## Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

### 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":... ### -478- quad JExocet   Base = r89c7   Target = (9)r2c89,(3)r6c89`

Interesting pattern and nice find, but the notions of "twin JExocet" and "quad JExocet" are nonsensical. In each case, there is one exocet with either one or two target pairs, respectively.

Are you familiar with the hub, spoke, and rim (HSR) pattern? When there are two hubs, should we call them "twin wheels"?
ronk
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### Re: Exotic patterns a resume

ronk wrote:
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":... ### -478- quad JExocet   Base = r89c7   Target = (9)r2c89,(3)r6c89`

Interesting pattern and nice find, but the notions of "twin JExocet" and "quad JExocet" are nonsensical. In each case, there is one exocet with either one or two target pairs, respectively.

Are you familiar with the hub, spoke, and rim (HSR) pattern? When there are two hubs, should we call them "twin wheels"?

The most important in that case is not the name used but the fact that anybody can tell exactly what is behind.
The second important thing was to find one example of that expected pattern.

On my side, I don't see any exocet in Platinum Blonde nor in that puzzle, so I feel comfortable with the terms used. I would have used the "siamese" qualifier that would have been politically correct in French but I accept that it is not in English.
champagne
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### Re: Exotic patterns a resume

champagne wrote: I would have used the "siamese" qualifier that would have been politically correct in French but I accept that it is not in English.

That cry of outrage came somewhat late, but "Siamese" would be politically acceptable in the UK if you wanted to use it.

Contemplating it again, other alternatives could be: pinto Exocet (a flying fish with different colours) or bipolar Exocet (a flying fish with mood swings if the medical analogy was considered!).
David P Bird
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### Re: Exotic patterns a resume

David P Bird wrote:Contemplating it again, other alternatives could be: pinto Exocet (a flying fish with different colours) or bipolar Exocet (a flying fish with mood swings if the medical analogy was considered!).

It's this propensity to name everything and to name things too quickly that gets us into these dilemmas with terminology. What's wrong with using established terms for a while to see how things settle out? So there are a few extra adjectives, or even an extra phrase required for a time, so what. Very few of us seem to have broken typing fingers.

David P Bird wrote:That cry of outrage came somewhat late ...

If you are referring to the timing of my objection to "twin JExocet", I hoped reason would prevail without needing to say anything.
ronk
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### Re: Exotic patterns a resume

champagne wrote: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.

Thanks, at least ten others have the same pattern as #12177, where assignment of any pair of base digits <abcd> in the base cells, results in candidates limited to <abcd> in the target cells.

ten more puzzles with #12177-like pattern: 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;
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;
ronk
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### Re: Exotic patterns a resume

I prepared in the skfr google project the entire file of puzzles rating (skfr) 10.0 and more

warning: that file contains all the puzzles I used as seed in my search including already known (see the readme file)

5million puzzles file
champagne
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### Re: Exotic patterns a resume

Groundhog Day (Platinum Blonde again)

here champagne wrote:ABI loop does not use the exocet property, but when it is established, my preferred proof is the double contradiction chain directly derived form ABI 's logic

proving <67> r12c7
Code: Select all
`      6r8c3    7r6c3                             UR r12c37                 7r4c1  6r4c5                   ALS r4c12567                          6r6c4   7r8c4          UR r12c47      6r7c1                       7r7c6          ALS r7c12567    6r4c5 ^6r7c1                               twin exocet property`

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`6r7c1 - 6r4c5 = 7r4c1 - 7r6c3 = 6r8c3 - 6r7c1     <6>r7c1 6r4c5 - 6r7c1 = 7r7c6 - 7r8c4 = 6r6c4 - 6r4c5    <6>r4c5contradiction, we must have 6r4c5 ^6r7c1`
we really use here the minimum of data

A "minimum of data" is also possible without using the "exocet property."

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`     6r8c3  7r6c3                       UR r12c37            7r4c1  6r4c5                AHS 679r4                   6r6c4  7r8c4         UR r12c47     6r7c1                7r7c6         AHS 4679r7     6r8c3         6r6c4                sashimi swordfish 6c347\r12            7r6c3         7r8c4         sashimi swordfish 7c347\r12`

Code: Select all
`6r8c3 = 7r6c3 - 7r4c1 = 6r4c5 - 6r6c4 = 7r8c4 - 7r7c6 = 6r7c1 - pseudo-loop==> r8c3,r6c4<>6 read left-to-right ==> contradiction, require 6r8c3=6r6c4==> r6c3,r8c4<>7 read right-to-left ==> contradiction, require 7r6c3=7r8c4`

Not sure why, but the Xsudo image below suggests the sashimi swordfish for digit <7> is not required.

____
Xsudo details: Show
Code: Select all
`000000012000000003002300400001800005060070800000009000008500000900040500475006000     16 Truths = {1V1 679R4 4679R7 679C3 679C4 12N7}     16 Links = {679c7 12n3 12n4 47n8 7n9 6b57 7b48 9b48}     4 AURs = (76)R21C73, (96)R21C73, (76)R21C74, (96)R21C74       AUR points {aur 6r1c7 7r2c3 9r2c3 7r2c4 9r2c4 }     9 Eliminations --> r126c7<>6, r467c7<>7, r479c7<>9`

The strong-inference-set 6r8c3 = 6r6c4 is the virtual set "1V1" in Xsudo terminology.
ronk
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### Re: Exotic patterns a resume

ronk wrote:A "minimum of data" is also possible without using the "exocet property."

Code: Select all
`     6r8c3  7r6c3                       UR r12c37            7r4c1  6r4c5                AHS 679r4                   6r6c4  7r8c4         UR r12c47     6r7c1                7r7c6         AHS 4679r7     6r8c3         6r6c4                sashimi swordfish 6c347\r12            7r6c3         7r8c4         sashimi swordfish 7c347\r12`

Code: Select all
`6r8c3 = 7r6c3 - 7r4c1 = 6r4c5 - 6r6c4 = 7r8c4 - 7r7c6 = 6r7c1 - pseudo-loop==> r8c3,r6c4<>6 read left-to-right ==> contradiction, require 6r8c3=6r6c4==> r6c3,r8c4<>7 read right-to-left ==> contradiction, require 7r6c3=7r8c4`

Not sure why, but the Xsudo image below suggests the sashimi swordfish for digit <7> is not required.

.

I am not by far expert in fish patterns.
I have a difficulty with that statement

Code: Select all
`     6r8c3         6r6c4                sashimi swordfish 6c347\r12`

I went in sudopedia to see what is written on sashimi swordfish, but it does not help much.

I then analysed the "6" floor

Code: Select all
`6.6 66. 6..6.6 66. 66.6.. .6. .66... .6. 66..6. ... ...... 66. 6666.. ... 666..6 ... .66... ..6 ...`

I was expecting that the assumption 6r8c3 false and 6r6c4 false would lead to a contradiction, but I come to that position

Code: Select all
`..6 6.. .....6 6.. ...... ... .66... .6. 6...6. ... ...... .6. 6..6.. ... ...... ... .66... ..6 ...`

With at the end 2 possibilities in an XWing pattern.

No idea where I am wrong.

Regarding the last XSUDO diagram, the concept of "virtual set" is quite new to me. I have to understand what is behind.
champagne
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### Re: Exotic patterns a resume

champagne wrote:I was expecting that the assumption 6r8c3 false and 6r6c4 false would lead to a contradiction, but I come to that position

Code: Select all
`..6 6.. .....6 6.. ...... ... .66... .6. 6...6. ... ...... .6. 6..6.. ... ...... ... .66... ..6 ...`

With at the end 2 possibilities in an XWing pattern. No idea where I am wrong.

This contradicts the opening premise r12c7=67. Also, Xsudo's virtual set allows a person to specify one derived sis, I.e., a non-native sis.
ronk
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### Re: Exotic patterns a resume

ronk wrote:This contradicts the opening premise r12c7=67. Also, Xsudo's virtual set allows a person to specify one derived sis, I.e., a non-native sis.

thanks I lost the opening premise.
champagne
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### Re: Exotic patterns a resume

ronk wrote:Not sure why, but the Xsudo image below suggests the sashimi swordfish for digit <7> is not required.

I had a look at the diagram to try to answer to that question.

6r8c3 6r6c4 sashimi swordfish 6c347\r12

due to the loop (seen by XSUDO in the diagram) both must be true
but then, with the assumption 67 r12c7 we come to

7r6c3 7r8c4 both false

champagne
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### Re: Exotic patterns a resume

While examining Champagne's collection of 1700 SK-loop puzzles, I couldn't get this puzzle to work.

Code: Select all
`Puzzle #1157:   03 K SK loop seen.txt4.......1.7..9..2...8...5...3.9.6.......7.......3.2.6...5.......2..6..7.1.....4.8;8941;tax;tarek071223170000- 95250 +-----------------------+ | 4 . . | . . . | . . 1 | | . 7 . | . 9 . | . 2 . | | . . 8 | . . . | 5 . . | |-------+-------+-------| | . 3 . | 9 . 6 | . . . | | . . . | . 7 . | . . . | | . . . | 3 . 2 | . 6 . | |-------+-------+-------| | . . 5 | . . . | . . . | | . 2 . | . 6 . | . 7 . | | 1 . . | . . . | 4 . 8 | +-----------------------+ r7  b9  Locked Candidate 1              <> 2    r7c45 r7  b9  Locked Candidate 1              <> 6    r7c12     b9  Naked  Quad                     <> 1359 r7c79 +--------------------------------------------------------------------------------+ |  4      *69+5    2369    |  25678   2358    3578    |  36789  *39+8    1       | | *36+5    7      *36+1    |  14568   9       13458   | *36+8    2      *36+4    | |  2369   *69+1    8       |  12467   1234    1347    |  5      *39+4    34679   | |--------------------------+--------------------------+--------------------------| |  2578    3       1247    |  9       1458    6       |  1278    1458    2457    | |  25689   145689  12469   |  1458    7       1458    |  12389   134589  23459   | |  5789    14589   1479    |  3       1458    2       |  1789    6       4579    | |--------------------------+--------------------------+--------------------------| |  3789   #489     5       |  1478    1348    134789  |  26     *39+1    26      | | *39+8     2     *39+4    |  1458    6       134589  | *39+1    7      *39+5    | |  1      #69      3679    |  257     235     3579    |  4      *39+5    8       | +--------------------------------------------------------------------------------+ # 176 eliminations remain (48=39)r8c13 - (39=15)r8c79 - (15=39)r79c8 - (39=48)r13c8 - (48=36)r1c79 - (36=15)r2c13 - (15=69)r13c2 - (??=??)r79c2 - loop  =>  ???`

Ironically, it appears to work as:

Code: Select all
` (39=48)r8c13 - (48=69)r79c2 - (69=15)r13c2 - (15=36)r2c13 - (36=48)r2c79 - (48=39)r13c8 - (39=15)r79c8 - (15=39)r8c79 - loop  =>  ...`

All of Champagne's puzzles have an SK-loop using four boxes. Does anyone know of an example using six boxes?
daj95376
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### Re: Exotic patterns a resume

daj95376 wrote:While examining Champagne's collection of 1700 SK-loop puzzles, I couldn't get this puzzle to work.
Code: Select all
` (48=39)r8c13 - (39=15)r8c79 - (15=39)r79c8 - (39=48)r13c8 - (48=36)r1c79 - (36=15)r2c13 - (15=69)r13c2 - (??=??)r79c2 - loop  =>  ???`

Ironically, it appears to work as:

Code: Select all
` (39=48)r8c13 - (48=69)r79c2 - (69=15)r13c2 - (15=36)r2c13 - (36=48)r2c79 - (48=39)r13c8 - (39=15)r79c8 - (15=39)r8c79 - loop  =>  ...`

This notation has always had a problem. It doesn't properly show that linking digits between AALSs might be shared by these AALSs. Ironically, AFAIK this sharing is always ultimately true for the sk-loop. Empirically proving it with a software program on a large database of sk-loop puzzles would be a worthwhile exercise. [edit: AALS was ALS, 2 plcs]

daj95376 wrote:All of Champagne's puzzles have an SK-loop using four boxes. Does anyone know of an example using six boxes?

No.
Last edited by ronk on Sun Jun 24, 2012 1:36 pm, edited 1 time in total.
ronk
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### Re: Exotic patterns a resume

daj95376 wrote:While examining Champagne's collection of 1700 SK-loop puzzles, I couldn't get this puzzle to work.

Code: Select all
`Puzzle #1157:   03 K SK loop seen.txt4.......1.7..9..2...8...5...3.9.6.......7.......3.2.6...5.......2..6..7.1.....4.8;8941;tax;tarek071223170000- 95250`

All of Champagne's puzzles have an SK-loop using four boxes. Does anyone know of an example using six boxes?

Interesting puzzle.

Clearly, in box 7, 48 can not be a solution for r79c2.

My first concern has been to see if the implicit logic I apply to justify eliminations in the SK loop was still valid.

It is, but it shows a possible window for a bug with 2 such situations in the same loop locking the flow on each side. May be other ways to justify the eliminations would still work.

As ronk said, anyway, all studied puzzles having the sk loop have shown that the 2 main belts are not valid. I should be in a position to test it soon for the entire file.

Regarding the 6 boxes loop, the constraints are very severe. I never found it, and I suspect that, if it does exist, it will come from a generation on patterns specifically designed to have a chance to show it.

Last but not least, that puzzle has also an exocet in r5c46 r6c2 r4c8.

As in puzzle 160, that exocet has only 2 pairs valid, 15 and 48.
I guess a solution similar to puzzle 160 can been found.
champagne
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### Re: Exotic patterns a resume

In my previous post, I was looking for confirmation that the puzzle didn't contain an acceptable SK-Loop. From the responses, I'm not sure if there's a consensus or not. So, I'll just proceed with puzzles that I consider to contain an (acceptable to me) SK-loop.

===== ===== ===== ===== ===== ===== ===== Moving On

Consider this puzzle:

Code: Select all
`98.7.....7.6.5......5...7..6...4.5.....3...8......2..1..9.6.4.....1....2.....8.3.     b5  Naked  Quad                     <> 1789 r5c6,r6c4 +--------------------------------------------------------------------------------+ |  9       8       1234    |  7       123     1346    |  1236    12456   3456    | |  7       1234    6       |  2489    5       1349    |  12389   1249    3489    | |  1234    1234    5       |  24689   12389   13469   |  7       12469   34689   | |--------------------------+--------------------------+--------------------------| |  6       12379   12378   |  89      4       179     |  5       279     379     | |  1245    124579  1247    |  3       179     56      |  269     8       4679    | |  3458    34579   3478    |  56      789     2       |  369     4679    1       | |--------------------------+--------------------------+--------------------------| |  12358   12357   9       |  25      6       357     |  4       157     578     | |  3458    34567   3478    |  1       379     34579   |  689     5679    2       | |  1245    124567  1247    |  2459    279     8       |  169     3       5679    | +--------------------------------------------------------------------------------+ # 172 eliminations remain (79=18)r56c5 - (18=79)r4c46 - (79=23)r4c89 - (23=69)r56c7 - (69=18)r89c7 - (18=57)r7c89 - (57=23)r7c46 - (23=79)r89c5 - SK_loop  =>  r4c2<>79; r7c2<>57; r9c4<>2; r8c6<>3; r7c1<>5; r1c7<>6; r4c3<>7; r2c7,r3c5<>9`

Now consider the solutions for the 16 cells in the SK-loop:

Code: Select all
` SK-loop cells w/solutions *--------------------------------------------------------------------* | 9      8      1234   | 7      3      146    | 12     456    3456   | | 7      1234   6      | 249    5      149    | 12     49     348    | | 1234   1234   5      | 2469   38     1469   | 7      469    3468   | |----------------------+----------------------+----------------------| | 6      13     13     |*8      4     *7      | 5     *2     *9      | | 245    24579  247    | 3     *1      5      |*6      8      4      | | 458    457    478    | 6     *9      2      |*3      47     1      | |----------------------+----------------------+----------------------| | 28     2      9      |*5      6     *3      | 4     *1     *7      | | 345    3456   34     | 1     *7      49     |*8      56     2      | | 145    14567  147    | 4     *2      8      |*9      3      56     | *--------------------------------------------------------------------* (79=18)r56c5 ->   r5c5 = 1   r6c5 = 9 (18=79)r4c46 ->   r4c4 = 8   r4c6 = 7 (79=23)r4c89 ->   r4c8 = 2   r4c9 = 9 (23=69)r56c7 ->   r5c7 = 6   r6c7 = 3 (69=18)r89c7 ->   r8c7 = 8   r9c7 = 9 (18=57)r7c89 ->   r7c8 = 1   r7c9 = 7 (57=23)r7c46 ->   r7c4 = 5   r7c6 = 3 (23=79)r89c5 ->   r8c5 = 7   r9c5 = 2`

In each case, the puzzle's solution contains a single value from each side of the (ab=cd) term.

FWIW: This happens in all 1,944 (acceptable to me) SK-loops that I found in champagne's 31,804 puzzles from HARD_11.

Now, I'm probably the only one who finds this interesting.
daj95376
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