## JExocet Pattern Definition

Advanced methods and approaches for solving Sudoku puzzles

### Re: JExocet Pattern Defintion

So the challenge for me is to find an example of this new type of secondary equivalence that:

(1) doesn't occur in a double Exocet situation;

(2) exhibits all of its possible features; and

(3) completely solves the puzzle.

That sounds tough... wait a Jiffy.... aaah ... I think I've got it:

The following puzzle is also from Champagne's huge grey area database

98.7.....6.....7....7.5.....6...4.3...98..5......2...1.2..1......5..86.......9.42

It has 2 Exocets; r2c8 r2c9 r1c3 r3c4 1249 and r3c1 r3c2 r2c4 r1c7 1234

However, for the purposes of this exercise I've ignored eliminations possible via the first Exocet.

Code: Select all
`*--------------------------------------------------------------------------------*| 9       8       1234     | 7       346     1236     |T123    A5-126  B45-6     || 6       5       1234     |T4-3     8      C123      | 7       129     49       ||B1234   B134     7        | 9       5       1236     | 12348   1268    468      ||--------------------------+--------------------------+--------------------------|| 5       6       28       | 1       9       4        | 28      3       7        || 1234    134     9        | 8       367     367      | 5       26      46       || 3478    347     348      | 36      2       5        | 489     689     1        ||--------------------------+--------------------------+--------------------------|| 3478    2       3468     | 346     1       367      | 89      5789    589      || 147     9       5        | 2       47      8        | 6       17      3        || 1378    137     1368     | 5       367     9        | 18      4       2        |*--------------------------------------------------------------------------------*`

We have a normal type of secondary equivalence r1c7==r2c6, r2c4 which produces no eliminations.

We have a tertiary equivalence r2c4==r1c89(5), r1c7 which produces 5 eliminations:

r1c8 <> 12 - base digits not in r2c4
r1c89 <> 6 - non-base digits (other than 5) in r1c89
r2c4 <> 3 - base digit in r2c4 not in either of r1c89

stte

Leren
Leren

Posts: 3216
Joined: 03 June 2012

### Re: JExocet/Exocet statistics

blue wrote:One more note: For both puzzle lists, there were puzzles containing 100-200 exocets (of general type).
This didn't happen for champagne's "potential hardest" list.
For the grey zone puzzles, it was rare: nothing with >= 100 exocets, in the "filtered" tables, 8 with >= 100 in the "all" tables.
For the green zone, it happens often enough to effect the "exocets per 'puzzle with an exocet'" ratio -- 39 and 475 puzzles, respectively.

After elimination of the candidates in direct contradiction with the clues, there remain in general between 200 and 250 candidates. I probably don't understand what "exocet of general type" means, but whatever it means, it seems very strange that there can be almost as many instances of a "pattern" as there are candidates. Obviously, they cannot have independent eliminations. Does your "exocet of general type" rely on indirect contradictions (with more or less unrestricted length) between candidates?

champagne wrote:First of all, I found only 75 puzzles having the exocet pattern in the rand 8.6 file.

blue wrote:
Code: Select all
`Grey Zone, only exocets with standard eliminations282588 puzzles       size                             Puzzles      +-------------------+--------------------+      |    2     3      4 |     5      6     7 |  +---+-------------------+--------------------+t | A |    -    38     13 |     -      -     - |     51y | B |    -    77     40 |     1      -     - |    118p | C |    -    48     12 |     -      -     - |     50e | D |    -   248     70 |     5      -     - |    323  +---+-------------------+--------------------+  | G |    1   292    216 |    50      -     - |    559  | H |    1   576    310 |    53      1     - |    941  | K |  134  2828   2447 |   587     47     3 |   6046  | O |  207  1395   1091 |   189     15     - |   2897  +---+-------------------+--------------------+         860  8925   6283    1188     91     5    10985`

75 for champagne
51 or 51+118 or ... for blue
I take the difference as resulting from different definitions, but the order of magnitude is the same, between 0,26% and 0,5%.

Now , if we could take into account the distribution of clues in the 75, the unbiased proportion of puzzles might be computed and appear to be up to 50 or 100 times less, because those with exocets concentrate on small numbers of clues. But it seems champagne is reluctant to reveal it.
denis_berthier
2010 Supporter

Posts: 1258
Joined: 19 June 2007
Location: Paris

### Re: JExocet/Exocet statistics

blue wrote:For eleven (and all):

Here are some statistics for the puzzles in eleven's Grey and Green Zone puzzle lists.
...
Code: Select all
`Grey Zone, all exocets282588 puzzles  | O | 3578 49186  20219 |  8069    224     6 |   81282  +---+-------------------+--------------------+  `

Code: Select all
`Green Zone,582178 puzzles  | O | 68709 345185 142340 | 32760   1102    24 |  590120`

Hi blue,
very interesting deep search.
I only looked for JEs in the grey area. It's clear that your results open other doors.

I see you included exocets of 2 digits with a significant count in the green area.

1) I have only 75 puzzles with a small number of puzzles having 2 exocets where you find 129 (A grey 3+4 digits) is it possible to match our lists.
here above my puzzles

Hidden Text: Show
9...8...5..1.53...2.....1..1.3.....74.2..8.9......1.2..754.9..6...3.......9..7...; ;1;1;6;r7c7 r7c8 r8c5 r9c5 r8c1 r9c1 1238
9....4....3..6..41.7...........4..85.4.8....3....324...2...36....3..5..9.6.....38; ;1;1;2;r2c1 r2c3 r1c7 r3c7 r1c4 r3c4 258
.8.6..4..6...5.89...2.......7.9.3......5...6.2...7.1.9.......7......5.3492.8.....; ;1;1;4;r1c9 r2c9 r5c7 r9c8 1357
...7...6...2....9.74..92..8..4.......2.1.9.8...3.2...7...9.3....8...1.2..36......; ;1;1;4;r4c8 r6c8 r3c7 r7c9 1345
7...5....8....7.69.2.8....52.....6....8.....1.......57..7.6.42......1....432.5...; ;1;1;2;r7c4 r7c6 r8c9 r9c9 r8c1 r9c1 389
.64.3.......2.53..1.......2...1...7...7.9....9..3..8.1.4.67..3.....29.....6......; ;1;1;2;r7c1 r9c1 r6c2 r6c3 r2c2 r2c3 578
...2.4..78...9.4.........1...7....3.......5.14..62....5.8.4712..6.....9..4.8.....; ;1;1;6;r2c9 r3c9 r9c7 r9c8 r6c7 r6c8 3589
.....1..64.....7....7.3...86..5.7.4..52...........2..58..9.56.4..........1.4..97.; ;1;1;0;r8c9 r9c9 r2c8 r4c7 123
9....2....5.1....2...54..........3.1..7..1..4..5...6....69...25.1....8...42.1..9.; ;2;2;66;r5c4 r5c5 r4c8 r6c8 r4c2 r6c2 3589;r6c5 r6c6 r4c8 r5c8 r4c2 r5c2 2378
8921........3....4.6...7.8.......76.7....3....2..4.9..1.7.........6.9....8.....4.; ;1;1;4;r4c1 r6c1 r3c3 r9c3 3469
..8..6.1.32.1........34..7..5.47.89.9.....7.......32.126...5...8..........9....5.; ;1;1;4;r1c5 r2c5 r6c4 r9c4 2589
8.......2.1..7...94.3..1.....618.2........4.6...36..7........8...953.7..5..7..93.; ;1;1;4;r8c1 r8c2 r9c6 r9c9 1468
8...1.7...9.8.2.....1..4..9...6....4..2.5.13....3.1.9...8....7...9.7...175...6...; ;1;1;0;r4c7 r4c8 r6c3 r6c5 258
......7.9.......5.8.9..31...3...5.8..4..26....2....475.1..3..67.....1..83...9....; ;1;1;6;r3c4 r3c5 r1c2 r2c2 r1c8 2457
.7....9.35.......2...4...5....86......23.4...1.6....2...4...1.....7.98.5....35...; ;1;1;6;r1c4 r2c4 r7c5 r7c6 r6c5 2569
78.........517..3...2..8.........6..1.8..5.7.3.7..6...2..4..8..8.9..........3.51.; ;1;1;4;r4c8 r4c9 r6c2 r6c5 1289
..7.....8.3....4..5..98.2....9..76.1...5..3..3......2.4...3...9...86.....914.....; ;1;1;2;r5c9 r6c9 r8c7 r8c8 r3c8 457
78...1.........1........564.......26..85.....9...843..1....6..7.3.7.9.....7.2.4..; ;1;1;6;r8c9 r9c9 r1c7 r1c8 r6c8 1235
7....4..9...82......8..9.6.9.4.6.....7....2..286....7.4......3.617.....4.5..1....; ;1;1;4;r1c3 r2c3 r5c1 r7c2 1259
...74.3.6.79......8...1..9......6..8.1..83......49.25...7.3...55.4....6..9...4...; ;1;1;6;r7c1 r9c1 r6c2 r6c3 r1c2 r1c3 1236
......7....2..6.54.5.....12...67.....2..8...76.........1....4...8..5.....753..2.8; ;1;1;4;r5c1 r5c3 r6c4 r4c7 1359
....67.............3.9....89....5...6.72...89.1......2..17......4..9.2.1..68.19.4; ;1;1;6;r3c5 r3c6 r1c8 r2c8 r1c3 r2c3 1245
...6.3....8..4...2.3....71.......2...1.....7....51.9....83.....3....564.4....1.95; ;1;1;6;r6c2 r6c3 r4c6 r5c6 r5c9 2347
6.2..5..79.8....1......29..1..9..8....6..7..1.....6.5........4.5..6..1....973....; ;1;1;4;r5c4 r6c4 r2c6 r7c5 2345
.5.68..13..1.4.5...9.1...............8..3.7.5..9..128......8..2......94.623......; ;1;1;0;r4c8 r5c8 r2c9 r7c7 369
....5.....461......39.4..7..7..1.......8.....62..........57.2..39..2..45.8...37..; ;1;1;6;r5c7 r5c8 r4c6 r6c6 r4c3 r6c3 1234
38....7.........14...6...3.8.7.23....1..4..5.....5.8..4.5......6...32...7.......9; ;1;1;4;r9c7 r9c8 r7c2 r8c4 2345
3...2...9.4.3....25.....31...8.9.1344.....9...6..5.......9.7..1..48..2....5.4..9.; ;1;1;2;r1c8 r2c8 r6c7 r6c9 r7c7 458
3.......26.2..794...7.4.8....3.......9....1.62.5.9.3..4....1..5..17........28....; ;1;1;0;r7c4 r7c5 r9c3 r8c8 369
.31.............9.2..6...7..8....3...239..4.......7....5.8..1....4.25.6.....4...8; ;1;1;2;r6c2 r6c3 r4c9 r5c9 r4c4 456
3..1..8.........216...8.5..1...64..525.3......7.5...3..3.8.....8.9..2.......1...4; ;1;1;4;r6c7 r6c9 r5c3 r5c6 1468
3.1....7...9....1.....46...2...9..3..85..72.9.....2.6..2...36....7.........9....5; ;1;1;0;r8c7 r8c9 r9c2 r9c6 134
..2..8....8.6...41..71......4..91.5........6.5.....7......59..81..4.3..........2.; ;1;1;0;r4c7 r4c9 r5c1 r6c4 238
....2...8.82.9.....61..4.3.......78....4..1..7.....3..62.34...73.75...6..5...9...; ;2;2;66;r1c7 r1c8 r2c1 r3c1 r2c4 1469;r2c7 r2c9 r1c1 r3c1 r1c4 1456
.2..4....7..2.8.....3.7..2.4...5..9......3..7659......37....6...41....79...5..8..; ;1;1;6;r2c2 r3c2 r9c1 r9c3 r5c1 r5c3 1689
.2....4.1..94..8....1..9..2.43.1....15..7.3...98..2.....4...5...8..9...7....8..6.; ;1;1;4;r3c7 r3c8 r2c2 r1c5 3567
..1.7..8......2...4..6.8.......2.....3....6728.......5..5...4.1.....4.6.12...7..8; ;1;1;6;r2c3 r3c3 r8c1 r8c2 r4c1 3678
.157..4..4......2....1..68....8...6.36...4......31..7.5..........9.2..581....9...; ;1;1;0;r5c8 r5c9 r4c3 r4c5 159
.....1...1.4.75.6...5.698.44..18..........52...17.6.....8.....7....9..5....53.4..; ;1;1;6;r8c9 r9c9 r4c7 r4c8 r2c7 2369
9..8.3....7.....4....2..5...1..34..2..95.6.1..6.....7.4.19.7.......85.........7..; ;1;1;2;r7c7 r7c9 r8c4 r9c4 r8c2 r9c2 238
9.65....4.78.....55......2.73...........7.1....41.8.5......9...3.9.8.6.....74...8; ;1;1;0;r2c7 r3c7 r6c9 r9c8 379
.8..6.3..2.6.4.....3.....2..6.2..9.77....1.3........12..9.18....1.....9..2...456.; ;1;1;0;r5c7 r6c7 r3c9 r8c9 468
8456....1........4.16..7...9...61.32....2.7.873.8..........35.958.........3..8...; ;1;1;4;r7c3 r8c3 r2c2 r5c1 1479
7..9...35..........8..6..4.9..1..473....9......45..6.2......51...6.......1...53.7; ;1;1;4;r7c5 r9c5 r1c6 r6c6 3478
.791....4.......2....87.3.91.4.2...52.........8.94........9.5......84..23..2.6..8; ;1;1;2;r1c1 r2c1 r7c2 r7c3 r6c3 568
7....43.2.8.2.3..1..5.1.......47..........25...8..5..49....861.....4......193...8; ;1;1;0;r7c4 r7c5 r8c3 r8c9 257
..........7..3.4.63..5692.8..7.....4.3967..1....8.2....95.........7....37...5....; ;1;1;2;r1c8 r2c8 r6c7 r6c9 r8c7 359
.6...98.7......4..8..4...9.7..54.........6...91...3.5...29..5..1.3.......9.62...1; ;1;1;6;r1c8 r2c8 r8c7 r8c9 r4c7 r4c9 1236
....58.3..36......5..7....1....13..641.2.....6......5........4...2.79....9.1..8..; ;1;1;0;r8c7 r8c9 r7c2 r7c4 356
5....6.2.4...78......9....8....1.9..24...7...9......6.........2.1.4.36....37...5.; ;1;1;2;r8c8 r8c9 r7c6 r9c6 r7c1 r9c1 789
.5..3.1...31..5.72...7..........46...23.91.4...........123....8.97.......6....219; ;1;1;0;r1c6 r3c6 r5c4 r8c5 268
4.91...2.76..........48......1...5......34..1.2.....67..6...9..95..13..6...2...5.; ;1;1;6;r1c5 r2c5 r4c4 r4c6 r9c6 2679
..3.....4.4213.....9.5.......9...83..1...3..5..8...7.....9....2..47.2.1.1....59.7; ;1;1;0;r8c5 r9c5 r3c6 r5c4 468
2.97......3..1.8.9..1...36..1.....5....4..73..7.1859..........6.5.........6..24..; ;1;1;2;r7c7 r8c7 r6c8 r6c9 r1c8 r1c9 125
..2.589......34.8....7.93...5..9...16...8.53...1........6..3...7...4..5........62; ;1;1;0;r1c4 r2c4 r5c6 r8c6 126
2......5...63.94.2..84......8...251....7....3....91.2...7....3..6..7.....2.....48; ;1;1;2;r8c7 r8c9 r7c4 r9c4 r9c3 125
......2.16.....459...2.3....9..6...5.....2...31.8.......9...16..4.....8.5.7..4...; ;1;1;6;r5c9 r6c9 r9c7 r9c8 r3c7 2368
.1...8...84..7......5.9.......7.5....2...689.3.....2.....4.79..5.........86.5217.; ;1;1;2;r3c1 r3c2 r1c7 r2c7 r1c4 r2c4 267
1...8..799.8.......75...38....6.7.3.2....3.5.......7.2.2...9...5......9.....4.1.5; ;1;1;2;r5c5 r6c5 r3c4 r3c6 r7c4 159
16........93....4.....7....4.6..18..8..2......5.7........32...96.2.9..38.4..1.5..; ;1;1;4;r1c4 r1c5 r3c3 r3c7 3459
1..5...4...6.2..1.532.9.....5.7.3..1.......8...1.69...42.........5....36......8.7; ;1;1;4;r4c8 r6c8 r3c7 r7c9 5679
.1...3...7..8..2.....4.16..5.9.1...6....3.9.......452.........72.3.5.1...8.......; ;2;2;24;r7c7 r9c7 r2c8 r2c9 r4c8 348;r5c9 r6c9 r2c8 r8c8 1348
..1......3...4.6.......3.57...45..362.....5...6.29........6....8.......992.73.4..; ;1;1;6;r7c7 r8c7 r6c8 r6c9 r1c8 r1c9 1378
83....5.22.....8...6..2...1..3..4......5..........697..29..1.4....3.......4....17; ;1;1;6;r1c5 r1c6 r2c8 r3c8 r2c3 1679
..5.7...6.134..95......94....7..21.5.4.1.........6......97......8.......7....1.32; ;1;1;0;r4c4 r6c4 r1c6 r9c5 389
4........7...925....5..8..2....1.37..9............3.4....2..1.5....69..464.13.9..; ;1;1;6;r3c1 r3c2 r1c8 r2c8 r1c4 1369
.3......7.97.6...5.4...79.....7.84...1.5........3..26..7.49.6......8...9..1......; ;1;1;6;r5c1 r5c3 r4c9 r6c9 r4c5 r6c5 2348
.3..7..9..5......7.....98.4.....6...21.........689....3..7..1.9.....825...2..4...; ;1;1;2;r6c1 r6c2 r4c7 r5c7 r5c6 457
3....1.6...4.....7.76..324....162.7....8....3.........83..9..2...7.......6.7.4.3.; ;1;1;4;r5c3 r6c3 r1c2 r9c1 2589
1...2...7.8.7...........5.4.2...3...7..8.....93.1....82...54.......3..2......769.; ;1;1;6;r7c2 r7c3 r8c9 r9c9 r8c4 1369
......12.....6..8.73......9.74..8..55....46....26..47...719....3.........9..2..5.; ;1;1;4;r5c8 r5c9 r6c2 r4c4 1289
..7..146.5......8.........98.5..39......8.1....97.4.....3......7....834.9...278..; ;1;1;0;r2c7 r3c7 r6c8 r7c9 257
......6.5.98.......258..97..7.4..1....3.9....9....8.......4...14....2.3.38.5.6..2; ;1;1;6;r3c5 r3c6 r1c1 r2c1 r2c9 1346
5....1.2.....3.9..9..6.5..1.73.6..8.............8.7....287...6..1..5....36..4....; ;1;1;4;r3c7 r3c8 r1c2 r1c5 3478
.3.25..8...6...4..........52..9......8.....246...1...98.51...3..1.3.........8..7.; ;1;1;0;r7c7 r7c9 r9c2 r8c5 269

2) your box extensions gives here impressive results. This is something I have to consider.

3) Non JE exocets have undoubtedly the same properties as JEs. I like very much JEs because a manual player can "easily" find them. Finding new patterns as rich as the JE pattern is IMO necessary to consider them as solving tools of practical use
I'll reactivate my code to try to meet your results and work on that aspect.
Last edited by champagne on Tue Jun 04, 2013 7:02 am, edited 1 time in total.
champagne
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Posts: 6205
Joined: 02 August 2007
Location: France Brittany

### Re: JExocet/Exocet statistics

champagne wrote: I found only 75 puzzles having the exocet pattern in the rand 8.6 file

Taking these data as they are:

Code: Select all
`Distribution of clues in the 75 list with exocet:nb-clues   nb-instances19         020         021         022         323         1424         1925         2426         1227         228         029         130         031         032         033         034         035         0`

Code: Select all
`Distribution of clues in the full list of 282588 puzzlesnb-clues   nb-instances19         020         221         28322         581423         3656324         8754725         9155726         4658627         1228328         179429         14930         1031         032         033         034         035         0`

Code: Select all
`Proportion of puzzles having an exocet:nb-clues   proportion19         020         021         022         3/581423         14/3656324         19/8754725         24/9155726         12/4658627         2/1228328         029         1/14930         031         032         033         034         035         0`

Results recalled from here: http://forum.enjoysudoku.com/the-real-distribution-of-minimal-puzzles-t30127-8.html
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`Weights:#clues      %puzzles20          0.021          0.00003422          0.003423          0.14924          2.2825          13.4226          31.9427          32.7428          15.4829          3.5630          0.4131          0.022`

Application of the formula in the above-mentioned post

Code: Select all
`Unbiased proportion of puzzles having an exocetnb-clues   weighted-proportion * 10022         3/5814 * 0.0034   = 1.75438596491228e-0623         14/36563 * 0.149  = 5.70522112518119e-0524         19/87547 * 2.28   = 0.00049481992529726925         24/91557 * 13.42  = 0.0035178085782627226         12/46586 * 31.94  = 0.0082273644442536427         2/12283 * 32.74   = 0.0053309452088252128         0                 = 029         1/149 * 0.022     = 0.000147651006711409`

Estimated unbiased proportion of puzzles having an exocet in the SER > 8.6 area
(+ 1.75438596491228e-06 5.70522112518119e-05 0.000494819925297269 0.00351780857826272 0.00822736444425364 0.00533094520882521 0.000147651006711409)

= 0.017777395760567%
= 0.018%

This is a small proportion (less than 2 in 10,000), although this is more than I expected. The reason is, there are more cases than expected with more than 24 clues.
denis_berthier
2010 Supporter

Posts: 1258
Joined: 19 June 2007
Location: Paris

### Re: JExocet Pattern Defintion

Hi Denis & champagne,

We may be getting different results because we don't apply the same list of "simple techniques" before the search -- champagne uses more then I do.

I mentioned this in the other thread -- if sometimes champagne's puzzles end up with a filled base or target cell in one of the JE's that I find, then (of course) he wouldn't find it.

For champagne, these are the 129 that I find in the grey area:
Hidden Text: Show
.8.6..4..6...5.89...2.......7.9.3......5...6.2...7.1.9.......7......5.3492.8.....;r1c9;r2c9;r5c7;r9c8;1357
.8.3.........7.1.8.39...72.4....59....5......9..6..41............68.3....7..2.34.;r6c5;r6c6;r4c3;r5c1;378
...7...6...2....9.74..92..8..4.......2.1.9.8...3.2...7...9.3....8...1.2..36......;r4c8;r6c8;r3c7;r7c9;1345
..671.93...8...........421.9..3..6......6......5..8.744...7..2..8...3....9.2.1...;r4c2;r5c2;r2c1;r3c1;1237
6....4.7.....7..........429.18...9.34....6..7....8....3......941....8....9.15....;r8c2;r8c3;r9c7;r9c9;267
.4.....93.....76..7.9.........2...5......68.41......3...29.1.....1..3.6..6...5..8;r4c7;r6c7;r8c9;r9c8;129
.....1..64.....7....7.3...86..5.7.4..52...........2..58..9.56.4..........1.4..97.;r8c9;r9c9;r2c8;r4c7;123
...964.....6....2.91.5..7...6.1.......2..5..91.92...8.4.7..8...8.....3.2.2.......;r8c2;r8c3;r9c5;r9c6;159
.....94.228..1...7.......1351.2..7.............4.31......95......9..2....6..7.85.;r6c7;r6c8;r5c1;r5c2;269
....9.31.2..14.5....3.5....5....174.....6.2...6..74.9..486....7........86.....42.;r2c2;r2c3;r3c7;r3c8;678
..9..1..5...2..4....57......93.1.5......2....8....9.2..8.....9.4....63...3.8...6.;r2c6;r3c6;r7c5;r9c5;345
...8.....9....5.76.....79..8.....3.2.2.....9....5..7..3.7...1...9..84...1.2.3..6.;r1c7;r2c7;r7c8;r9c9;458
8....9.........159...4...2........3.1..2..76..7..93..268..2.....3.....4....16....;r5c5;r5c6;r4c9;r6c7;458
..8..6.1.32.1........34..7..5.47.89.9.....7.......32.126...5...8..........9....5.;r1c5;r2c5;r6c4;r9c4;2589
.8...4..2..2....68...3...9....7.......5...6..12.8....5...9.3....192......3.6.8.21;r9c1;r9c3;r8c5;r8c6;457
.8...2..3....8.....2.64...57....423....1.......5.6..988.........46..15........9.2;r4c9;r5c9;r7c8;r9c8;146
8.......2.1..7...94.3..1.....618.2........4.6...36..7........8...953.7..5..7..93.;r8c1;r8c2;r9c6;r9c9;1468
7..9...5.2.3.......9.1........21...4......38.1..67..........8....6.......2158.96.;r7c2;r8c2;r4c1;r6c3;458
78.........517..3...2..8.........6..1.8..5.7.3.7..6...2..4..8..8.9..........3.51.;r4c8;r4c9;r6c2;r6c5;1289
7....4..9...82......8..9.6.9.4.6.....7....2..286....7.4......3.617.....4.5..1....;r1c3;r2c3;r5c1;r7c2;1259
.7...49.....392...1....6........53.64......9..9.....45....3..5.98..7.2....2..8...;r5c7;r6c7;r7c9;r9c8;178
.7...3..8.....647...8....9..8...5..9..72685....1......5.....8.....35...1....29...;r1c5;r3c5;r4c4;r6c4;179
......7....2..6.54.5.....12...67.....2..8...76.........1....4...8..5.....753..2.8;r5c1;r5c3;r4c7;r6c4;1359
.....71.....2.....7...93..8.13....5.25...9..74........1..57..8.5..3.1.6..2....4..;r5c3;r6c3;r7c2;r8c2;689
....6.78....48..3.74......6689.......3...58.1.......9...6549..8....1..........2..;r3c7;r3c8;r1c4;r1c6;129
6.4.....1.5.2.9.....2.34.7....3.7..62.....13...7...4.2....85...5..9...43.........;r5c2;r5c3;r6c4;r6c5;589
6.2..5..79.8....1......29..1..9..8....6..7..1.....6.5........4.5..6..1....973....;r5c4;r6c4;r2c6;r7c5;2345
....5.8..72.....4...87.1...3......98...1.8..5......2.....3.7.1..9......6...96..7.;r2c5;r2c6;r3c7;r3c9;369
...5.........81..5.63..9...62....5...5.....49..4.3..284...2.73.2....39.4.........;r3c4;r3c5;r1c9;r2c7;247
5...7.48....1....6....267....9......4..8....326....5..3.56...9.....31....4.7.9...;r7c5;r9c5;r2c6;r3c4;458
.5.68..13..1.4.5...9.1...............8..3.7.5..9..128......8..2......94.623......;r4c8;r5c8;r2c9;r7c7;369
5..4..3.8.8...1.....62.........2.49..4...8......7...1.86.....5..3.....7.97.65....;r7c3;r9c3;r1c2;r2c1;124
...5.......2..9..151.3.6.....4..1.6...74...8..6....2....8..73.5.......7.9...8....;r2c4;r2c5;r1c1;r1c2;478
5.1...8.4...48.........23.....934.......2..3..9.....65..71.....6.....78.3..6..5..;r5c2;r5c3;r4c9;r6c7;478
5......18.2..........831.5...4..5.9....31....692........7...6.....6.4....8..5...9;r8c2;r8c3;r7c9;r9c7;135
....48..7..79.....5..3...8.1..7...25..2..9.7...9.2.6.4.....6.....32...1.6.....3..;r8c1;r8c2;r9c5;r9c6;4789
4..6......1.........94.7..8.8...239..3..8..179.........56.7..8.........5.4.2.17..;r2c4;r2c6;r1c3;r3c1;358
.45....3.......9..2.1..4..6.235.6...61............3...3...2..418..3.7........5.8.;r1c7;r1c9;r2c4;r2c6;128
42..........8493..93...2..8..6...7......9..4.....6.19.5....4.7.1...........657...;r3c4;r3c5;r2c2;r2c3;157
.......41...62..3.1....85.6............8.29.3.9..36..8.24.8.........9...5.63.....;r4c4;r6c4;r1c5;r3c5;459
38....7.........14...6...3.8.7.23....1..4..5.....5.8..4.5......6...32...7.......9;r9c7;r9c8;r7c2;r8c4;2345
.38.49.....1...9.....36..4.5...32..9.2.......7.....56....9..6.4...2.4....1....8..;r4c3;r5c3;r8c2;r9c1;469
3.7..8.9.2.15......5..9....8.56..4...2.8.37..6...4..........8.2...7.......2....51;r9c4;r9c6;r7c2;r8c7;3469
3.......26.2..794...7.4.8....3.......9....1.62.5.9.3..4....1..5..17........28....;r7c4;r7c5;r8c8;r9c3;369
3...26....2.75.....7.....517....43...8.3..4.7....8..2..4..7.........96.......8.19;r3c4;r3c5;r2c1;r2c3;489
291....5.5..7...4............3.9...4.4....81..5..8...99.231.........529......6...;r2c7;r2c9;r3c4;r3c6;129
..2..8....8.6...41..71......4..91.5........6.5.....7......59..81..4.3..........2.;r4c7;r4c9;r5c1;r6c4;238
....28....4........5..1...3..48...5.91.2..7.......3.6.46........7..3628...5....17;r4c2;r6c2;r7c3;r9c1;238
2..5......6.31..4.4.1..63....7.4....856.........16..3..9....8....4.5...77......9.;r8c7;r8c8;r7c1;r9c2;126
......2..5.1.2..9...83...45..9.43.5....582.3..........2.......7.1..5....687....1.;r8c1;r8c3;r7c7;r9c9;349
.2....4.1..94..8....1..9..2.43.1....15..7.3...98..2.....4...5...8..9...7....8..6.;r3c7;r3c8;r1c5;r2c2;3567
..179....34....1......1.5...6.......1....293..59....2..92..43..5...81.4.4........;r8c3;r9c3;r1c1;r3c2;678
..1.7...8.265....19....8....1.....8.69...42...8..9.54.3....5.......3..9..6.1.....;r7c2;r8c2;r1c1;r3c3;457
..1....6....4....5...12.49...435..8......6...6..9.....7..8...1332......9..67....8;r5c8;r6c8;r8c7;r9c7;257
..1.......5..9...23.....9....4.5..3..6...2..8.98..7....162.........8..4......312.;r5c4;r6c4;r8c6;r9c5;1469
5...6.3.....4...52.92..76..9.8........7.86....6......13...........3...25.41..9..3;r6c1;r6c3;r4c5;r4c6;2345
.9....83...3.........4.5....82....71.4..1.3.......4..6..675....72.1..6.....6...53;r9c1;r9c3;r7c6;r8c5;489
9.6...7.....5.9....14.8..5..2..3...7.8..2...3.6715.....4....1.......8......4...2.;r5c1;r5c3;r4c7;r4c8;145
9.65....4.78.....55......2.73...........7.1....41.8.5......9...3.9.8.6.....74...8;r2c7;r3c7;r6c9;r9c8;379
9.6.....5.1..3...68....51...9.7..53..........1.2....94....53...3...1.....6827....;r2c3;r3c3;r5c1;r6c2;357
...9..64.7....49......5..3...458.1...3.7...6.2.1.......1...........7..8.3..6.2.7.;r3c7;r3c9;r1c6;r2c4;278
......943.5........6......7....5.81.5....2..6..941.7.54.....2.....9.4...7182.....;r9c5;r9c6;r7c8;r8c7;356
91.7.....37....51...6...9....3...6..7....41...4.....7.....53...2...1...983.6.2..5;r1c8;r3c8;r7c7;r8c7;238
89......7......8.1..374....9..28.7...2..53.1..6..7.59.2...3.....3...5......6..1..;r8c5;r9c5;r1c6;r2c6;129
..8...7...32....95...7....31....9....5..3..2....8.........4...8...58...1.24....6.;r2c4;r2c5;r1c8;r3c7;146
.8..6.3..2.6.4.....3.....2..6.2..9.77....1.3........12..9.18....1.....9..2...456.;r5c7;r6c7;r3c9;r8c9;468
..8...56.1732..............7....6.5.5..13...7..25...8..2.3...7..97...4.....69....;r8c8;r9c8;r1c9;r3c9;123
.8..5...17.5....3..3.12...8..8..2......6.842...4.1.....6....5.....59.3.......7.92;r1c7;r1c8;r3c1;r3c3;469
8456....1........4.16..7...9...61.32....2.7.873.8..........35.958.........3..8...;r7c3;r8c3;r2c2;r5c1;1479
...8..1....6.7..3......4827.....7.15...4......5.6..3.9.35..1....69......47.....8.;r5c8;r6c8;r7c7;r8c7;467
7..9...35..........8..6..4.9..1..473....9......45..6.2......51...6.......1...53.7;r7c5;r9c5;r1c6;r6c6;3478
....7...69..3..2.1.....2.4...1548.6....7.......3...8...5.92.....6.8.5..9......1..;r8c5;r9c5;r5c6;r6c6;136
..7..58.1...92.5....9..8..4.....3...3..7...1.....4..2..43.1...7.8..97....9....3..;r7c1;r8c1;r1c2;r3c2;256
7....43.2.8.2.3..1..5.1.......47..........25...8..5..49....861.....4......193...8;r7c4;r7c5;r8c3;r8c9;257
.....6.4..5....8..4..81.....3.1...7.6....7.5...1.25..632.......7.......3..6..95.7;r1c9;r2c9;r4c7;r5c7;129
6.4.2..3......4.7.1...6..2.....517..8..6.......57..2....35......8.97.4..........9;r7c7;r7c8;r9c5;r9c6;168
....58.3..36......5..7....1....13..641.2.....6......5........4...2.79....9.1..8..;r8c7;r8c9;r7c2;r7c4;356
5.....7.6.3...7.1...8.6.9..3..68......42....1.9....2......5.6..8..3....59..1...2.;r5c1;r6c1;r2c3;r3c2;167
.5..3.1...31..5.72...7..........46...23.91.4...........123....8.97.......6....219;r1c6;r3c6;r5c4;r8c5;268
48........6.2..3....9.....51...8....2.69...7.7....19..9....3.........569..5..7..4;r5c5;r5c6;r4c3;r6c2;345
..4728....5...62..........7..2.8.6...89..1..5........8..59....29.....31..1.2.3...;r8c3;r9c3;r2c1;r3c2;678
.47.......1.3...6..3..5...7...1...286........2....7.1......1.....9.6...1...2.85..;r8c4;r8c6;r7c1;r7c2;3457
.42.3..7..51..4..9...5.....7...458.36.....7.........2.............3.6....3..8..41;r5c9;r6c9;r1c7;r3c7;456
3.5.4..8..1...8..5...39..1..3....2.7.9.....61....64......7.....8.9....7.7...82...;r7c1;r7c3;r8c5;r8c6;136
..3.....4.4213.....9.5.......9...83..1...3..5..8...7.....9....2..47.2.1.1....59.7;r8c5;r9c5;r3c6;r5c4;468
3.....4.2..26......6.4...9.14.256...9.....1....6..8..5..........2.1.........9.31.;r3c1;r3c3;r2c7;r2c9;1578
.2.9..4..6...4...1....5....3.....7....8.953.........86..2....6..5...4.7...4..2.1.;r2c6;r3c6;r4c4;r6c5;1378
..2.589......34.8....7.93...5..9...16...8.53...1........6..3...7...4..5........62;r1c4;r2c4;r5c6;r8c6;126
2....1....9......17..8.39...6..7...3...1.5.6...5.3..4.1.37..8...8......6....2....;r7c6;r8c6;r4c4;r6c4;469
.1..92.......1..2....6.74.95..8.......4...8..6......931..7...3......5.8.4.7.6....;r2c4;r2c6;r1c7;r1c9;358
1......8....71..36.6.3.4.5....5..6..75..6...2..9.......1...5..9.....8.1.9...4.5..;r7c4;r8c4;r1c6;r2c6;269
.....17.86.8..........67..34.........2..9.6...6..73..128..5.1.4......2.....98....;r2c7;r2c9;r1c4;r1c5;245
.....1.649......3.143.....5.5...2...8..17..9..9.86.7......8.2.......7...5.862..7.;r7c4;r8c4;r1c5;r2c5;345
..1..5.......7...9....268..92..5...3..53.2.84.3.....514...9.....9...7...8..2..7..;r2c4;r3c4;r4c6;r6c5;148
1..5...4...6.2..1.532.9.....5.7.3..1.......8...1.69...42.........5....36......8.7;r4c8;r6c8;r3c7;r7c9;5679
.1.......4.92...13....59..8.8..4....1..6.....9.........9...7.3...7.3.4..64.5.2..9;r2c7;r3c7;r7c9;r9c8;2567
.......1..4.9........1.35.6.1..3..6..3...7.5...46....8.86.7....7.1.9....3.....28.;r4c4;r5c4;r7c6;r8c6;258
...8.........5.821.2..7...9.589..1....6........4.8.9.74..........91....6..3..94..;r2c4;r2c6;r1c1;r1c2;346
75.2...63.83............9.72....5.1.....6......68........416.3.3...7.2..1..5...4.;r9c2;r9c3;r7c7;r7c9;789
6.......7.37.5.461...9....3..6.....2.5....1..72...16..5..1..7.......3..4....27.3.;r8c7;r9c7;r1c8;r3c8;589
..5.7...6.134..95......94....7..21.5.4.1.........6......97......8.......7....1.32;r4c4;r6c4;r1c6;r9c5;389
..4...7....8.6.3..6..3.9.18.5.......29......6..6..45.3..9836...7.25..............;r8c7;r8c8;r9c1;r9c2;368
....3..4...8.5.......8..12........9..247.....8.1.4.7..7..1.8...1.64.9...........1;r5c7;r5c9;r4c4;r6c6;356
3....1.6...4.....7.76..324....162.7....8....3.........83..9..2...7.......6.7.4.3.;r5c3;r6c3;r1c2;r9c1;2589
26.4.......12.......7.96..............26.87....8.75.6.......8..34......2.25.....1;r5c8;r5c9;r6c1;r6c2;139
......12.....6..8.73......9.74..8..55....46....26..47...719....3.........9..2..5.;r5c8;r5c9;r4c4;r6c2;1289
8..96..1..76.1....1.......3...4.28.....8.1.5..........3.76....9.4.2...6.6.9...4..;r7c7;r7c8;r8c3;r9c2;128
......8.....1...591.926......4.31....7.....95......7.......6.....3..2.4..28.93...;r1c5;r2c5;r5c6;r6c6;458
.7.5...3.45...3..........48...681..9..9...6...2..7.3.......62.51..2.......2....17;r1c3;r2c3;r5c2;r6c1;168
7.3..1.4...59..8..48.23.1..6.7.....9...1.....2...65........46.....8....3.......8.;r1c7;r1c9;r2c2;r3c3;269
7...2.8.4....7...1..84...2.1.....368.2.....4....6.7.9..65......37.......4...51..3;r8c4;r8c6;r7c7;r7c9;249
..7..146.5......8.........98.5..39......8.1....97.4.....3......7....834.9...278..;r2c7;r3c7;r6c8;r7c9;257
6.........5...24..3.9.6..1.....2......69....17.3...89...58....7............59.6.8;r4c7;r5c7;r1c9;r3c9;235
5....9.1.4..6..5.....4....6.9.......6.8...1.........83..182.....2..3..79.6...4...;r4c8;r5c8;r7c9;r8c7;456
.....5.7.6.....5.893.6........9..8...2.53......9..2...84.....9.....4..21.....1...;r7c5;r7c6;r8c7;r9c9;356
....53.466...2......3...8..4.....6.3.897....1.5.2.......4..7..........6216.....8.;r7c5;r8c5;r5c6;r6c6;146
.5...2.6.9..8....5.....1..94.36..1.8.8......47..........8.2.41..2.1...36.....65..;r2c3;r3c3;r5c1;r6c2;126
..45..6...........5..6....3....28.6..9...6.8..281.97..........23.....5.4..2..3.1.;r5c1;r5c3;r4c4;r6c5;347
....4..5.3.....4866.....7..7...8..4..9...5.6..8..3...7..24.85....13...2....29....;r8c1;r8c2;r9c7;r9c9;468
......4..3...7.9.....9...1..27.4..5.83.......6....8......5.4...4.27..1...58.....6;r7c2;r8c2;r1c3;r2c3;169
.3.....87.9.........1.....3.....6.2.8..2..31..7.5...4.95..176....7.6......38.54..;r4c2;r5c2;r8c1;r9c1;146
.3.25..8...6...4..........52..9......8.....246...1...98.51...3..1.3.........8..7.;r7c7;r7c9;r8c5;r9c2;269
..2..9.......45....9....3.2...8579.4.7......5.4.......46..7...913...48....7.3....;r7c3;r8c3;r5c1;r6c1;589
284.......7.6....4..68..9.....9..3.5...5..7121.3.6........95..........8..4.1.2...;r2c6;r3c6;r4c5;r5c5;134
.....25.838.........47...9....2..9..823.4.1.6..6......6.........37.....4..5684...;r1c5;r3c5;r4c6;r6c6;136
.....2.53..3.87..22...4..........56.....68.3...7.....8..1..6...7.4....96.95.3.1..;r7c1;r7c2;r8c7;r9c8;238
2...........517..2....2.4.57.3..9.2...92..6......3....18......9.7....5..4..3.8...;r4c9;r6c9;r8c8;r9c8;1478
17......2..9...1.7.5.9..........19.6...5...78..4........6..4...3...8.2.4..52.68..;r7c4;r7c5;r9c8;r9c9;139
1...4...69.471........581.....17..3..3......8...4...1...........62...4..3..8...92;r1c4;r3c4;r7c5;r8c5;239

For Denis, here are the statistics by clue count for JE3/JE4 and JE3/4 with eliminations:

Code: Select all
`Green zone:    Puzzles  JE3  JE4  JE3  JE420        821      66722    11495    9    7    5    523    71975   83   29   22    724   175668  167   66   61   2225   190921  215   43   71   2126   100264  104   30   42   1327    27129   32    9    9    728     3985    2    229      30730       1931        732        233        3Grey zone:    Puzzles  JE3  JE4  JE3  JE420        221      28322     5814    3    1    1    123    36563   17    5    6    424    87547   29    6   10    225    91557   39   10   16    626    46586   14    2    527    12283    2    128     179429      14930       10`

denis_berthier wrote:
blue wrote:One more note: For both puzzle lists, there were puzzles containing 100-200 exocets (of general type).
This didn't happen for champagne's "potential hardest" list.
For the grey zone puzzles, it was rare: nothing with >= 100 exocets, in the "filtered" tables, 8 with >= 100 in the "all" tables.
For the green zone, it happens often enough to effect the "exocets per 'puzzle with an exocet'" ratio -- 39 and 475 puzzles, respectively.

After elimination of the candidates in direct contradiction with the clues, there remain in general between 200 and 250 candidates. I probably don't understand what "exocet of general type" means, but whatever it means, it seems very strange that there can be almost as many instances of a "pattern" as there are candidates. Obviously, they cannot have independent eliminations. Does your "exocet of general type" rely on indirect contradictions (with more or less unrestricted length) between candidates?

By "exocet of general type", I meant exocets the way champagne defined them (including JE).
I use single digit templates in the search, requiring that every viable template for a base digit, either doesn't contain a base cell, or (does, and also) does contain a target cell (at least one).
[ I think that corresponds with champagne's definition. ]

The puzzles with a large number number of exocets, seem to be solvable using single digit templates.
After applying the "simple solving techniques", they seem to have a small number of empty cells, and a small number of candidates and digits with candidates.

Here is an example with 220 exocets with (standard) eliminations.

Code: Select all
`5...6.......7...4..392.1.5.2.1..6.......2.4........2.6.5.....37..6.17.....2.3.... ED=7.6/1.2/1.2+-------------+-----------------+-------------+| 5   4    7  | 389  6     389  | 39   1   2  || 1   2    8  | 7    59    359  | 6    4   39 || 6   3    9  | 2    4     1    | 7    5   8  |+-------------+-----------------+-------------+| 2   789  1  | 4    789   6    | 35   89  35 || 89  6    35 | 389  2     3589 | 4    7   1  || 4   789  35 | 1    5789  3589 | 2    89  6  |+-------------+-----------------+-------------+| 89  5    4  | 6    89    2    | 1    3   7  || 3   89   6  | 589  1     7    | 589  2   4  || 7   1    2  | 589  3     4    | 589  6   59 |+-------------+-----------------+-------------+73 "live" candidates`

The 220 exocets (with types):
Hidden Text: Show
g.4(3589) r12c6 r5c4 r6c5
h.2(89) r46c8 r19c7
h.3(589) r89c4 r26c5
h.4(3589) r5c13 r6c56
k.2(89) r46c8 r18c4
k.2(89) r46c8 r1c4 r2c5
k.2(89) r46c8 r1c4 r5c6
k.2(89) r46c8 r1c4 r7c1
k.2(89) r46c8 r1c4 r9c9
k.2(89) r46c8 r1c47
k.2(89) r46c8 r1c7 r5c1
k.2(89) r46c8 r1c7 r6c6
k.2(89) r46c8 r1c7 r7c5
k.2(89) r46c8 r1c7 r8c2
k.2(89) r46c8 r27c5
k.2(89) r46c8 r2c5 r5c1
k.2(89) r46c8 r2c5 r6c6
k.2(89) r46c8 r2c5 r8c2
k.2(89) r46c8 r2c5 r9c7
k.2(89) r46c8 r56c6
k.2(89) r46c8 r5c1 r8c4
k.2(89) r46c8 r5c1 r9c9
k.2(89) r46c8 r5c16
k.2(89) r46c8 r5c6 r7c5
k.2(89) r46c8 r5c6 r8c2
k.2(89) r46c8 r5c6 r9c7
k.2(89) r46c8 r6c6 r7c1
k.2(89) r46c8 r6c6 r8c4
k.2(89) r46c8 r6c6 r9c9
k.2(89) r46c8 r7c1 r9c7
k.2(89) r46c8 r7c5 r8c4
k.2(89) r46c8 r7c5 r9c9
k.2(89) r46c8 r8c2 r9c9
k.2(89) r46c8 r8c24
k.2(89) r46c8 r8c4 r9c7
k.2(89) r46c8 r9c79
k.3(359) r2c56 r4c9 r8c4
k.3(389) r1c46 r2c9 r6c6
k.3(389) r1c46 r2c9 r9c7
k.3(389) r1c46 r49c7
k.3(389) r1c46 r4c7 r5c1
k.3(389) r1c46 r4c7 r6c6
k.3(389) r1c46 r4c7 r7c5
k.3(389) r1c46 r4c7 r8c2
k.3(389) r1c46 r4c78
k.3(389) r1c46 r6c36
k.3(589) r89c4 r2c5 r5c3
k.3(589) r89c4 r2c56
k.3(589) r89c4 r49c9
k.3(589) r89c4 r5c36
k.3(589) r89c7 r1c4 r4c9
k.3(589) r89c7 r4c89
k.3(589) r89c7 r4c9 r5c1
k.3(589) r89c7 r4c9 r6c6
k.3(589) r89c7 r4c9 r7c5
k.3(589) r89c7 r4c9 r8c2
k.3(589) r9c79 r18c4
k.3(589) r9c79 r6c6 r8c4
k.4(3589) r12c6 r6c35
o.2(89) r57c1 r18c4
o.2(89) r57c1 r19c7
o.2(89) r57c1 r1c4 r2c5
o.2(89) r57c1 r1c4 r5c6
o.2(89) r57c1 r1c4 r9c9
o.2(89) r57c1 r1c47
o.2(89) r57c1 r1c7 r4c8
o.2(89) r57c1 r1c7 r6c6
o.2(89) r57c1 r1c7 r7c5
o.2(89) r57c1 r1c7 r8c2
o.2(89) r57c1 r27c5
o.2(89) r57c1 r2c5 r4c8
o.2(89) r57c1 r2c5 r6c6
o.2(89) r57c1 r2c5 r8c2
o.2(89) r57c1 r2c5 r9c7
o.2(89) r57c1 r4c28
o.2(89) r57c1 r4c8 r5c6
o.2(89) r57c1 r4c8 r8c4
o.2(89) r57c1 r4c8 r9c9
o.2(89) r57c1 r56c6
o.2(89) r57c1 r5c6 r7c5
o.2(89) r57c1 r5c6 r8c2
o.2(89) r57c1 r5c6 r9c7
o.2(89) r57c1 r6c6 r8c4
o.2(89) r57c1 r6c6 r9c9
o.2(89) r57c1 r7c5 r8c4
o.2(89) r57c1 r7c5 r9c9
o.2(89) r57c1 r8c2 r9c9
o.2(89) r57c1 r8c24
o.2(89) r57c1 r8c4 r9c7
o.2(89) r57c1 r9c79
o.2(89) r7c1 r8c2 r18c4
o.2(89) r7c1 r8c2 r19c7
o.2(89) r7c1 r8c2 r1c4 r2c5
o.2(89) r7c1 r8c2 r1c4 r5c6
o.2(89) r7c1 r8c2 r1c4 r9c9
o.2(89) r7c1 r8c2 r1c47
o.2(89) r7c1 r8c2 r1c7 r4c8
o.2(89) r7c1 r8c2 r1c7 r5c1
o.2(89) r7c1 r8c2 r1c7 r6c6
o.2(89) r7c1 r8c2 r1c7 r7c5
o.2(89) r7c1 r8c2 r27c5
o.2(89) r7c1 r8c2 r2c5 r4c8
o.2(89) r7c1 r8c2 r2c5 r5c1
o.2(89) r7c1 r8c2 r2c5 r6c6
o.2(89) r7c1 r8c2 r2c5 r9c7
o.2(89) r7c1 r8c2 r4c28
o.2(89) r7c1 r8c2 r4c8 r5c6
o.2(89) r7c1 r8c2 r4c8 r8c4
o.2(89) r7c1 r8c2 r4c8 r9c9
o.2(89) r7c1 r8c2 r56c6
o.2(89) r7c1 r8c2 r5c1 r8c4
o.2(89) r7c1 r8c2 r5c1 r9c9
o.2(89) r7c1 r8c2 r5c16
o.2(89) r7c1 r8c2 r5c6 r7c5
o.2(89) r7c1 r8c2 r5c6 r9c7
o.2(89) r7c1 r8c2 r6c6 r8c4
o.2(89) r7c1 r8c2 r6c6 r9c9
o.2(89) r7c1 r8c2 r7c5 r8c4
o.2(89) r7c1 r8c2 r7c5 r9c9
o.2(89) r7c1 r8c2 r8c4 r9c7
o.2(89) r7c1 r8c2 r9c79
o.2(89) r7c15 r18c4
o.2(89) r7c15 r19c7
o.2(89) r7c15 r1c4 r2c5
o.2(89) r7c15 r1c4 r5c6
o.2(89) r7c15 r1c4 r9c9
o.2(89) r7c15 r1c47
o.2(89) r7c15 r1c7 r4c8
o.2(89) r7c15 r1c7 r5c1
o.2(89) r7c15 r1c7 r6c6
o.2(89) r7c15 r1c7 r8c2
o.2(89) r7c15 r2c5 r4c8
o.2(89) r7c15 r2c5 r5c1
o.2(89) r7c15 r2c5 r6c6
o.2(89) r7c15 r2c5 r8c2
o.2(89) r7c15 r2c5 r9c7
o.2(89) r7c15 r4c28
o.2(89) r7c15 r4c8 r5c6
o.2(89) r7c15 r4c8 r8c4
o.2(89) r7c15 r4c8 r9c9
o.2(89) r7c15 r56c6
o.2(89) r7c15 r5c1 r8c4
o.2(89) r7c15 r5c1 r9c9
o.2(89) r7c15 r5c16
o.2(89) r7c15 r5c6 r8c2
o.2(89) r7c15 r5c6 r9c7
o.2(89) r7c15 r6c6 r8c4
o.2(89) r7c15 r6c6 r9c9
o.2(89) r7c15 r8c2 r9c9
o.2(89) r7c15 r8c24
o.2(89) r7c15 r8c4 r9c7
o.2(89) r7c15 r9c79
o.3(389) r15c4 r6c36
o.3(389) r1c67 r2c5 r5c4
o.3(389) r1c67 r2c5 r6c3
o.3(389) r1c67 r58c4
o.3(389) r1c67 r5c4 r9c9
o.3(389) r1c67 r5c46
o.3(389) r1c67 r5c6 r6c3
o.3(389) r1c67 r6c3 r7c1
o.3(389) r1c67 r6c3 r8c4
o.3(389) r1c67 r6c3 r9c9
o.3(389) r5c14 r1c4 r6c3
o.3(389) r5c14 r4c8 r6c3
o.3(389) r5c14 r6c3 r7c5
o.3(389) r5c14 r6c3 r8c2
o.3(389) r5c14 r6c3 r9c7
o.3(389) r5c14 r6c36
o.3(589) r27c5 r56c6
o.3(589) r7c5 r9c4 r1c4 r4c9
o.3(589) r7c5 r9c4 r1c4 r8c7
o.3(589) r7c5 r9c4 r4c89
o.3(589) r7c5 r9c4 r4c9 r5c1
o.3(589) r7c5 r9c4 r4c9 r6c6
o.3(589) r7c5 r9c4 r4c9 r8c2
o.3(589) r7c5 r9c4 r4c9 r9c7
o.3(589) r7c5 r9c4 r6c6 r8c7
o.3(589) r8c27 r19c4
o.3(589) r8c27 r1c4 r4c9
o.3(589) r8c27 r4c89
o.3(589) r8c27 r4c9 r5c1
o.3(589) r8c27 r4c9 r6c6
o.3(589) r8c27 r4c9 r7c5
o.3(589) r8c27 r4c9 r9c7
o.3(589) r8c27 r6c6 r9c4
o.3(589) r8c47 r26c5
o.3(589) r8c47 r2c5 r5c3
o.3(589) r8c47 r2c56
o.3(589) r8c47 r49c9
o.3(589) r8c47 r5c36
o.3(589) r8c7 r9c9 r26c5
o.3(589) r8c7 r9c9 r2c5 r5c3
o.3(589) r8c7 r9c9 r2c56
o.3(589) r8c7 r9c9 r4c9 r8c4
o.3(589) r8c7 r9c9 r5c36
o.3(589) r9c47 r1c4 r4c9
o.3(589) r9c47 r4c89
o.3(589) r9c47 r4c9 r5c1
o.3(589) r9c47 r4c9 r6c6
o.3(589) r9c47 r4c9 r7c5
o.3(589) r9c47 r4c9 r8c2
o.3(589) r9c49 r26c5
o.3(589) r9c49 r2c5 r5c3
o.3(589) r9c49 r2c56
o.3(589) r9c49 r4c9 r8c4
o.3(589) r9c49 r5c36
o.3(789) r47c5 r1c4 r6c2
o.3(789) r47c5 r6c2 r9c7
o.3(789) r47c5 r6c26
o.3(789) r4c58 r1c4 r6c2
o.3(789) r4c58 r6c2 r9c7
o.3(789) r4c58 r6c26
o.3(789) r6c28 r1c7 r4c5
o.3(789) r6c28 r24c5
o.3(789) r6c28 r4c5 r5c6
o.3(789) r6c28 r4c5 r8c4
o.3(789) r6c28 r4c5 r9c9
o.4(3789) r4c5 r5c4 r6c23
o.4(5789) r6c58 r2c6 r4c2
o.4(5789) r6c58 r4c2 r5c3

126 of them are 2-digit exocets.

Regards,
Blue.
blue

Posts: 601
Joined: 11 March 2013

### Re: JExocet Pattern Defintion

blue wrote:Here is an example with 220 exocets with (standard) eliminations.
Code: Select all
`5...6.......7...4..392.1.5.2.1..6.......2.4........2.6.5.....37..6.17.....2.3.... ED=7.6/1.2/1.2`

[...]
The puzzles with a large number number of exocets, seem to be solvable using single digit templates.

Code: Select all
`whip[2]: c1n8{r5 r7} - b8n8{r7c5 .} ==> r5c4 <> 8whip[2]: r5n8{c1 c6} - c5n8{r6 .} ==> r7c1 <> 8singles to the end`

This illustrates what you say about 1-digit templates.

Generally speaking, I don't think exocets will have much interest in the "green zone". Of course, all depends on what rules one chooses to use before them.

A short comment about the stats with/without eliminations: they give a rough idea of how useful it is to make a difference between useful instances and useless ones.
denis_berthier
2010 Supporter

Posts: 1258
Joined: 19 June 2007
Location: Paris

### Re: JExocet Pattern Defintion

blue wrote:For champagne, these are the 129 that I find in the grey area:

I tried a quick match "by eyes", but it seems that the appearance of JE's is very sensitive to the level of moves at the start.

each of the 2 lists has puzzles not in the other one.

this requires some investigations to do later

I work currently on a similar task which is to filter trivial puzzles in the sample I made in the vicinity of the hardest.
champagne
2017 Supporter

Posts: 6205
Joined: 02 August 2007
Location: France Brittany

### Re: JExocet Pattern Defintion

Thanks for the analysis, champagne, blue and Denis.
Your results are much better than i had expected to get out of my puzzle sets.
I am short of time now, but as soon as i can, i will have a closer look at the details of blues' stats.
eleven

Posts: 1783
Joined: 10 February 2008

### Re: JExocet/Exocet statistics

Hi Denis,

denis_berthier wrote:
Code: Select all
`Weights:#clues      %puzzles20          0.021          0.00003422          0.003423          0.14924          2.2825          13.4226          31.9427          32.7428          15.4829          3.5630          0.4131          0.022`

Application of the formula in the above-mentioned post

Code: Select all
`Unbiased proportion of puzzles having an exocetnb-clues   weighted-proportion * 10022         3/5814 * 0.0034   = 1.75438596491228e-0623         14/36563 * 0.149  = 5.70522112518119e-0524         19/87547 * 2.28   = 0.00049481992529726925         24/91557 * 13.42  = 0.0035178085782627226         12/46586 * 31.94  = 0.0082273644442536427         2/12283 * 32.74   = 0.0053309452088252128         0                 = 029         1/149 * 0.022     = 0.000147651006711409`

It seems like you should be using a different set of weights, specifically for grey zone puzzles.
Weights from a table built like this:

Code: Select all
`Weights:#clues      %puzzles   Prob(in grey zone)   product        %grey_zone_puzzles20          0.0        P2021          0.000034   P2122          0.0034     P2223          0.149      P2324          2.28       P2425          13.42      P25                  X25=13.42*P25  100*X25/(X20+X21+...+X31)26          31.94      P26                  (etc.)         (etc.)27          32.74      P2728          15.48      P2829          3.56       P2930          0.41       P3031          0.022      P31`

I may be wrong, but it doesn't seem like the probabilities (P20-P31) would be the same (or even roughly the same) for each clue count. You probably have the right kind of data to compute the values -- for each clue count, a truly random selection of puzzles.
[ "Probabliity", maybe isn't the right word. "Percentage" or "fraction" would be better. It's the same number in any case. ]

Regards,
Blue.
blue

Posts: 601
Joined: 11 March 2013

### Re: JExocet/Exocet statistics

Hi Blue,

blue wrote:It seems like you should be using a different set of weights, specifically for grey zone puzzles.

In theory, you are right.
However (and this is one thing I should have recalled in the other thread), the correlation coefficient between SER (or W rating) and #clues is very small (0.12), so I don't think the weights depend much on the SER (at least for non-extreme numbers of clues and non-extreme SER - but this is precisely what we have). In any case, it can't change the order of magnitude of the result.
Considering that there are many other causes of uncertainty or debate about what should be taken into account (exact definitions, rules applied before, my "grey zone" vs champagne's broader "grey area", ...), I think more detailed calculations are not necessary.
denis_berthier
2010 Supporter

Posts: 1258
Joined: 19 June 2007
Location: Paris

### Re: JExocet Pattern Defintion

FWIW, here is a solution of a puzzle studied by Leren ...

98.7.......7.65.........7..4...3..2..1......9..95..8..1......4...59..6.......2..3; ;2;0;match type;50;r1c5 r1c6 r3c3 r2c7 1234;r2c1 r2c2 r3c4 r1c7 234;;;4;;

#1. SER=9.7; UP22; r4c6=9=r3c5; LC(5B1) :=> -5r3c89; UP24
#2. ALS(234)r2c12 :
Code: Select all
`+------------------------+-----------------------+-----------------------+| 9       8      146(23) | 7        124    134   | 145(23)  1356   12456 || (23)    4-23   7       | 148(23)  6      5     | 149(23)  1389   1248  || 2356    23456  146(23) | 148(23)  9      1348  | 7        1368   12468 |+------------------------+-----------------------+-----------------------+| 4       567    68      | 168      3      9     | 15       2      1567  || 235678  1      68(23)  | 468(2)   2478   4678  | 45(3)    3567   9     || 2367    2367   9       | 5        1247   1467  | 8        1367   1467  |+------------------------+-----------------------+-----------------------+| 1       23679  68(23)  | 68(3)    578    3678  | 59(2)    4      2578  || 2378    2347   5       | 9        1478   13478 | 6        178    1278  || 678     4679   468     | 1468     14578  2     | 159      15789  3     |+------------------------+-----------------------+-----------------------+`
a. r2c12=23->HP(23)r57c3; FSF(2C437)+FSF(3C734) has no solution :=> r2c2=4; r9c3=4; UP25
b. r2c12=24->FSF(2C437) :=> r3c4=2; Contradiction(Singles) :=> r2c12=34
c. FSF(3C437)+XW(4C47) :=> r1c56=12; UP81
JC Van Hay

Posts: 719
Joined: 22 May 2010

### Re: JExocet Pattern Defintion

Here's my current draft for specifying the eliminations from a Double Exocet with 4 targets. In Lerens example I made such a mess of, the unconditional eliminations would kill the puzzle in one shot. It looks like a good one to use as an example.

Double JEs

Depending on the positions of the base cells and their corresponding targets there may be either 3 or 4 target cells.

When there are 4 target cells
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`*-------------*-------------*-------------*    ab" = base digits r1c12  ab' = targets | ab" ab" \   | cdx cd' cdx | *   *   *   |    cd" = base digits r3c89  cd' = targets| cdx cdx cd' | *   \   *   | ab' abx abx |    x  = any other digits | *   *   *   | abx ab' abx | \   cd" cd" |    \  = companion cells    *-------------*-------------*-------------*    *  = abcd can be eliminated`
This is how the two pairs of base digits are forced to repeat.

As with the single JE, the target cells (ab)r2c6,r34 and (cd)r1c5,r2c3 must contain different digits.

1. Unconditional Eliminations
a) Any base digit in the 6 cells seen by both base pairs and 2 two cells seen by all 4 targets
b) Any non-base digit in the 4 target cells
c) Fin cells for the partial fish for each of the 4 base digits

2. Conditional Eliminations
a) If one of the target cells is known, the same digit can be eliminated from the other 3 target cells.
b) If any of the cells containing 'x' digits are known, the non-base digits in the same mini-line can be eliminated.
c) If one of the 'x' digits is locked in a mini-line the other 'x' digits in the mini-line can be eliminated

3. Pattern Inferences
a) Instances of the same digit in each pair of target cells are weakly linked
b) The non base candidates in the mini-lines containing a target cell form a weak inference set
c) A digit confined to a mini-line containing a target cell will make a hidden triple with the true base digits in that target.

4 Proof
1) The digits occupying the two pairs of base cells must also occupy a target cell to bring the number of truths in the partial fish columns to 3.
2) But if a digit is true on both pairs of base cells, it can't be true in any of the target cells as each base pair see the target cells for the other.
3) Consequently no digit can be common to both base pairs and, together, they must hold 4 different digits.
4) From 1) this in turn will require the 4 target cells to hold one instance of each of the base digits.
David P Bird
2010 Supporter

Posts: 1007
Joined: 16 September 2008
Location: Middle England

### Re: JExocet Pattern Defintion

to go in the direction of a better efficiency of JEs found in the green area, I added three filters

1) no analysis if the number of unknown go below 50
2) no JE accepted if one of the digits of the base is known in the band
3) no JE without elimination if it is a single JE (target 2 cells)

I did not retain David's request for point 3 (no JE without elimination) because it killed some double exocet patterns.
The new run cleared 87% of the JE found in the first run in the green area.

I have now 0.5% of selected puzzles against 3.78% and I reached in the green area a volume authorizing the uploading of the full lot of puzzles eligible to the JE in that area.

I am checking the status for other kind of exocets (excluding the last findings of blues) to decide of the best way to share that.

More filters can be studied on the reduced file
champagne
2017 Supporter

Posts: 6205
Joined: 02 August 2007
Location: France Brittany

### Re: JExocet Pattern Defintion

An improved solution for puzzle 98.7.......7.65.........7..4...3..2..1......9..95..8..1......4...59..6.......2..3 is as follows:

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`*--------------------------------------------------------------------------------*| 9       8       12346    | 7       124     134      | 12345   1356    12456    || 23      234     7        | 12348   6       5        | 234-19  1389    1248     || 235-6   2345-6  1234-6   | 12348   9       1348     | 7       1368    12468    ||--------------------------+--------------------------+--------------------------|`

Exocet 1 : r1c5 r1c6 r3c3 r2c7 1234;

Eliminate non-base candidates in Targets => - 9 r2c7, - 6 r3c3;

Tertiary Equivalence r2c7==r3c12(5), r3c3 => - 6 r3c12, - 1 r2c7; lclste

Leren
Leren

Posts: 3216
Joined: 03 June 2012

### Re: JExocet Pattern Defintion

While it's gone quiet here...

I've been exploring the possible configurations of the target cells in different types of single and double JEs with paired target cells in different boxes. The paired targets will either be collinear (one the same line) or diagonal (on different lines). We can therefore categorise single and double JEs by the number of target cells they have and whether these are diagonal (D) or collinear (C) for each pair of base cells.

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`*-------*-------*-------*  *-------*-------*-------*| B B . | . . . | . . . |  | B B . | . . . | . . . |    B, b = base cells | . . . | . \ . | T . . |  | . . . | . T . | T . . |    T, t = target cells| . . . | . T . | \ . . |  | . . . | . \ . | \ . . |    \ = companion cells*-------*-------*-------*  *-------*-------*-------*    JE2D                        JE2C     *-------*-------*-------*  *-------*-------*-------*   *-------*-------*-------*  | B B t | . \ . | . . . |  | B B \ | . \ . | . . . |   | B B \ | . \ . | . . . |  | . . \ | . T'. | \ . . |  | . . t | . T'. | \ . . |   | . . t | . T'. | T . . |  | . . . | . \ . | T b b |  | . . . | . \ . | T b b |   | . . . | . \ . | \ b b |*-------*-------*-------*  *-------*-------*-------*   *-------*-------*-------*JE3DD                       JE3DC                        JE3CC*-------*-------*-------*  *-------*-------*-------*   *-------*-------*-------*  | B B \ | . t . | . . . |  | B B t | . t . | . . . |   | B B t | . t . | . . . || . . t | . \ . | T . . |  | . . \ | . \ . | T . . |   | . . \ | . \ . | \ . . || . . . | . T . | \ b b |  | . . . | . T . | \ b b |   | . . . | . T . | T b b |*-------*-------*-------*  *-------*-------*-------*   *-------*-------*-------*JE4DD                       JE4DC                       JE4CC        *-------*-------*-------*  *-------*-------*-------*   *-------*-------*-------*  | B B t | . . \ | . . . |  | B B \ | . . \ | . . . |   | B B \ | . . \ | . . . || . . \ | \ . t | T . . |  | . . t | \ . t | T . . |   | . . t | T . t | T . . || . . . | T . . | \ b b |  | . . . | T . . | \ b b |   | . . . | \ . . | \ b b |*-------*-------*-------*  *-------*-------*-------*   *-------*-------*-------*JE4DD                       JE4DC                       JE4CC        *-------*-------*-------*  *-------*-------*-------*   *-------*-------*-------*  | B B t | . . \ | . . . |  | B B t | . . t | . . . |   | B B t | . . t | . . . || . . \ | T . t | \ . . |  | . . \ | T . \ | \ . . |   | . . \ | \ . \ | \ . . || . . . | \ . . | T b b |  | . . . | \ . . | T b b |   | . . . | T . . | T b b |*-------*-------*-------*  *-------*-------*-------*   *-------*-------*-------*JE4DD                       JE4DC                       JE4CC`

For JE+ or Twin JExocet patterns the D or C suffix won't be known as there is uncertainty which object cell in a pair will be the target and which will be the companion. In these cases a T suffix should be used.

I'm using these grids to check what inferences that will be available under different conditions. In the case of the Twin JExocets some inferences won't be available until the identity of the target cell is established which is easy enough to describe. So far I haven't looked at cases where the two targets associate with a base pair are in the same box because I'd like to see if they survive the screening regime Champagne's now using. I have an intuition that they may be rather trivial to solve and might not get through.

I suggest that this categorisation system should be adopted in place of the one based on the number of digits in the base sets which is proving troublesome. It allows the available inferences to be identified quite neatly and should go a long way to satisfying Denis' requirements.
David P Bird
2010 Supporter

Posts: 1007
Joined: 16 September 2008
Location: Middle England

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