r3c6,r4c7,r5c1,r6c5,r7c2,r8c9,r9c4 }, non-productive
 for '7' = { r1c8,r2c1,r3c4,r4c9,r5c2,r6c5,r7c7,r8c3,r9c6 }, non-productive
 for '7' = { r1c8,r2c3,r3c4,r4c9,r5c2,r6c5,r7c1,r8c7,r9c6 }, non-productive
 for '7' = { r1c9,r2c1,r3c4,r4c5,r5c2,r6c8,r7c7,r8c3,r9c6 }, non-productive
 for '7' = { r1c9,r2c1,r3c4,r4c8,r5c2,r6c5,r7c7,r8c3,r9c6 }, non-productive
 for '7' = { r1c9,r2c3,r3c4,r4c5,r5c2,r6c8,r7c1,r8c7,r9c6 }, non-productive
 for '7' = { r1c9,r2c3,r3c4,r4c8,r5c2,r6c5,r7c1,r8c7,r9c6 }, non-productive
 for '7' = { r1c9,r2c3,r3c4,r4c8,r5c2,r6c5,r7c7,r8c1,r9c6 }, non-productive
 for '7' = { r1c9,r2c4,r3c1,r4c8,r5c2,r6c5,r7c7,r8c3,r9c6 }, non-productive
 for '9' = { r1c9,r2c1,r3c4,r4c3,r5c6,r6c8,r7c5,r8c2,r9c7 }, non-productive
 for '9' = { r1c9,r2c1,r3c6,r4c4,r5c3,r6c8,r7c5,r8c2,r9c7 }, non-productive

 Templates: 46 54 58 8 108 33 44 25 58


 <1236>   accepted = 2620 combinations
 <1236>   <>3  r8c4
 <1236>   <>8  r8c45

 r8c45,r9c89   locked for candidates


 <1268>   accepted = 2962 combinations
 <1268>   <>3  r8c5

 r8c5,r9c8   locked for candidates


 <1367>   accepted = 1422 combinations
 <1367>   <>8  r7c78

 r7c78,r8c13   locked for candidates
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Re: bi bi pattern in hardest puzzles

Postby daj95376 » Wed May 16, 2012 5:23 am

A JExocet?

Code: Select all
12..5.7....7.8..6....7....12......3...58..6...3..6...4..25..1......9....9....4.5.

 +--------------------------------------------------------------------------------+
 |  1       2       34689   | T3469    5       369     |  7       489     389     |
 | B345    B459     7       |  12349   8       1239    |  23459   6       2359    |
 |  34568   45689   34689   |  7       234     2369    | T234589 S2489    1       |
 |--------------------------+--------------------------+--------------------------|
 |  2       146789  14689   |  149     147     1579    | *589     3       5789    |
 |  47      1479    5       |  8       12347   12379   |  6       1279    279     |
 |  78      3       189     |  129     6       12579   | *2589    12789   4       |
 |--------------------------+--------------------------+--------------------------|
 |  34678   4678    2       |  5       37      3678    |  1       4789    36789   |
 |  345678  145678  13468   |  1236    9       123678  |  2348    2478    23678   |
 |  9       1678    1368    |  1236    1237    4       |  238     5       23678   |
 +--------------------------------------------------------------------------------+
 # 178 eliminations remain

 ### -3459- JExocet   Base = r2c12   Target = r1c4==r3c8,r3c7

Technically, there are two rows, [r46], that contain the candidate <5> in [c347] outside [band 1], but all of the cells are in [c7].
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Re: bi bi pattern in hardest puzzles

Postby David P Bird » Wed May 16, 2012 7:42 am

daj wrote:Technically, there are two rows, [r46], that contain the candidate <5> in [c347] outside [band 1], but all of the cells are in [c7].

An interesting case but the givens (5)r4c3 and (5)r7c4 must be included in the appraisal of condition 3, so it isn't a JExocet.

However it can be considered to be an Almost JExocet which would be made if (5)r3c9 were true. In that case if (5) is true in one of the base cells, it must also be true in the r3c7 target cell.

Developing this further, depending on where (5) is true in r24c9 there are two alternative forms of the JExocet pattern both of which will exclude the common non-members from the target cells:

(3459)JExocet:r2c12:r1c4,r3c7 = (5)r46c7 - (5)r4c9 = (5)r2c9 – (5)r2c12 = (349)JExocet:r2c12:r1c4,r3c7 => r1c4 <> 6, r3c7 <> 28
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Re: bi bi pattern in hardest puzzles

Postby ronk » Wed May 16, 2012 12:51 pm

David P Bird wrote:An interesting case but the givens (5)r4c3 and (5)r7c4 must be included in the appraisal of condition 3, so it isn't a JExocet.
...
(3459)JExocet:r2c12:r1c4,r3c7 = (5)r46c7 - (5)r4c9 = (5)r2c9 – (5)r2c12 = (349)JExocet:r2c12:r1c4,r3c7 => r1c4 <> 6, r3c7 <> 28

It isn't ... and then it is?

[edit: clarify the contradiction somewhat]
Last edited by ronk on Wed May 16, 2012 2:54 pm, edited 1 time in total.
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Re: bi bi pattern in hardest puzzles

Postby David P Bird » Wed May 16, 2012 2:24 pm

ronk wrote:
David P Bird wrote:An interesting case but the givens (5)r4c3 and (5)r7c4 must be included in the appraisal of condition 3, so it isn't a JExocet.
...
(3459)JExocet:r2c12:r1c4,r3c7 = (5)r46c7 - (5)r4c9 = (5)r2c9 – (5)r2c12 = (349)JExocet:r2c12:r1c4,r3c7 => r1c4 <> 6, r3c7 <> 28

It isn't ... and then it is?

If that notation doesn't satisfy you then suggest one that does.

When you do, consider how the inference between a fish and its fin is notated. An established JExocet pattern is a Boolean node just like an established fish or an established locked set.
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Re: bi bi pattern in hardest puzzles

Postby ronk » Wed May 16, 2012 2:47 pm

David P Bird wrote:consider how the inference between a fish and its fin is notated. An established JExocet pattern is a Boolean node just like an established fish or an established locked set.

I understand that, and have no problem with the AIC, but rather the contradiction between "why" it isn't ... and then "why" it is. In the former it's the clues; in the latter it's the "fins."
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Re: bi bi pattern in hardest puzzles

Postby daj95376 » Thu May 17, 2012 12:02 am

David P Bird wrote:An interesting case but the givens (5)r5c3 and (5)r7c4 must be included in the appraisal of condition 3, so it isn't a JExocet.

paraphrase DPB wrote:Here is a re-write of the revised JExocet pattern specifications:

Code: Select all
    *-------*-------*-------*
    | B B . | . . . | . . . |  B = Base Cells
    | . . . | Q . . | R . . |   
    | . . . | Q . . | R . . |  Q = 1st Target Pair
    *-------*-------*-------*  R = 2nd Target 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 . . |   
    *-------*-------*-------*

Conditions:

1) The base cells are restricted to a total of three or four candidate values (the base set).

2) Target pairs must have one cell that contains at least one candidate value from the base set (the target cell), and the other cell doesn't contain any candidate values from the base set (the empty companion cell).

3) Outside the JExocet band, no base set value can simultaneously occupy more than two of the cross-line cells.

I don't think anyone believes that the grid fails to meet JExocet conditions (1&2). That leave a disagreement over it meeting JExocet condition (3) for value <5>. As DPB mentioned, the givens r5c3=5 and r7c4=5 occupy two cross-line cells. That leaves dealing with r46c7 containing the candidate <5>. Using the following chain:

Code: Select all
(5)r2c12 - (5)r3c12 = (5)r3c7 - (5)r46c7

I now deduce that cross-line cells r46c7 can not contain the value <5> when <5> is true in the base cells. It seems to me that I've shown that the grid qualifies as a JExocet.

Personally, I think condition (3) is at best vague!
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Re: bi bi pattern in hardest puzzles

Postby David P Bird » Thu May 17, 2012 7:56 am

daj wrote:Personally, I think condition (3) is at best vague!

You neglected to include the rest of the clarification of condition 3 that I gave:
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
                                v           v                         v   
 . . \ | \ . . | \ . .      . . 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 . .
2 Parallel lines (I)        2 Parallel Lines (II)     2 Orthogonal Lines

Our differences stem from our different interpretations of what a "pattern" is. AFAIAC a pattern consists of a defined number of recognisable elements which can be identified (in various configurations) without using anything more complex than counting.

If that is accepted, then an Almost pattern is one that may be established as a result of a logical chain being followed, which is what happens here.

There is a telling distinction between the two IMO. The eliminations from an existing pattern are justified just by identifying the pattern whereas those for an Almost pattern need the logic that establishes it to be notated as well.

Consider now that a chain or net that is used to establish the pattern can be of indefinite length and complexity, so that taken together the extended "pattern" is uncontained and can consist of any number of component elements.

This is the interpretation that champagne uses which is defined <here>.

It's up to you to decide what the term pattern covers and the boundary line that is crossed when it ceases to be a pattern and becomes something else. You can also choose to follow the precedents set by previously accepted patterns (as I consider I have done) or not. Depending on your decision you can then revise your various definitions accordingly.

If you choose to publish them then from my experience don't expect any thanks for your efforts or for the criticisms that you'll inevitably get to be constructive.
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Re: bi bi pattern in hardest puzzles

Postby daj95376 » Thu May 17, 2012 6:28 pm

David P Bird wrote: AFAIAC a pattern consists of a defined number of recognisable elements which can be identified (in various configurations) without using anything more complex than counting.

Acknowledged. I was willing to include short X-Chains that can be detected within the JExocet chute:

Code: Select all
(5)r2c12 - (5)r3c12 = (5)r3c7

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.

Maybe you should change the text in blue to ... all occurrences.
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Re: bi bi pattern in hardest puzzles

Postby David P Bird » Fri May 18, 2012 7:47 am

daj95376 wrote:
David P Bird wrote: AFAIAC a pattern consists of a defined number of recognisable elements which can be identified (in various configurations) without using anything more complex than counting.

Acknowledged. I was willing to include short X-Chains that can be detected within the JExocet chute:

Good.

Now I guess the one-band Exocets that don't contain the JExocet pattern at the outset should all resolve to Almost JExocets in some form or another, and the one you found will probably be the simplest of them all.

It would be interesting to see how many of those you identified only need an un-branched chain to make the eliminations. (Another open question is how many JExocets are Almost Double JExocets.)

daj95376 wrote:
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.
Maybe you should change the text in blue to ... all occurrences.

Thank you, yes that’s an improvement, and I've edited the <defining post>.
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Re: bi bi pattern in hardest puzzles

Postby daj95376 » Fri May 18, 2012 9:03 am

David P Bird wrote:Now I guess the one-band Exocets that don't contain the JExocet pattern at the outset should all resolve to Almost JExocets in some form or another, and the one you found will probably be the simplest of them all.

It would be interesting to see how many of those you identified only need an un-branched chain to make the eliminations.

I'm not sure of your point, but maybe this will be of some help.

Of the 24,411 Exocet puzzles in champagne's file "03 E ...", I can resolve 24,057of them if I disable the short X-Chain logic for the chute. However, if I enable the short X-Chain logic for the chute, then I'm able to resolve an additional 287 puzzles.

[Addendum:]

Of the 287 additional puzzles, 158 contain double Exocets.
Last edited by daj95376 on Fri May 18, 2012 11:56 pm, edited 1 time in total.
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Re: bi bi pattern in hardest puzzles

Postby ronk » Fri May 18, 2012 11:31 am

daj95376 wrote:
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.

Maybe you should change the text in blue to ... all occurrences.

While answers to the following may be deduced by reading elsewhere, they are not answered by reading the defining post.

I'd like to see clarification of whether "openings" or "occurrences" applies to candidates only, or candidates, givens, and placements. And where is "cross-line" defined? Is this a column containing a strong-inference-set or a row with a weak-inference set? If the former, what is the "cross-line" crossing?

"JExocet band" doesn't appear to be defined there either.
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Re: bi bi pattern in hardest puzzles

Postby daj95376 » Fri May 18, 2012 5:46 pm

FWIW: Anomalies

There is an inconsistency in the puzzles across Champagne's files in folder Hard_11.

Here is the puzzle with sequence number 226 in file "02 index.txt".

Code: Select all
98.7..6..5..9..7......84...6..5..9......7..3.....2...61......97.65...1.....1.....;226

Here is the puzzle with sequence number 226 in file "03 E Exocet seen.txt".

Code: Select all
1......8...71....6.9.....5...56....7..17.4..5......34.57.2.............2..2.61...;226
;elev;91;3;4;r7c5 r7c6 r8c1 r8c3;r7c5 r7c6 r8c3 r9c9;r9c1 r9c2 r7c9 r8c4;;;

Unfortunately, not all puzzles in the 03E-file are in row MinLex format.

Normally, it wouldn't matter if the two files matched ... provided ... all of the Exocet puzzles in the 02-file were present in the 03E-file. However, there are 7,393 more puzzles in the 02-file than the 03E-file ... and ... there are at least 1,273 Exocet puzzles among them.

While normalizing all puzzles in both files to row MinLex format, I lost access to the sequence numbers and Exocet information. From now on, I'll only be presenting bare puzzles in row MinLex format. :(



===== ===== ===== ===== ===== ===== ===== =====


BTW: Here's my latest notes paraphrasing DBP's "conditions".

1) The base cells are restricted to a total of three or four candidate values (the base set).

2) Target pairs must have one cell that contains at least one candidate value from the base set (the target cell), and the other cell doesn't contain any candidate values from the base set (the companion cell).

3) Outside the chute containing the JExocet cells (B+Q+R), no base set value can simultaneously occupy more than two of the cross-line cells.

This is satisfied when all occurrences -- candidates, givens, and placements -- for a base set value in the cross-line cells can be covered by no more than two lines.
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