## Sharks - a Truth Balancing Method

Advanced methods and approaches for solving Sudoku puzzles

### Sharks - a Truth Balancing Method

David P Bird wrote:This produces a (2347)Shark:r23468c4579 covering set but it doesn't balance and is out by one. Hence one of the cells I listed shouldn't be reduced.

chanpagne has commented before on the similarites between SK Loops and Exocets, and since my explorations into Sharks I'm now much more aware of them.

OK, I didn't realize your "shark" POV had migrated to this thread and again put us on different planets, perhaps even in different universes. I will leave it to others to comprehend "sharks", but would you please not mention sk-loop and then use your "shark" POV in the same sentence? Steve Kurzhal's never used clues as part of his hidden-pair-loop.

As to the similarities between the sk-loop and the exocet, you are preaching to the choir.
Last edited by ronk on Sun Apr 29, 2012 5:15 pm, edited 1 time in total.
ronk
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### Re: bi bi pattern in hardest puzzles

Withdrawn
Last edited by David P Bird on Sun Apr 29, 2012 5:55 pm, edited 1 time in total.
David P Bird
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### Re: bi bi pattern in hardest puzzles

David P Bird wrote:
ronk wrote:As to the similarities between the sk-loop and the exocet, you are preaching to the choir.
The trouble is working out what the choristers have remembered since last week. It certainly seems they should brush up on their SK Loop catechism.

You should probably re-read (what remains of) the original hidden-pair-loop thread by Steve_k in the Eureka! sub-forum. You might recognize that "Ronk" fella there early on as me.

David P Bird wrote:Steve never used truth and link set diagrams either.

Those diagrams didn't exist then, so you are correct. However, now that they do, such a diagram can illustrate Kurzhal's logic exactly.

Easter Monster hidden pair loop: Show
Code: Select all
`001000002030004050600000700000058040000070000050903000007000600090300080200000001     16 Truths = {1267R2 1267R8 1267C2 1267C8}     16 Links = {45n2 2n4 28n5 8n6 56n8 1b37 2b19 6b37 7b19}     13 Eliminations --> r2c45<>8, r5c2<>48, r5c8<>39, r1c1<>7, r2c5<>9, r3c3<>2, r7c1<>1,      r8c5<>4, r8c6<>5, r9c3<>6`

____

The same cannot be said for your s***k diagrams, but who knows, perhaps someday someone will write such a tool. I'm not going to hold my breath though.

David P Bird wrote:This produces a (2347)Shark:r23468c4579 covering set but it doesn't balance and is out by one. Hence one of the cells I listed shouldn't be reduced.

Translation especially for you:
This can be reduced using a Multi-fish approach, but the S***k implementation I use is restricted, and I only know that eliminations will be possible in all but one of the cells I listed.

You are talking about a puzzle with an exocet single, right? So how do you get all the way from a reduction being invalid in only one of several cells ... to a reduction being valid in only two cells? Must be a replacement set of teeth that s***ks get.

Switch from a s***k argument to an exocet argument! Rather obscure, don't you think?
ronk
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### Re: bi bi pattern in hardest puzzles

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Last edited by David P Bird on Sun Apr 29, 2012 5:55 pm, edited 1 time in total.
David P Bird
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### Re: bi bi pattern in hardest puzzles

David P Bird wrote:It's just a pity that you've given up trying to understand the logic behind Sharks when you've persevered so much in the past on other topics.

I've lost my Babel fish, please can you define just what the term "Exocet single" means?

I don't recall "persevering" through any of your topics since braids.

An exocet single is one half the size of an exocet double. Perhaps the missing half was consumed by a shark.
ronk
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### Re: bi bi pattern in hardest puzzles

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David P Bird
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### Re: Sharks - a Truth Balancing Method

Here's an interesting example from champagne's collection picked up first <here>

It contains a rather rare JExocet pattern where the two target cells see each other. Note how the Jexcocet digits appear as givens in boxes 4678 in an Almost SK Loop configuration. Selecting the first 8 lines as r4689c1289 as usual for an SK Loop it transpires that there are three options for selecting the 9th line that give different eliminations.

The first balance also illustrates a case where there are adjustments to be made both to the home minimum and the away maximum truth counts. Also note that it makes the JExocet exclusions in the target cells.

............281.....27.61.......9..5..6.1.8...4.....3...1.7.2..3.......925.....4.
Code: Select all
` *-------------------------*--------------------------*-------------------------* | 1456789 136789  345789  | 3459%    3459    345%    | 345679  256789  234678  |  | 45679   3679    34579%  | 2        8       1       | 345679% 5679    3467    |  % = JExocet Cells | 4589    389     2       | 7        3459    6       | 1       589     348     |  *-------------------------*--------------------------*-------------------------*  # = JExocet   | 178     12378   378     | 3468     2346    9  #    | 467     1267    5 #     |      Givens | 579     2379    6       | 345 %    1       23457   | 8       279     247     |  | 15789   4 #     5789    | 568      256     2578    | 679     3 #     1267    |  *-------------------------*--------------------------*-------------------------* | 4689    689     1       | 345689 % 7       3458    | 2       568     368     |  | 3 #     678     478     | 14568    2456    2458    | 567     15678   9 #     |  | 2       5 #     789     | 13689    369     38      | 367     4 #     13678   |   *-------------------------*--------------------------*-------------------------*`
1st Balance: Show
Code: Select all
`    v      v                       v                     v      v          H   A  *----------------------*---------------------*-----------------------*  Min Max  | .      .      345789 | 3459 #  (T)  345 #  | 345679  .      .      |       4  | .      .      3459-7 | x       (F)  x      | 3459-67 .      .      |       2  | .      .      x      | x       (T)  x      | x       .      .      |       0  *----------------------*---------------------*-----------------------* >| x      1278-3 .      | .       2346 (T)    | .       x      5 #    |<  1  | .      .      x      | 345 #   (F)  345-27 | x       .      .      |       2 >| 178-59 4 #    .      | .       256  .      | .       3 #    x      |<  2  *----------------------*---------------------*-----------------------*  | .      .      x      | 3459-68 (F)  345-8  | x       .      .      |       2 >| 3 #    x      .      | .       2456 .      | .       1678-5 9 #    |<  2 >| x      5 #    .      | .       369  .      | .       4 #    1678-3 |<  2  *----------------------*---------------------*-----------------------*   -   -    ^      ^                       ^                     ^       ^         7   10(3459)Shark:r4689c12589 Truths Home Min = 7 + 2(c5)  Away Max = 10 – 1(r1) Home r4c2,r6c1,r8c8,r9c9 <> 3459, Away r2c47,r5c6,r7c46 <> 12678  (No eliminations possible in r1 or c5) 13 Eliminations in total`
2nd Balance: Show
Code: Select all
`    v        v                                             v       v          H   A   *-------------------------*---------------------*------------------------* Min Max >| 1678-459 1678-39 .      | (T)    (T)    (T)   | .      2678-59 24678-3 |  0    | .        .       3459 # | x      x      x     | 3459 # .       .       |      2  | .        .       x      | x      3459 # x     | x      .       .       |      1    *-------------------------*---------------------*------------------------* >| x        x       .      | .      .      .     | .      x       5 #     |  1  | .        .       x      | 345 #  x      345 # | x      .       .       |      2 >| x        4 #     .      | .      .      .     | .      3 #     x       |  2  *-------------------------*---------------------*------------------------*  | .        .       x      | 3459 # x      345 # | x      .       .       |      2 >| 3 #      x       .      | .      .      .     | .      x       9 #     |  2 >| x        5 #     .      | .      .      .     | .      4 #     x       |  2  *-------------------------*---------------------*------------------------*  -   -    ^        ^                                             ^       ^          7   7 (3459)Shark:r14689c1289 Truths: Home Min & Away Max = 7Home r1c1289 <> 3459 8 Eliminations in total`
3rd Balance: Show
Code: Select all
`    v     v              v             v               v      v         H   A  *--------------------*----------------------*----------------------* Min Max    | .     .     345789 | 3459#  3459#  (T)    | 345679 .      .      |      4  | .     .     3459 # | x      x      (F)    | 3459 # .      .      |      2  | .     .     x      | x      3459#  (F)    | x      .      .      |      1  *--------------------*----------------------*----------------------* >| x     x     .      | .      .      9#     | .      x      5 #    |< 2  | .     .     x      | 345 #  x      (T)    | x      .      .      |      1 >| x     4 #   .      | .      .      278-5  | .      3 #    x      |< 2  *--------------------*----------------------*----------------------*  | .     .     x      | 3459 # x      (T)    | x      .      .      |      1 >| 3 #   x     .      | .      .      28-45  | .      x      9 #    |< 2 >| x     5 #   .      | .      .      8-3    | .      4 #    x      |< 2   *--------------------*----------------------*----------------------*  -   -     ^     ^              ^             ^               ^      ^         8   9 (3459)Shark:r14689c1289 Truths: Home Min = 8 Away Max = 9 – 1(r1) Home r679 <> 3459  (No eliminations possible in r1)4 Eliminations in total`

In all there are 25 eliminations resulting from the 3 different balances although in practice some of them could be made in simpler follow-on steps after each step.
David P Bird
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### Re: bi bi pattern in hardest puzzles

withdrawm
Last edited by David P Bird on Sun Apr 29, 2012 5:57 pm, edited 1 time in total.
David P Bird
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### Off-topic

David, I can only speak for myself. I do use braids when solving on pencil & paper. I understand but don't use "Anchor-5" canonicalization. I think I understand Graded Equivalence Marks, but don't think it's practical because it's too easy to get lost in the punctuation symbols. I do use "proving loops" but, like others, call them derived inferences instead.

If others have found these older "topics" more useful, good for them and you. As to this topic, despite your three explanations, I truly don't understand "sharks." It didn't help that the first was in terms of colors, the second in terms of quadrants, and the third in terms of (I forget). But, as of now, no one else has indicated they understand either.

I'm certain there are many sudoku readers who don't understand what I write, or like what I write, or use what I write either. But I believe I would have enough sense to refrain from asking someone to try again to understand, especially after twice being told they'd given up.

BTW your waxing pedantic a second time about the similarities of sk-loops and exocets, i.e., "preaching to the choir" a second time, wasn't well received either.
ronk
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### Re: Sharks - a Truth Balancing Method

 The explanation given here is not water-tight, and the eliminations are therefore not proven. See <here>.

In this puzzle there is an Almost Multi-sector Locked Set nested inside an Almost Shark.

....5...9.5.1...3.....37...2..6..8...6..1..7...4..5.....9.....2.3...1.6.8.....4..;136;elev;117;2BN D1D3

Code: Select all
`   v                v                                   v               v          H   A  *-------------------------*-------------------------*-------------------------*  Min Max>| 1367-4  12478   1367-28 | 248     5       2468    | 167-2   1248    9       |<  1 | 4679    5       2678    | 1       2489-6  2489-6  | 267     3       4678    |       2 | 1469    2489-1  1268    | 2489    3       7       | 1256    248-15  14568   |       3 *-------------------------*-------------------------*-------------------------*>| 2       179     1357    | 6       479     349     | 8       1459    135-4   |<  2 | 359     6       358     | 2489-3  1       2489-3  | 2359    7       345     |       2>| 137-9   1789    4       | 23789   2789    5       | 136-29  129     136     |<  1 *-------------------------*-------------------------*-------------------------*>| 1567-4  147     9       | 34578   4678    3468    | 1357    158     2       |<  2 | 457     3       257     | 2489-57 2489-7  1       | 579     6       578     |       2>| 8       127     1567-2  | 23579   2679    2369    | 4       159     1357    |<  2 *-------------------------*-------------------------*-------------------------*   -   -       ^                ^                                   ^               ^          8   9`

(2489)AlmostShark:r14679c1379 Home Min Truths = 8, Away Max Truths = 9
Home PEs r1c138, r3c9, r6c17, r7c1, r9c3 <> 2489
Away PEs r2c56, r3c8, r5c46, r8c45 <> 13567

This puzzle has an Almost Shark where the minimum number of truths in the Home cells is one less than the maximum number of truths in the Away cells. The Potential Eliminations are shown for both cell sets but we know that just one of these is invalid.

Noticing that boxes 4679 nearly contain an SK Loop, the equivalent Almost Multi-sector Locked Set can be composed:
(35)r5,(89)b4,(17)c2,(24)b7,(57)r8,(89)b9,(15)c8,(249)b6 [16 available intersection cells occupied by 17 candidates]

To reduce this to a locked set one of the digits must be eliminated, and because this pattern is contained in 4 boxes, it must therefore occur in an uncovered cell in one of them.

The Shark PEs cover all the possibilities for locating the evicted digit, so one of these cells must hold the invalid PE which allows the eliminations in the other 5 boxes to be made (14 eliminations in 11 cells).

There must be many ways to view this situation using truth and link sets but this approach is very similar to locating common exclusions when avoiding overlapping Deadly Patterns.
Last edited by David P Bird on Sun Jul 15, 2012 7:00 am, edited 1 time in total.
David P Bird
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### Re: Sharks - a Truth Balancing Method

David P Bird wrote:In this puzzle there is an Almost Multi-sector Locked Set nested inside an Almost Shark.

....5...9.5.1...3.....37...2..6..8...6..1..7...4..5.....9.....2.3...1.6.8.....4..;136;elev;117;2BN D1D3

this may be off topic, but following the exotic strategy we have

a Jexocet in r13c4

an abi loop for pairs 28 48 in base
an easy elimination of 89 in base so '8' is not valid in base

a relatively easy elimination of 49 in base

we are left with 29 and 24 in base

29 has nearly a unique solution for digits 2489

24 has only a possibility with '2' in r5c6

Comparing these 2 options , we have immediately

r4c6=2
r7c2=4
r8c3=2
r2c7=2
r5c9=4
r6c8=2
and for sure r8c5=49

in that position, serate does not pass rating 9.0
champagne
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### Re: Sharks - a Truth Balancing Method

David P Bird wrote:In this puzzle there is an Almost Multi-sector Locked Set nested inside an Almost Shark.

....5...9.5.1...3.....37...2..6..8...6..1..7...4..5.....9.....2.3...1.6.8.....4..;136;elev;117;2BN D1D3

(2489)AlmostShark:r14679c1379 Home Min Truths = 8, Away Max Truths = 9
Home PEs r1c138, r3c9, r6c17, r7c1, r9c3 <> 2489
Away PEs r2c56, r3c8, r5c46, r8c45 <> 13567

David, without an assist from aals r1c4=248 (r13c4=2489 is even better), there is no logic set using digits <2489> that can produce an exclusion. Are you using other digits?
ronk
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### Re: Sharks - a Truth Balancing Method

ronk wrote:... there is no logic set using digits <2489> that can produce an exclusion.

Too bad ... because templates logic loves <2489>.

Code: Select all
` +--------------------------------------------------------------------------------+ |  13467   12478   123678  |  248     5       2468    |  1267    1248    9       | |  4679    5       2678    |  1       24689   24689   |  267     3       4678    | |  1469    12489   1268    |  2489    3       7       |  1256    12458   14568   | |--------------------------+--------------------------+--------------------------| |  2       179     1357    |  6       479     349     |  8       1459    1345    | |  359     6       358     |  23489   1       23489   |  2359    7       345     | |  1379    1789    4       |  23789   2789    5       |  12369   129     136     | |--------------------------+--------------------------+--------------------------| |  14567   147     9       |  34578   4678    3468    |  1357    158     2       | |  457     3       257     |  245789  24789   1       |  579     6       578     | |  8       127     12567   |  23579   2679    2369    |  4       159     1357    | +--------------------------------------------------------------------------------+ # 179 eliminations remain Templates: 56 59 16 50 32 20 87 26 28 <2489>   accepted = 23 template combinations <2489>   <>2  r9c2,r1239c3,r689c4,r68c5,r56c7,r13c8         -14 <2489>   <>4  r1c126,r2c59,r3c29,r4c89,r5c46,r7c1456,r8c1   -16 <2489>   <>8  r3c4,r8c5                                     - 2 <2489>   <>9  r5c6,r6c8,r9c5                                - 3 <2489>   <>1  r6c8,r7c2                                     - 2 <2489>   <>3  r4c6,r5c69                                    - 3 <2489>   <>5  r5c9,r8c3                                     - 2 <2489>   <>6  r2c1                                          - 1 <2489>   <>7  r2c1,r7c2,r8c35                               - 4                                                             ===                                                              47 eliminations r1c4,r2c1,r3c4,r4c6,r5c69,r6c8,r7c2,r8c35   locked for candidates <2489>`
daj95376
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### Re: Sharks - a Truth Balancing Method

daj95376 wrote:
ronk wrote:... there is no logic set using digits <2489> that can produce an exclusion.

Too bad ... because templates logic loves <2489>.

I don't believe you disabled constraints due to r1c4=248, r3c4=2489, and uniqueness. AFAICT David P Bird is using none of these.
ronk
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### Re: Sharks - a Truth Balancing Method

Ronk, until you remove all the irrelevant posts you dumped in this thread, I will continue to treat you as an adversary. All I will therefore say is that my methods are described <here>. Take note of the sentence that starts "Cells in the grid (including the givens) ...".
David P Bird
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