## Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

### Re: Exotic patterns a resume

champagne I now understand your distinctions, and so it seems does ronk. As the analysis you then need to perform to convert a partial Exocet to an Exocet is outside my experience I'll stay quiet on that subject.

You wrote:That thread is titled "exotic patterns a resume" and I opened it to exchange on all tools that can be used in hardest puzzles. I hope it will stay true and I would not see it limited to the Jexocet.

Yes I can appreciate that. I consider it your thread and won't do anything to spoil your aim for it.

All I would ask is that when you cover the topic of what to do once an Exocet (and presumably a JExocet) is found, you distinguish between the two of them when the methods diverge. If that is done then it probably wouldn't be necessary to split the thead into two.
David P Bird
2010 Supporter

Posts: 1040
Joined: 16 September 2008
Location: Middle England

### Re: Exotic patterns a resume

ronk wrote:Below is (I think) a "partial exocet" for puzzle #12177, simpler than the one on your web page. Note the targets are r4c2=1236 and r7c1=1236 just as if it were a "full exocet." This can only happen because there is an indication for the other target. Evidently this cause has yet to be formulated in the definition, so I'll try to do so.
___

interesting view it seems we have to interleaved partial exocet (unchecked for r12c7 as target)
clearly a logic to investigate

BTW I am not sure I published the list of puzzles having a similar potential
champagne
2017 Supporter

Posts: 6742
Joined: 02 August 2007
Location: France Brittany

### Re: Exotic patterns a resume

FWIW: For puzzle "12177", three of the four values in r12c3 work as a JExocet:

Code: Select all
`98.7.....7...6......5..97..5....84...9.6...3...4.2...1.5....8.....3....6....1..2.;10.80;10.80;10.50;GP;kz0;12177;23 +--------------------------------------------------------------------------------+ |  9       8       1236    |  7       345     12345   |  12356   1456    2345    | |  7       1234    123     |  12458   6       12345   |  12359   14589   234589  | |  12346   12346   5       |  1248    348     9       |  7       1468    2348    | |--------------------------+--------------------------+--------------------------| |  5       12367   12367   |  19      379     8       |  4       679     279     | |  128     9       1278    |  6       457     1457    |  25      3       2578    | |  368     367     4       |  59      2       357     |  569     56789   1       | |--------------------------+--------------------------+--------------------------| |  12346   5       123679  |  249     479     2467    |  8       1479    3479    | |  1248    1247    12789   |  3       45789   2457    |  159     14579   6       | |  3468    3467    36789   |  4589    1       4567    |  359     2       34579   | +--------------------------------------------------------------------------------+ # 173 eliminations remainr12c3=1 => r4c2=1 and/or r7c1=1r12c3=3 => r4c2=3 and/or r7c1=3r1 c3=6 => r4c2=6`

That leaves r12c3=2, which doesn't comply with my understanding of a JExocet. However, of the 13 combinations of <1236> that are acceptable for this grid, only 5 combinations contain r12c3=2, and each of these contain values from the base set in r4c2 and r7c1.

Hidden Text: Show
Code: Select all
` +-----------------------+ | 9 8 3 | 7 . 1 | 6 . 2 | | 7 . 2 | . 6 3 | 1 . . | | 1 6 5 | 2 . 9 | 7 . 3 | |-------+-------+-------| | 5 2 . | 1 3 8 | 4 6 . | | . 9 1 | 6 . . | 2 3 . | | 6 3 4 | . 2 . | . . 1 | |-------+-------+-------| | 3 5 6 | . . 2 | 8 1 . | | 2 1 . | 3 . . | . . 6 | | . . . | . 1 6 | 3 2 . | +-----------------------+ +-----------------------+ | 9 8 3 | 7 . 1 | 2 6 . | | 7 . 2 | . 6 3 | 1 . . | | 6 1 5 | 2 . 9 | 7 . 3 | |-------+-------+-------| | 5 6 . | 1 3 8 | 4 . 2 | | 2 9 1 | 6 . . | . 3 . | | . 3 4 | . 2 . | 6 . 1 | |-------+-------+-------| | 3 5 6 | . . 2 | 8 1 . | | 1 2 . | 3 . . | . . 6 | | . . . | . 1 6 | 3 2 . | +-----------------------+ +-----------------------+ | 9 8 6 | 7 . 1 | 2 . 3 | | 7 . 2 | . 6 3 | 1 . . | | 3 1 5 | 2 . 9 | 7 6 . | |-------+-------+-------| | 5 6 . | 1 3 8 | 4 . 2 | | 2 9 1 | 6 . . | . 3 . | | . 3 4 | . 2 . | 6 . 1 | |-------+-------+-------| | 6 5 3 | . . 2 | 8 1 . | | 1 2 . | 3 . . | . . 6 | | . . . | . 1 6 | 3 2 . | +-----------------------+   # in solution +-----------------------+ | 9 8 2 | 7 . 3 | 1 6 . | | 7 . 3 | 1 6 . | 2 . . | | 6 1 5 | 2 . 9 | 7 . 3 | |-------+-------+-------| | 5 6 1 | . 3 8 | 4 . 2 | | 2 9 . | 6 . 1 | . 3 . | | . 3 4 | . 2 . | 6 . 1 | |-------+-------+-------| | 3 5 6 | . . 2 | 8 1 . | | 1 2 . | 3 . . | . . 6 | | . . . | . 1 6 | 3 2 . | +-----------------------+ +-----------------------+ | 9 8 2 | 7 . 3 | 1 6 . | | 7 . 3 | . 6 1 | 2 . . | | 6 1 5 | 2 . 9 | 7 . 3 | |-------+-------+-------| | 5 6 . | 1 3 8 | 4 . 2 | | 2 9 1 | 6 . . | . 3 . | | . 3 4 | . 2 . | 6 . 1 | |-------+-------+-------| | 3 5 6 | . . 2 | 8 1 . | | 1 2 . | 3 . . | . . 6 | | . . . | . 1 6 | 3 2 . | +-----------------------+`

I'm assuming that the relationship on <2> is represented somewhere in the results posted by others.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: Exotic patterns a resume

daj95376 wrote:I'm assuming that the relationship on <2> is represented somewhere in the results posted by others.

Not yet. I've been trying to find something simple, but so far, nothing as simple as expected. For #12177:
1. r12c3=1 implies strong inference (1)r4c2 = (1)r7c1
2. r12c3=3 implies (3)r4c2 = (3)r7c1
3. r1c3=6 implies r4c2=6 as a hidden single
Combine any two of a, b, and c, and there is effectively a remote hidden pair.

But there's still the <2>. If r12c3=12, based on Xsudo's result there is apparently the strong inference (126)r4c2 = (126)r7c1. But we already know of the existence of (1)r4c2 = (1)r7c1, implying (26)r4c2 = (26)r7c1. To be clear, this means if both candidates are missing from r4c2, one of them must exist in r7c1. I say "apparently" because I don't see it in the strong inferences of the Xsudo graphic, only as inferred from the candidates remaining in the target cells.

The result is similar for r12c3=23, i.e., (236)r4c2 = (236)r7c1.

The result for r12c3=26 is r4c2=6 and r7c1=26, allowing for the possibility of both target cells holding <6>.

champagne wrote:BTW I am not sure I published the list of puzzles having a similar potential

I don't believe you have yet. A few more might help clarify the rules for "partial exocets."
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Exotic patterns a resume

What bothers me about puzzle #12177 is that, even though three of the values in r12c3 act like an Exocet with respect to cells r4c2 and r7c1, the final solution does not.

Code: Select all
` +-----------------------+ | 9 8 6 | 7 . 1 | 2 . 3 | | 7 . 2 | . 6 3 | 1 . . | | 3 1 5 | 2 . 9 | 7 6 . | |-------+-------+-------| | 5 6 . | 1 3 8 | 4 . 2 |   r4c2=6 | 2 9 1 | 6 . . | . 3 . | | . 3 4 | . 2 . | 6 . 1 | |-------+-------+-------| | 6 5 3 | . . 2 | 8 1 . |   r7c1=6 | 1 2 . | 3 . . | . . 6 | | . . . | . 1 6 | 3 2 . | +-----------------------+   # in solution`

Would someone please remind me of the final objective???
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: Exotic patterns a resume

daj95376 wrote:What bothers me about puzzle #12177 is that, even though three of the values in r12c3 act like an Exocet with respect to cells r4c2 and r7c1, the final solution does not.

Would someone please remind me of the final objective???

that thread is dedicated to any "exotic pattern" that can help to solve potential hardest puzzles.

puzzle 12177 is a puzzle with a very high solving potential in floors 1236.
The final objective here is to find (if any )an easy logic similar to the already known that can lead to eliminations;

It appears that that puzzle is a partial "exocet pattern" and I developed a full solution based on that property.
Ronk has the finger on something different, but not yet clear in it's last post.

it's quite clear that the solution in that case is not one of the pair complying with the exocet digit per digit rules, so the result in the target is unpredictable.
champagne
2017 Supporter

Posts: 6742
Joined: 02 August 2007
Location: France Brittany

### Re: Exotic patterns a resume

here is a list of puzzles (including puzzle 12177) having a high solving potential using only 4 or 5 digits.
Unless I made an error in the selection process, there should be no exocet, no sk loop, no rank 0 multifish in it.

The last data in each line is the smallest digits group showing a good potential.
For some of these puzzles, a 5 digits group showed a much higher potential, but it seems reasonable to focus on the smallest group.

Hidden Text: Show
98.7.....7...6......5..97..5....84...9.6...3...4.2...1.5....8.....3....6....1..2.;12177;GP;kz0;1236;
98.7..6..5...6......6....7.8..4....3.4...2.1...5.9......8.5.7.....3...4......1..2;12742;GP;kz0;1234;
98.7.....6...9.7....7..5...5...4..3..4...2..1..98.......65..9......3...4.....1.2.;14518;GP;kz1a;1234;
..34..7...5...9..6..9.2.....1..97.6....2..1..8.....9...7..156......3..7........5.;2447;elev;1652;2348;
1...5......7.....6.897.......89....3.7.......5...3.4...3.6....8.....21......4..2.;5586;elev;L550;1245;
98.7..6..7...9..85..4......8...7.3....5.....4.....2.1.6..9...2..9..3.8.......1...;13227;GP;kz0;1245;
98.7..6....5.6........9..4.3......2..2...97....12....4.6..2.8....38..........7.5.;19896;GP;KZ1C;1345;
.....6.8...71..2.....32...1..1.4...7.6.....5.9.........9.........42....38....5.7.;2325;elev;L206;12347;
1....6....5.1...3...9.2..............7...5.1.....3.4.8..8...9.4..2.9....7....3.6.;5233;elev;2544;2489;
98.7..6......96..........5.7....94...3.4.......287....6...8.7...2.....3...1.....5;9470;GP;cy4;1235;
98.7.....6...8.7....7..5...5...4..3..4...2..1..96.......85..9......3..4......1..2;11747;GP;kz0;1234;
98.7..6..5...6......6.98...4..3...5...2.....1....7.9..1......2..3...78....5.....4;12758;GP;kz0;1245;
98.7.....7...6......5..87..5....98...7.6...4...3.2...1.5....3.....4...2.....1...6;16434;GP;Kz1 b;1246;
98.76....54....7.......5.8.8......4....3....2....1.6..7..6....3.5...9.7....2..1..;23722;GP;KZ1C;1236;
98.76....54....7.......5.8.8......4....3..6......2...17..6....2.5...9.7....1..3..;29918;GP;2011_12;1236;
..34..7...5...9.2.....1....23.....5...1.6.3..8..........46..........8.9....17.6..;5416;elev;2183;2589;
98.7.....6...5.8....5....7..4......3..98.........42.1...65..7......1..4......3..2;10031;GP;22ky5;1234;
98.7.....6...5.9....5....7..4......3..89.........42.1...65..7......1..4......3..2;10067;GP;22ky5;1234;
champagne
2017 Supporter

Posts: 6742
Joined: 02 August 2007
Location: France Brittany

### Twin JExocet Continuation

98.7..6..5.7.4..3...2......4...3..1..7......8..6...2.....3.4.9.....95.......7...1;r9c4 r9c6 r7c1 r8c8 268 Lot3:414

Code: Select all
` *-------------------------*-------------------------*-------------------------* | 9       8       134     | 7       125     13-2    | 6       245     45-2    |  | 5       16      7       | 12689   4       12689   | 189     3       29      |  | 136     1346    2       | 1569-8  1568    1369-8  | 14579-8 4578    4579    |  *-------------------------*-------------------------*-------------------------* | 4       259     589     | 25689   3       26789   | 579     1       5679    |  | 123     7       1359    | 14569-2 1256    169-2   | 3459    456     8       |  | 138     1359    6       | 1459-8  158     179-8   | 2       457     34579   |  *-------------------------*-------------------------*-------------------------* | 278-16  1256    158     | 3       16-28   4       | 578     9       2567    |  | 278-136 1346-2  134-8   | 16-28   9       5       | 3478    28-467  23467   |  | 36-28   34569-2 3459-8  | 28-6    7       28-6    | 345-8   456-28  1       |  *-------------------------*-------------------------*-------------------------*`

(268)TwinJExocet:r9c46,r8c8,(7)r78c1 => r7c1 <> 1, r8c1 <> 13, r8c8 <> 47

Compatibility check:
(2)r8c8 = (2)r1c8 - (2)r2c8 = (2#2)r29c46
(6)r8c8 = (6)r5c8 - (6)r9c1 = (6#2)r59c46 (incompatible)
(8)r8c8 = (8)r3c8 - (8)r2c7 = (8#2)r29c46
. . => r78c1,r9c46,r8c8 <> 6, (base & target cells)
. . r9c18 <> 28, r9c2 <>2, r9c7 <> 8, r7c5,r8c4 <> 28, (seen by base cells)
. . r8c2 <> 2, r8c3 <> 8, (seen by targets (278)r78c1 & (28)r8c8 )
. . r1c68 <> 2, r3c467 <> 8, (fin cells to "skewed" Swordfish)
. . r5c46 <> 2, r6c46 <> 8 (seen by the alternative X-wings (2)r9+[2|5]c46 & (8)r9+[2|4]c46)
(32 eliminations to this point from the nearly resolved pattern)

The key step now is to analyse the URs that can be made with the twin digit (7)r78c1 in the JExocet band
The threats are (27)r78c19 and (78)r78c16

(7)r6c8 = (7-8)r3c8 = (8-2)r8c8 =[JE]= (2#2)r78c19 -[UR]- (7#2)r78c19 = (7#2)r78c17 => r4c7 <> 7

This step, which is dependent on the derived JExocet inference, opens up the puzzle to being solvable by AICs. I suspect it may be a common feature of Twin JExocets, and without it I would have to resort to it nets.
David P Bird
2010 Supporter

Posts: 1040
Joined: 16 September 2008
Location: Middle England

### Re: Twin JExocet Continuation

David P Bird wrote:98.7..6..5.7.4..3...2......4...3..1..7......8..6...2.....3.4.9.....95.......7...1;r9c4 r9c6 r7c1 r8c8 268 Lot3:414

That one is clearly in Platinum Blonde's family.

It is number 414, does it mean that others are not
champagne
2017 Supporter

Posts: 6742
Joined: 02 August 2007
Location: France Brittany

### Re: Exotic patterns a resume

David's latest puzzle for consideration. A modest observation.

Code: Select all
`98.7..6..5.7.4..3...2......4...3..1..7......8..6...2.....3.4.9.....95.......7...1;r9c4 r9c6 r7c1 r8c8 268 Lot3:414 +--------------------------------------------------------------------------------+ |  9       8       134     |  7       125     123     |  6       245     245     | |  5       16      7       |  12689   4       12689   |  189     3       29      | |  136     1346    2       |  15689   1568    13689   |  145789  4578    4579    | |--------------------------+--------------------------+--------------------------| |  4       259     589     |  25689   3       26789   |  579     1       5679    | |  123     7       1359    |  124569  1256    1269    |  3459    456     8       | |  138     1359    6       |  14589   158     1789    |  2       457     34579   | |--------------------------+--------------------------+--------------------------| |  12678   1256    158     |  3       1268    4       |  578     9       2567    | |  123678  12346   1348    |  1268    9       5       |  3478    24678   23467   | |  2368    234569  34589   |  268     7       268     |  3458    24568   1       | +--------------------------------------------------------------------------------+ # 173 eliminations remain r9c46=26 and r8c8<>2|6   =>   r78c1=26 r9c46=28 and r8c8<>2|8   =>   r78c1=28 r9c46=68 and r8c8<>6|8   =>   r78c1=68 r8c8=4   =>   r78c1<>7   =>   X-Wing r78\c79   =>   r36c8=7   =>   r8c8<>4 r8c8=7   =>   r78c1<>7   =>   ~7[r7]                          =>   r8c8<>7`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: Exotic patterns a resume

daj95376 wrote:David's latest puzzle for consideration. A modest observation.

r9c46=26 and r8c8<>2|6 => r78c1=26
r9c46=28 and r8c8<>2|8 => r78c1=28
r9c46=68 and r8c8<>6|8 => r78c1=68

r8c8=4 => r78c1<>7 => X-Wing r78\c79 => r36c8=7 => r8c8<>4
r8c8=7 => r78c1<>7 => ~7[r7] => r8c8<>7
[/code]

No objection to any elimination based on the specificity of the puzzle.

What is interesting in David's path is that

- the puzzle is recognised as a twin exocet
- the abi loop works for 26 68 (invalid) leaving only 28 as valid

So in once, he comes to 32 eliminations.

The puzzle in not yet solved, but it is severely downgraded.
champagne
2017 Supporter

Posts: 6742
Joined: 02 August 2007
Location: France Brittany

### Re: Twin JExocet Continuation

champagne wrote:
David P Bird wrote:98.7..6..5.7.4..3...2......4...3..1..7......8..6...2.....3.4.9.....95.......7...1;r9c4 r9c6 r7c1 r8c8 268 Lot3:414
That one is clearly in Platinum Blonde's family.

Yes it is, and back in Jan 2009 Allan Barker posted a Truth/Link Solution ("TLS", aka "logic set", aka "SLG") using the then unnamed exocet with an "undecided target cell" (r8c46) and four AURs in this morph of Platinum Blonde, for 36 exclusions. For details, see link. Truths 679R5 are not actually required, however, for exactly the same exclusions.

ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Exotic patterns a resume

Since we have a twin JExocet, I guess it's time to look for a quad JExocet.

Code: Select all
`Puzzle #3323 in "02 index.txt":98.7..6....5.6.......9.4...4..3..9..37...8.....6.9......2.1.3.........52........1 +------------------------------------------------------------------------------------------+ |  9        8        134      |  7        235      1235     |  6        1234      345      | |  127      1234     5        |  128      6        123      |  12478   Q4789-123 Q4789-3   | SL on <9> |  1267     1236     137      |  9        2358     4        |  12578    12378     3578     | |-----------------------------+-----------------------------+------------------------------| |  4        125      18       |  3        257      12567    |  9        12678     5678     | |  3        7        9        |  12456    245      8        |  1245     1246      456      | |  1258     125      6        |  1245     9        1257     |  124578  R3478-12  R3478-5   | SL on <3> |-----------------------------+-----------------------------+------------------------------| |  5678     4569     2        |  4568     1        5679     |  3        46789     46789    | |  1678     13469    13478    |  468      3478     3679     | B478      5         2        | |  5678     34569    3478     |  24568    234578   235679   | B478      46789     1        | +------------------------------------------------------------------------------------------+ # 183 eliminations remain ### -478- quad JExocet   Base = r89c7   Target = (9)r2c89,(3)r6c89`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: Exotic patterns a resume

daj95376 wrote:Since we have a twin JExocet, I guess it's time to look for a quad JExocet.

Code: Select all
`Puzzle #3323 in "02 index.txt":98.7..6....5.6.......9.4...4..3..9..37...8.....6.9......2.1.3.........52........1 +------------------------------------------------------------------------------------------+ |  9        8        134      |  7        235      1235     |  6        1234      345      | |  127      1234     5        |  128      6        123      |  12478   Q4789-123 Q4789-3   | SL on <9> |  1267     1236     137      |  9        2358     4        |  12578    12378     3578     | |-----------------------------+-----------------------------+------------------------------| |  4        125      18       |  3        257      12567    |  9        12678     5678     | |  3        7        9        |  12456    245      8        |  1245     1246      456      | |  1258     125      6        |  1245     9        1257     |  124578  R3478-12  R3478-5   | SL on <3> |-----------------------------+-----------------------------+------------------------------| |  5678     4569     2        |  4568     1        5679     |  3        46789     46789    | |  1678     13469    13478    |  468      3478     3679     | B478      5         2        | |  5678     34569    3478     |  24568    234578   235679   | B478      46789     1        | +------------------------------------------------------------------------------------------+ # 183 eliminations remain ### -478- quad JExocet   Base = r89c7   Target = (9)r2c89,(3)r6c89`

Fine and a quick look tells me it should be 47 in the base (abi loop works)
champagne
2017 Supporter

Posts: 6742
Joined: 02 August 2007
Location: France Brittany

### Re: Exotic patterns a resume

champagne wrote:Fine and a quick look tells me it should be 47 in the base (abi loop works)

After which my quick look says a (1256)Shark or Multi-fish, followed by a step to avoid a (37)UR:r36c89 should do it.
David P Bird
2010 Supporter

Posts: 1040
Joined: 16 September 2008
Location: Middle England

PreviousNext