## exocet pattern in hardest puzzles

Advanced methods and approaches for solving Sudoku puzzles

### Re: bi bi pattern in hardest puzzles

ronk wrote:
daj95376 wrote:I believe David was looking for a productive example of this form of JExocet. I'm sorry if another example has already been posted.

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`Puzzle:   182;elev;L14;1;2;r8c3 r9c3 r1c2 r5c21....6.8....7....3....2.4....5.4....6....8.5....3..2....8..1.9..1......796.......`

I don't believe anyone has systematically filtered champagne's latest "03 E exocet seen.txt" file for this property, so there could be quite a few more.

I tested champagne's latest "03 E ..." file and found 166 JExocet patterns with target cells in the same line. Only four failed to produce a direct elimination.
daj95376
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### Re: bi bi pattern in hardest puzzles

daj95376 wrote:I tested champagne's latest "03 E ..." file and found 166 JExocet patterns with target cells in the same line. Only four failed to produce a direct elimination.

Thanks daj95376. Interpreting someone else's numbers is dangerous, but ...
earlier champagne wrote:2973 puzzles out of 5297 in the file of "nothing identified" have shown the searched pattern.

I think this means 2807 (=2973-166) exocets have less than a full complement of exocet digits in each of the target cells.
ronk
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### Re: bi bi pattern in hardest puzzles

ronk wrote:
daj95376 wrote:I tested champagne's latest "03 E ..." file and found 166 JExocet patterns with target cells in the same line. Only four failed to produce a direct elimination.

Thanks daj95376. Interpreting someone else's numbers is dangerous, but ...
champagne wrote:2973 puzzles out of 5297 in the file of "nothing identified" have shown the searched pattern.

I think this means 2807 (=2973-166) exocets have less than a full complement of exocet digits in each of the target cells.

I think we are talking apples and oranges. That's what I get for going back to an older message when the current topic is about number of base candidates in the target cells. Fortunately, my point is of little consequence.

With respect to the current topic, maybe someone should check the known (J)Exocet patterns and generate a distribution of the number of base candidates found in the target cells.
daj95376
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### Re: bi bi pattern in hardest puzzles

daj95376 wrote:
ronk wrote:I think this means 2807 (=2973-166) exocets have less than a full complement of exocet digits in each of the target cells.

I think we are talking apples and oranges. That's what I get for going back to an older message when the current topic is about number of base candidates in the target cells. Fortunately, my point is of little consequence.

AFAIK it wasn't the current topic. I was just using your number to guesstimate a number and reason for the additional exocets found after champagne "widened" his search.

daj95376 wrote:With respect to the current topic, maybe someone should check the known (J)Exocet patterns and generate a distribution of the number of base candidates found in the target cells.

Good idea, are you volunteering?
ronk
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### Re: bi bi pattern in hardest puzzles

ronk wrote:
daj95376 wrote:With respect to the current topic, maybe someone should check the known (J)Exocet patterns and generate a distribution of the number of base candidates found in the target cells.

Good idea, are you volunteering?

Individual cell counts:

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` *** number of puzzles  = 24,411   in file "03 E ..." *** number of JExocets = 29,321 ***   3   base values and   3   in target cell =       4   target cells ***   4   base values and   3   in target cell =   3,367   target cells ***   4   base values and   4   in target cell =  55,271   target cells`

Note: Tungsten Rod and Fata Morgana (probably) account for "4 target cells".

JExocets for pairwise cell counts:

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` ***  3 x 3  base values in target cells =      20   JExocets ***  3 x 4  base values in target cells =   1,711   JExocets ***  4 x 3  base values in target cells =   1,620   JExocets                                             -----                                             3,331   JExocets ***  4 x 4  base values in target cells =  25,970   JExocets`

Correlation between individual cell counts and JExocets for pairwise cell counts:

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` ***   4   base values and   4   in target cell =  55,271   target cells                 ( 2x * JExocet count )           -51,940   4 x 4  cells                                                   ------                                                    1,711   3 x 4  cells                                                    1,620   4 x 3  cells ***   4   base values and   3   in target cell =   3,367   target cells                 ( 1x * JExocet count )           - 1,711   3 x 4  cells                 ( 1x * JExocet count )           - 1,620   4 x 3  cells                                                   ------                                                       36   3 x 3  from 4-value                 ( 2x * JExocet count )                40   3 x 3  cells                                                  -    36   3 x 3  from 4-value                                                   ------ ***   3   base values and   3   in target cell =       4   target cells`

[Edit: completely replaced content of message.]
Last edited by daj95376 on Fri May 04, 2012 6:14 pm, edited 8 times in total.
daj95376
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### Re: bi bi pattern in hardest puzzles

daj95376 wrote:Assuming that my new JExocet solver is running properly, then here's the distribution for the number of base cell values found across the individual target cells. Note: only considered 3/4 possible candidate values in base cells.

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` *** number of puzzles  = 24,411   in file "03 E ..." *** number of JExocets = 29,321 ... *** distribution for   3   base candidates =   3,371   target cells *** distribution for   4   base candidates =  55,271   target cells                                               ------                                               58,642   target cells`

That was quick, thanks, but would you please rerun to get pairwise, I.e., 4x4, 4x3, 3x3, ... distributions?
ronk
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### Re: bi bi pattern in hardest puzzles

daj95376 wrote:
Code: Select all
` *** number of puzzles  = 24,411   in file "03 E ..." *** number of JExocets = 29,321 ***   3   base values and   3   in target cell =       4   target cells ***   4   base values and   3   in target cell =   3,367   target cells ***   4   base values and   4   in target cell =  55,271   target cells`

Note: Tungsten Rod and Fata Morgana are (probably) the two 3x3 entries.

[Edit: partitioned results ala ronk's request.]

Just a remark before I leave for sea activities

The criteria to enter the data base of potential hardest leaves outside nearly all exocets with a base of 3 digits.

The ratio would be very different with a lower cut off

champagne
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### Re: bi bi pattern in hardest puzzles

My JExocet program didn't accept this puzzle. The reason was because it counted three cross columns -- [c356] -- when testing the base cells for value=3. However, there aren't any intersecting cells in [r4], so the Exocet target cell in [r4] must be true. Does this scenario qualify as a JExocet ???

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`98.7..6..7......8...5.....767.9...4..3..2.......3.7...49.6....8....1.9........46.;25333;GP;KC40b;4;4;r2c7 r3c7 r4c9 r7c8     Exocet ... but is it a JExocet ???;r2c7 r3c7 r7c8 r8c8     r4c9==r8c8 secondary dependency, i.e., equivalent;r8c9 r9c9 r1c8 r4c7     Exocet ... but is it a JExocet ???;r8c9 r9c9 r1c8 r3c8     r4c7==r3c8 secondary dependency, i.e., equivalent +-----------------------------------------------------------------------------------------+ |  9        8        1234     |  7        345      12345    |  6        1235     12345    | |  7        1246     12346    |  1245     34569    1234569  |  1235     8        123459   | |  123      1246     5        |  1248     34689    1234689  |  123      1239     7        | |-----------------------------+-----------------------------+-----------------------------| |  6        7        128      |  9        58       158      |  12358    4        1235     | |  158      3        1489     |  1458     2        14568    |  1578     1579     1569     | |  1258     1245     12489    |  3        4568     7        |  1258     1259     12569    | |-----------------------------+-----------------------------+-----------------------------| |  4        9        1237     |  6        357      235      |  12357    12357    8        | |  2358     256      23678    |  2458     1        23458    |  9        2357     235      | |  12358    125      12378    |  258      35789    23589    |  4        6        1235     | +-----------------------------------------------------------------------------------------+ # 182 eliminations remain`
daj95376
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### Re: bi bi pattern in hardest puzzles

daj95376 wrote:My JExocet program didn't accept this puzzle. The reason was because it counted three cross columns -- [c356] -- when testing the base cells for value=3. However, there aren't any intersecting cells in [r4], so the Exocet target cell in [r4] must be true. Does this scenario qualify as a JExocet ???

It does. My posts here and here might help.
ronk
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### Re: bi bi pattern in hardest puzzles

I've updated my JExocet program to include the above scenario and one other that's similar. I now find JExocets for all but 67 puzzles in champagne's "03 E ..." file. Of those, 65 puzzles contain the target cells in a single mini-unit. These two puzzles complete the non-JExocet puzzles.

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`...4....94....923..8..2...4..6..3...8..59...2.......7.3..9....5..8..21...1...5...;1952;elev;1806;2;2;2BN F1F3;not in band;;;; +--------------------------------------------------------------------------------+ |  12567   23567   12357   |  4       135678  1678    |  5678    1568    9       | |  4       567     157     |  1678    15678   9       |  2       3       1678    | |  15679   8       13579   |  1367    2       167     |  567     156     4       | |--------------------------+--------------------------+--------------------------| |  12579   24579   6       |  1278    1478    3       |  4589    14589   18      | |  8       347     1347    |  5       9       1467    |  346     146     2       | |  1259    23459   123459  |  1268    1468    1468    |  345689  7       1368    | |--------------------------+--------------------------+--------------------------| |  3       2467    247     |  9       14678   14678   |  4678    2468    5       | |  5679    45679   8       |  367     3467    2       |  1       469     367     | |  2679    1       2479    |  3678    34678   5       |  346789  24689   3678    | +--------------------------------------------------------------------------------+ # 180 eliminations remain`

Code: Select all
`98.7..6..7......8...6.5....5.....4...4...3.....95...6.3...2.1....8.....2..59...7.;21774;GP;KZ1C;1;2;r1c5 r1c6 r2c3 r2c9;;;;; +--------------------------------------------------------------------------------+ |  9       8       1234    |  7       134     124     |  6       12345   1345    | |  7       5       1234    |  12346   13469   12469   |  239     8       1349    | |  124     123     6       |  12348   5       12489   |  2379    12349   13479   | |--------------------------+--------------------------+--------------------------| |  5       12367   1237    |  1268    16789   126789  |  4       1239    13789   | |  1268    4       127     |  1268    16789   3       |  25789   1259    15789   | |  128     1237    9       |  5       1478    12478   |  2378    6       1378    | |--------------------------+--------------------------+--------------------------| |  3       679     47      |  468     2       45678   |  1       459     45689   | |  146     1679    8       |  1346    13467   14567   |  359     3459    2       | |  1246    126     5       |  9       13468   1468    |  38      7       3468    | +--------------------------------------------------------------------------------+ # 176 eliminations remain`

[Edit: updated the puzzle counts above.]
Last edited by daj95376 on Tue May 08, 2012 11:23 pm, edited 1 time in total.
daj95376
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### Re: bi bi pattern in hardest puzzles

daj95376 wrote:I now find JExocets for all but 56 puzzles in champagne's "03 E ..." file. Of those, 54 puzzles contain the target cells in a single mini-unit. These two puzzles complete the non-JExocet puzzles.

Code: Select all
`98.7..6..7......8...6.5....5.....4...4...3.....95...6.3...2.1....8.....2..59...7.;21774;GP;KZ1C;1;2;r1c5 r1c6 r2c3 r2c9;;;;;`

daj95376, it's good to see more corroboration of champagne's findings, thanks. This seems more like a 3-digit "exocet" where the base cells each contain the same extra candidate value ("digit"). As a result, as David P Bird observed elsewhere (sorry, no link), this digit must ultimately be placed in one of the base cells, I.e., r1c56=1. [edit: Add second diagram and logic set, which replaces truths 234R2 with 234B1, i.e., daj95376's empty rectangle POV.]

___ ____ (clickable thumbnail images)

Code: Select all
`With truths 234R2 (left diagram):     14 Truths = {234R2 234C348 1N56}     17 Links = {1234r1 23r4 2r5 4r7 34r8 2n3 234b2 234b3} With truths in 234B1(right diagram):     14 Truths = {234R2 234C348 1N56}     17 Links = {1234r1 23r4 2r5 4r7 34r8 2n3 234b2 234b3}For both:     4 Eliminations --> r1c389<>1, r2c3<>1`

[edit: After restricting the "3-digit jellyfish" to r2c348 (or c348b1), a minimal cover set ("link set") that provided r2c3<>1 was chosen.]

While XSUDO recognizes (1)r1c5=(1)r1c6 as a derived strong inference ("sis"), the program requires the 2n3 link in order for this derived sis to be true. I don't understand this requirement, even though r2c3 is one of champagne's identified target cells. After the eliminations shown above, we are left with [edit: locked candidates 1b1\r3 to get] hidden single r2c9=1. Whether or not this should be considered an exocet target is debatable IMO. Also, note truths 234R2 [edit: or 234B1] which are not in a common exocet.

daj95376 wrote:
Code: Select all
`...4....94....923..8..2...4..6..3...8..59...2.......7.3..9....5..8..21...1...5...;1952;elev;1806;2;2;2BN F1F3;not in band;;;;`

This "exocet" was detailed here.
Last edited by ronk on Sun May 06, 2012 4:49 pm, edited 1 time in total.
ronk
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### Re: bi bi pattern in hardest puzzles

I don't know if I will be in or off topic ...

Code: Select all
`98.7..6..7......8...6.5....5.....4...4...3.....95...6.3...2.1....8.....2..59...7.;21774;GP;KZ1C;1;2;r1c5 r1c6 r2c3 r2c9;;;;; +--------------------------------------------------------------------------------+ |  9       8       1234    |  7       134     124     |  6       12345   1345    | |  7       5       1234    |  12346   13469   12469   |  239     8       1349    | |  124     123     6       |  12348   5       12489   |  2379    12349   13479   | |--------------------------+--------------------------+--------------------------| |  5       12367   1237    |  1268    16789   126789  |  4       1239    13789   | |  1268    4       127     |  1268    16789   3       |  25789   1259    15789   | |  128     1237    9       |  5       1478    12478   |  2378    6       1378    | |--------------------------+--------------------------+--------------------------| |  3       679     47      |  468     2       45678   |  1       459     45689   | |  146     1679    8       |  1346    13467   14567   |  359     3459    2       | |  1246    126     5       |  9       13468   1468    |  38      7       3468    | +--------------------------------------------------------------------------------+`

Here is my analysis.

1. The missing clues in the line of boxes are 1234,1278,46,12,14689,359 from RowOfBoxes 1 to ColumnOfBoxes 3.
2. Mini-lines containing the missing clues : r1c56=1234 and r3c12=1234 in RowOfBoxes 1.
3. Single digit analysis of the first mini-line :

1r1c56-1r2c456=1r2c39
||
2r1#c6-2r2c46=FXW(2R26)-2r451#c3=2r2c3
||
3r1#c5-3r89c5=3r8c4-3r8c8=FXW(3C28)-3r41#c3=3r2c3
||
4r1#6c56-4r3c46.r9c56=FXW(4R39)-4r21#c9=4r2c3

:=> r1c56=1a, r2c3=a, r2c9=1, where a=2,3 or 4
4. Collecting the base sets and putting them in Xsudo gives the following :

Code: Select all
`+--------------------------+--------------------------------+-----------------------------+| 9       8        4-1(23) | 7          (134)     (124)     | 6       245-1(3)  345-1     || 7       5        (234-1) | 36(24-1)   369(4-1)  69(24-1)  | 39(2)   8         -39(+1-4) || 12(4)   12(3)    6       | 238-1(-4)  5         289-1(-4) | 2379    29-1(34)  379-1(4)  |+--------------------------+--------------------------------+-----------------------------+| 5       1267(3)  17(23)  | 1268       16789     126789    | 4       129(3)    3789-1    || 1268    4        17(2)   | 1268       16789     3         | 25789   1259      5789-1    || 18(2)   17(23)   9       | 5          178(4)    178(24)   | 378(2)  6         378-1     |+--------------------------+--------------------------------+-----------------------------+| 3       679      47      | 468        2         45678     | 1       459       45689     || 146     1679     8       | 146(3)     1467(3)   14567     | 359     459(3)    2         || 126(4)  126      5       | 9          168(34)   168(4)    | 38      7         368(4)    |+--------------------------+--------------------------------+-----------------------------+{1R2 2R26 4R2369 2C3 3C238 1N56 3B8}:=> r13456c9<>1, r2c3456<>1, r3c468<>1, r2c9<>349, r1c38<>1, r3c46<>4, r2c9=1`

4. The second mini-line leads to nowhere.

The above explains my understanding of bi (bi) pattern (or exocet).

Regards, JC.

[edit : removal of some typos]
Last edited by JC Van Hay on Sun May 06, 2012 9:05 pm, edited 1 time in total.
JC Van Hay

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### Re: bi bi pattern in hardest puzzles

I believe that the collection of JExocet examples has now been extended to cover all the eventualities that were considered, so have tidied up the definition of the pattern I gave <here>.

I should stress that this definition is for those players who don't employ net-based solving methods.

Other players, looking for Exocets, don't need condition 3. Indeed, they may also seek alternative target cells, when they would only rely on identifying the base cells. For them it would be more useful to have some other method of categorising the circumstances that identify bi-bi base and target cell pairings.
David P Bird
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### Re: bi bi pattern in hardest puzzles

JC Van Hay wrote:I don't know if I will be in or off topic ...

I had a quick look, not enough time for a better answer before next week.

It seems to me that the XSUDO construction is not limited to a proof of the exocet.

That puzzle has a high potential for eliminations just taking the reduced PM 1234. Many SLG should work

The maximum requirement for digit 14 should be truths 14r2 (links 24b2 2n3 2n8)

The situation for digits 2 and 3 is more complex.
The proof uses XWings

champagne

EDIT: That puzzle has a relatively low ED 11.0
My solver solves it "easily", but miss most of the potential of the exocet floors.
The elimination shown in the post is not seen by my solver
champagne
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### Re: bi bi pattern in hardest puzzles

daj95376 wrote:I've updated my JExocet program to include the above scenario and one other that's similar. I now find JExocets for all but 67 puzzles in champagne's "03 E ..." file. Of those, 65 puzzles contain the target cells in a single mini-unit.

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.
ronk
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