## "Potential Hardest" 2

Post puzzles for others to solve here.

### "Potential Hardest" 2

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`+-------+-------+-------+| . . . | 9 . . | . . 8 || . 7 6 | . . . | . . . || 8 . . | 5 . 4 | . . 3 |+-------+-------+-------+| . . . | . . 9 | 2 . . || . . . | . . . | . 3 . || 1 . . | 3 . . | . . 5 |+-------+-------+-------+| . 1 . | . 3 . | . . 4 || 4 . . | . 9 . | . 5 . || . 5 . | 4 . . | 8 . . |+-------+-------+-------+...9....8.76......8..5.4..3.....92.........3.1..3....5.1..3...44...9..5..5.4..8..`

(As a reminder, these are puzzles which are rated 11+ by SE, but fall to some advanced technique not implemented by SE.)
Last edited by mith on Sat Sep 12, 2020 5:16 pm, edited 1 time in total.
mith

Posts: 481
Joined: 14 July 2020

### Re: "Potential Hardest" 2

version 1: Show
I have no idea how this was supposed to be solved...

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`.------------------------.--------------------------.-----------------------.| #235     234    12345  |  9       1267     12367  |  1567   1267    8     ||  2359    7      6      |  128     128      1238   |  1459   1249    129   ||  8       29     129    |  5       1267     4      |  1679   12679   3     |:------------------------+--------------------------+-----------------------:| s3567    3468   34578  | s1678    145678   9      |  2      14678  s167   || s25679   24689  245789 | s12678   1245678  12678  |  14679  3      s1679  ||  1       24689  24789  |  3       24678    2678   |  4679   46789   5     |:------------------------+--------------------------+-----------------------:| t2679   m1     m2789   |  2678    3        5      |  679    2679    4     ||  4       268    278    |  12678   9        12678  | m3!    m5!     t1267  ||  23679   5      2379   |  4      b7#2-16  b7#2-16 |  8     s12679  s12679 |'------------------------'--------------------------'-----------------------'`

Step 1. Impossible JExocet:

(2)r9c56 = ! JE:(167)r9c56,r7c1,r8c9 (missing mirror r8c78) ! => +2 r9c56

Steps 2,3. T&E (1):

(21)r9c56 ->[basics]-> ! => -1 r9c56
(26)r9c56 ->[basics, Grouped Kite *]-> ! => -6 r9c56

(*): [(6)r8c9 = r45c9 - r6c78 = (6)r6c2 => -6r8c2]

Added. Step 2 as 13x13 TM)

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` 2r8c9  2r2c9        2r2c4 2r5c4 2r8c9  ........... 2r7c8        2r2c1 2r5c1 2r7c1 2r1c1        2r3c8 ........... 2r3c23 2r3c5                                 2r9c5 2r9c6 1r9c89 .............................. 1r9c6 1r9c5        2r2c5 .............................. 1r2c5 8r2c5        2r2c4 .................................... 8r2c4 1r2c4                                 6r3c5 ....................... 6r3c78                                 7r3c5 .............................. 7r3c78        2r1c8 ................................................ 6r1c8  7r1c8  1r1c8 1r4c9  .................................... 1r4c5 ..... 1r4c4 ............. 1r4c8==================================================================================-1r8c9`

Code: Select all
`.-----------------------.----------------------.----------------------.| 235    234     12345  | 9      1267    12367 |  1567   1267    8    || 2359   7       6      | 128    128     1238  |  1459   1249    129  || 8      29      129    | 5      1267    4     |  1679   12679   3    |:-----------------------+----------------------+----------------------:| 3567   3468    34578  | 1678   14568   9     |  2      14678  b167  || 25679  24689   245789 | 12678  124568  1268  |  14679  3      b1679 || 1      24689  d24789  | 3      2468    268   | c4679  c46789   5    |:-----------------------+----------------------+----------------------:| 2679   1       2789   | 68     3       5     |  679    2679    4    || 4      268     28-7   | 168    9       168   |  3      5      a267  || 369    5       39     | 4      27      27    |  8      169     169  |'-----------------------'----------------------'----------------------'`

Step 4. Grouped Kite:

(7)r8c9 = r45c9 - r6c78 = (7)r6c3 => -7 r8c3; stte

version 2: Show
Step 2.
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`.--------------------.-------------------------.------------------------.| 2     34    345    |  9       167      1367  |  1567   e167     8     || 35    7     6      | e128    e128      1238  |  1459    1249   c129   || 8     9     1      |  5      e267      4     | e67    de267     3     |:--------------------+-------------------------+------------------------:| 3567  3468  34578  | f1678   f145678   9     |  2      f14678  g167   || 5679  2468  245789 |  12678   1245678  12678 |  14679   3       1679  || 1     2468  24789  |  3       24678    2678  |  4679    46789   5     |:--------------------+-------------------------+------------------------:| 679   1     2789   |  678     3        5     |  679     2679    4     || 4     268   278    |  1678    9        1678  |  3       5      b267-1 || 3679  5     379    |  4      e12'67    12'67 |  8      a1679   a1679  |'--------------------'-------------------------'------------------------'`

(1)r9c89 = [(2)r8c9 = r2c9 - r3c8 = ((2,1,8,1)r39c5,r2c54 & (671)b3p782) - r4c458 = (1)r4c9] => -1 r8c9

10x10 TM
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` 2r8c9  2r2c9        2r3c8 2r3c5              2r9c5 2r9c6 1r9c89 ........... 1r9c6 1r9c5        2r2c5 ........... 1r2c5 8r2c5        2r2c4 ................. 8r2c4 1r2c4              6r3c5 ....................... 6r3c78              7r3c5 .............................. 7r3c78                                            6r1c8  7r1c8  1r1c8 1r4c9  ................. 1r4c5 ..... 1r4c4 ............. 1r4c8===============================================================-1r8c9`

Step 3.
Code: Select all
`.----------------------.-------------------------.------------------------.| 2       34    345    | 9      167       1367   |  1567   167      8     || 35      7     6      | 128    128       1238   |  1459   1249     129   || 8       9     1      | 5      267       4      |  67     267      3     |:----------------------+-------------------------+------------------------:| 3567    3468  34578  | 1678   14578/6   9      |  2      14678   b167   || 5679    2468  245789 | 12678  124578/6  1278/6 |  14679  3       b1679  || 1      d2468  24789  | 3      2478/6    278/6  | c4679   c46789   5     |:----------------------+-------------------------+------------------------:| 679     1     2789   | 78/6   3         5      |  679    2679     4     || 4      *28/6  278    | 178/6  9         178/6  |  3      5       a267   || 379/6   5     379    | 4      27-6      27-6   |  8      179/6    179/6 |'----------------------'-------------------------'------------------------'`

T&E (1): (6)r9c56 ->[basics, Grouped Kite *]-> ! => -6 r9c56

(*): [(6)r8c9 = r45c9 - r6c78 = (6)r6c2 => -6r8c2]

Step 4.
Code: Select all
`.---------------------.---------------------.-----------------------.| 2     34     345    | 9      167     1367 |  1567    167     8    || 35    7      6      | 128    128     1238 |  1459    1249    129  || 8     9      1      | 5      267     4    |  67      267     3    |:---------------------+---------------------+-----------------------:| 3567  3468   34578  | 1678   14568   9    |  2       14678  b167  || 5679  2468   245789 | 12678  124568  1268 |  14679   3      b1679 || 1     2468  d24789  | 3      2468    268  | c4679   c46789   5    |:---------------------+---------------------+-----------------------:| 679   1      2789   | 68     3       5    |  679     2679    4    || 4     268    28-7   | 168    9       168  |  3       5      a267  || 369   5      39     | 4      27      27   |  8       169     169  |'---------------------'---------------------'-----------------------'`

Grouped Kite:

(7)r8c9 = r45c9 - r6c78 = (7)r6c3 => -7 r8c3; stte

Step 1.
Code: Select all
`.------------------------.---------------------------.-----------------------.| +2-35    234    12345  |  9        1267     12367  |  1567   1267    8     || s2359    7      6      | s128      128      1238   |  1459   1249   s129   ||  8       29     129    |  5        1267     4      |  1679   12679   3     |:------------------------+---------------------------+-----------------------:| s3567    3468   34578  | s1678     145678   9      |  2      14678  s167   || s25679   24689  245789 | s12678    1245678  12678  |  14679  3      s1679  ||  1       24689  24789  |  3        24678    2678   |  4679   46789   5     |:------------------------+---------------------------+-----------------------:| t2679   m1     m2789   |  678-2    3        5      |  679    2679    4     ||  4       268    278    |  1678-2   9        1678-2 | m3!    m5!     t1267  ||  23679   5      2379   |  4       b167+2   b167+2  |  8     s12679  s12679 |'------------------------'---------------------------'-----------------------'`

(DP) Impossible JExocets (missing mirror r8c78):

!'JE:(167|1267)r9c56,r7c1,r8c9 = (2,2)r9c56,r1c1 => +2 r9c56,r1c1

Or simply (because 2r1c1 is not needed):

!'JE:(167)r9c56,r7c1,r8c9 = (2)r9c56 => +2 r9c56

Step 2.
Code: Select all
`.-----------------------.-------------------------.-----------------------.|  2       34    345    |  9       167      1367  |  1567    167     8    ||  35      7     6      |  128     128      1238  |  1459    1249    129  ||  8       9     1      |  5       267      4     |  67      267     3    |:-----------------------+-------------------------+-----------------------:| s3567    3468  34578  | s1678    145678   9     |  2       14678  s167  || s5679    2468  245789 | s12678   1245678  12678 |  14679   3      s1679 ||  1       2468  24789  |  3       24678    2678  |  4679    46789   5    |:-----------------------+-------------------------+-----------------------:|  679     1     2789   |  678     3        5     | b679    b679+2   4    ||  4       268   278    | t1678   m9       m1678  |  3       5       1267 || t679.3  m5    t79.3   |  4       1267     1267  |  8      s1679   s1679 |'-----------------------'-------------------------'-----------------------'`

(DP) Impossible JExocet (missing mirror r9c23, due to locked 3r9c13):

!'JE:(679)r7c78,r8c4,r9c13 = (2)r7c8 => +2 r7c8; btte
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2672
Joined: 22 May 2017

### Re: "Potential Hardest" 2

Senior Exocet --> lclste

SE-True.png (32.07 KiB) Viewed 418 times

Senior Exocet:Base Cells-r9c5,r9c6;Target Cells-r1c1,r8c9;Cross Cells-r1c49,r2c149,r3c149,r4c149,r5c149,r6c149,r7c19,r8c1
1r8 locked in target Cell;"S" Cells Need Include:2r8,6r8,7r8,
Non BaseCands In Target Cells: r1c1<>35
True BaseCands False In Another Target:r8c9<>2
True BaseCands False In Base Cells Constraint:r8c46,r9c1389,r7c4<>2
yzfwsf

Posts: 363
Joined: 16 April 2019

### Re: "Potential Hardest" 2

Ah, one step after all. I just had it split over two from the solver.
mith

Posts: 481
Joined: 14 July 2020

### Re: "Potential Hardest" 2

yzfwsf wrote:Senior Exocet

Nice. So that was the "official technique" for this puzzle? I kind of guessed that it might be, but couldn't imagine r1c1 as a target. Having zero experience with SExocets didn't help either.

In fact, this was my first ever live puzzle where I found and applied any kind of an Exocet pattern fully manually. In that light, I'm quite happy with what I found, assuming it was valid logic. I guess normal JExocets should be more or less trivial in comparison.

It was basically my last significant bucket list item. Since I was already feeling vindicated, thanks to the latest gruesome discussion, I can now retire without too many regrets. Thanks, mith, for helping with both of those goals. Live long and prosper.
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2672
Joined: 22 May 2017

### Re: "Potential Hardest" 2

se.png (69.78 KiB) Viewed 367 times

Sue [25,238] 61 Candidates,
17 Truths = {1267R8 267C1 1267C4 1267C9 9N56}
24 Links = {2r1259 6r459 7r459 1n1 5n4 28n9 1b8 2b13578 6b78 7b78}
38 Eliminations, 3 Assignments --> [2C1*2r1*1n1*2b1] => r1c1=2, [2C9*2r2*2n9*2b3] => r2c9=2, [2C4*2r5*5n4*2b5] => r5c4=2, (1n1) => r1c1<>3, (1n1) => r1c1<>5, (2r1*2b1) => r1c2<>2, (2r1*2b1) => r1c3<>2, (2r1) => r1c5<>2, (2r1) =>
r1c6<>2, (2r1*2b3) => r1c8<>2, (2C1*2r2*2b1) => r2c1<>2, (2C4*2r2) => r2c4<>2, (2r2) => r2c5<>2, (2r2) => r2c6<>2, (2r2*2b3) =>
r2c8<>2, (1C9*2n9) => r2c9<>1, (2n9) => r2c9<>9, (2b1) => r3c2<>2, (2b1) => r3c3<>2, (2b3) => r3c8<>2, (2C1*2r5) =>
r5c1<>2, (2r5) => r5c2<>2, (2r5) => r5c3<>2, (1C4*5n4) => r5c4<>1, (6C4*6r5*5n4) => r5c4<>6, (7C4*7r5*5n4) => r5c4<>7, (5n4) =>
r5c4<>8, (2r5*2b5) => r5c5<>2, (2r5*2b5) => r5c6<>2, (2b5) => r6c5<>2, (2b5) => r6c6<>2, (2C1*2b7) => r7c1<>2, (2b7) =>
r7c3<>2, (2C4*2b8) => r7c4<>2, (2R8*2C4*2b8) => r8c4<>2, (2R8*2b8) => r8c6<>2, (2R8*2C9*8n9) => r8c9<>2, (2C1*2r9*2b7) => r9c1<>2, (2r9*2b7) =>
r9c3<>2, (2r9) => r9c8<>2, (2C9*2r9) => r9c9<>2
yzfwsf

Posts: 363
Joined: 16 April 2019

### Re: "Potential Hardest" 2

Sorry, I find the Senior Exocet presentations a bit terse.
My references for the Senior Exocet pattern are: David's Compendium and his own reference blue's initial post.
The puzzle above doesn't meet these pattern criteria (cover houses > 2 ) So, a pattern extension is used here.

The following statements given by yzfwsf's solver are enigmatic to me... (Edit: fixed yzfwsf username)
1r8 locked in target Cell;

"S" Cells Need Include:2r8,6r8,7r8,

Does the first one mean: "digit one has only one possible target cell => +1r9c56 & -1r89c9 => row 8 void of 1" i.e. the exocet property is demonstrated for digit 1 (no need to count the cover houses) ?

For the second sentence, which cells in row 8 are considered "S" Cells ?
And eventually, which sectors are cover houses for digits 2, 6, 7 ?

I expect for such hardest puzzles a bit more explanations from experts.

@mith: it's a good idea to post this kind of puzzles from time to time, provided it is made with some teaching purpose.
Last edited by Cenoman on Tue Sep 15, 2020 1:58 pm, edited 1 time in total.
Cenoman
Cenoman

Posts: 1665
Joined: 21 November 2016
Location: Paris, France

### Re: "Potential Hardest" 2

Cenoman wrote:Sorry, I find the Senior Exocet presentations a bit terse.

Me too, at first. I think it works, though, if the same extensions are allowed as for JExocets.

The puzzle above doesn't meet these pattern criteria (cover houses > 2 ) So, a pattern extension is used here.

Indeed. It's the same as with the previous "Jellyfish" JExocet, except this one is also a "Mutant" (one S-line is a row). I think such extensions are logical generalizations and should be allowed, though they should probably be mentioned somehow, just like exotic fishes are known by their special prefixes.

Technically the normal fish terms could be used with some of these extended [J/S]Exocets, and I would actually like it. Why invent new terms when we already have descriptive ones that many would understand? Personally I also think the [J/S]Exocet notation should be upgraded to include the fish part (with fish notation), especially in more complicated cases like this. Obviously listing just the base and target cells doesn't fully describe the pattern (not even close). Besides, both are ambiguous terms to begin with, but that's a different problem.

The following statements given by ysfwsf's solver are enigmatic to me...
yzfwsf wrote:1r8 locked in target Cell;

Does the first one mean: "digit one has only one possible target cell => +1r9c56 & -1r89c9 => row 8 void of 1" i.e. the exocet property is demonstrated for digit 1 (no need to count the cover houses) ?

The way I see it is that the SExocet uses R8 as a horizontal S-line (truth) for all digits 1267. Unlike the other digits, 1 doesn't need any other S-lines because all of its candidates in row 8 are restricted to box 8 and the target cell r8c9. Thus, 1R8 is covered by 1b8 and 8n9 directly, i.e. 1r9c56 -> -1r8c46 -> 1r8c9. Obviously it means that there can be no other target for digit 1, because it would be forced into one directly if it were a true base candidate. That is actually true for 6 and 7 also, but not as directly.

yzfwsf wrote:"S" Cells Need Include:2r8,6r8,7r8,

For the second sentence, which cells in row 8 are considered "S" Cells ?

The whole S-cell concept is so confusing in complex cases that I wouldn't know. For digit 1 there are only three candidates in row 8 -- two in box 8 (same as the base cells) and one in r8c9 (target). Conventionally none of them would be S-cells, I think, but this is not a conventional situation so I don't know. For the other digits 267 I guess at least r8c23 are S-cells (of 267R8) covered by 267b7.

The cause of confusion is that traditionally only the cells outside of the JExocet band have been considered S-cells. That's a design flaw in the pattern, because it makes certain generalizations difficult to describe accurately (including the basic SExocet). It would be better to consider all candidates in a given S-house as S-candidates that need covering one way or another. Even better if they were called something else, as the "S-cell" is a loaded and non-descriptive term.

In basic JExocets the S-candidates within the JExocet band are implicitly covered by the base box and base line, and the rest explicitly. Thus only the latter are counted as S-cells (the others are "escape cells"). That approach simplifies that particular situation, but it also complicates other situations where that abstraction doesn't work. In fact, it also makes the simple situation harder to understand for a novice.

And eventually, which sectors are cover houses for digits 2, 6, 7 ?

In row 8 or in general? In row 8 they're covered by boxes 7 and 8 (267b78) and the target cell r8c9 (8n9). In general also by rows 2r2, 67r4, 267r59 and the other target 1n1.

I expect for such hardest puzzles a bit more explanations from experts.

Problem is, these kinds of situations are hard to explain with pure [J/S]Exocet terms. Terms like "S-cells" and "cross-lines" etc. are just confusing in more complicated scenarios, as far as I'm concerned. It's much easier to just view them as normal base\cover problems with the corresponding terms that are non-ambiguous. Here's how I see the truths and links in this case (correctness not guaranteed, as I don't have XSudo):

Exocet (type: Senior, size: Jellyfish, shape: Mutant) :

15x18 {1267R8 267C149 9N56 \ 2r2 67r4 267r59 267b7 1267b8 1n1 8n9} => -35 r1c1 (=> +2 r1c1, +2 r9c56, -2 r8c9); btte

It's a bit simpler than yzfwsf's 17x24 XSudo diagram that provides many more eliminations. The main difference is that mine doesn't use 1C49 as truths -- only 1R8. The obvious problem with the set logic presentation alone is that it's extremely difficult to decipher what it actually proves. It's also difficult to write a single matrix to demonstrate it.

What it should prove is that 1n1 an 8n9 are local Rank 0 regions, which allows eliminating all non-base digits from them, in this case placing 2 in r1c1. I'm not sure if it proves anything else directly, but basic Exocet logic then means that 2 must be a true base candidate, thus true in r9c56 and false in the other target r8c9, which is enough for the solution.

Added. Here's my attempt to demonstrate it with separate sub-matrices, one for each digit assumed in r9c56.

Digit 1: Show
Code: Select all
`        1b8========================================       1r9c56                     | 9N56 * 1r8c9 1r8c46                     | 1R8======================================== 1r8c9`

Digit 2: Show
Code: Select all
`       2r9,b8  2r2   2r5   2b7========================================       2r9c56                     | 9N56 * 2r8c9 2r9c9  2r2c9               | 2C9       2r78c4 2r2c4 2r5c4         | 2C4 2r1c1 2r9c1  2r2c1 2r5c1 2r7c1   | 2C1 2r8c9 2r8c46             2r8c23  | 2R8========================================|2r1c1|2r8c9`

Digit 6: Show
Code: Select all
`       6r9,b8  6r4   6r5   6b7========================================       6r9c56                     | 9N56 * 6r8c9 6r9c9  6r4c9               | 6C9       6r78c4 6r4c4 6r5c4         | 6C4       6r9c1  6r4c1 6r5c1 6r7c1   | 6C1 6r8c9 6r8c46             6r8c2   | 6R8======================================== 6r8c9`

Digit 7: Show
Code: Select all
`       7r9,b8  7r4   7r5   7b7========================================       7r9c56                     | 9N56 * 7r8c9 7r9c9  7r4c9               | 7C9       7r78c4 7r4c4 7r5c4         | 7C4       7r9c1  7r4c1 7r5c1 7r7c1   | 7C1 7r8c9 7r8c46             7r8c3   | 7R8======================================== 7r8c9`

All the other digits except 2 have only one possible target. Since two digits must go to r9c56, one of 167 must go to r8c9 and 2 must go to r1c1.

@mith: it's a good idea to post this kind of puzzles from time to time, provided it is made with some teaching purpose.

I think it's an excellent idea, though a bit late for me. Personally I haven't had any motivation to work on the hardest puzzles on my own, except for the examples in David's compendium and some MSLS/SK-Loop examples. When posted as preselected and public problems like this, it's much more interesting and educational, because you get to actually think about them (instead of knowing in advance what to expect) and can learn from others' solutions.

For a long time now, I haven't bothered to solve any puzzles besides what's posted in the Puzzles here, so this is basically the only way for me to ever gain experience and routine with the exotic techniques. So far I've been satisfied with understanding the theory behind them, but it obviously doesn't fully compensate for the lack of experience.

--
Edit. Removed incorrectly used term "cross-line" (when a cover house was meant).
Last edited by SpAce on Mon Sep 14, 2020 9:42 pm, edited 1 time in total.
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2672
Joined: 22 May 2017

### Re: "Potential Hardest" 2

Hi SpAce,

Many thanks for your long response. I have tried to deepen the pattern, and I get conclusions similar to yours.

Preliminary remark: I will use the following acronyms, BD (Base Digit), CL (Cross-Line), CH (Cover House

I'm not much fond of r8c46 as "S"-cells for digit 1. In none of David's or blue's diagrams, cells in sight of the base cells are used as "S"-cells. That's makes sense to me, as "S"-cells are part of a "fish" used to demonstrate: BD digit True in the base-cells => same BD True in one target cell.

But here, 1r9c56 => 1r8c9 is so obvious that there is no need, to care for the 1s any further, especially with such complex process. Note: one could also consider r123456c78 as "S"-cells for digit 1; four CH's (r1234) vs four CL's (c4789)! (I'm kidding... but it works.) I guess that the inference 1r9c56 => 1r8c9 is meant by yzfwsf's
1r8 locked in target Cell;

As regards BD 2,6,7, the "standard" Senior Exocet would be there, w/o the spoiler candidates 267r8c1. There is a need for one more CH, the additional "S"-cells of which shall see the second target r8c9; r8c23 only are compliant, and the additional CH is box 7.
Code: Select all
` +---------------------------+----------------------------+--------------------------+ | t235     234     12345    |  9       1267      12367   |  1567    1267    8       |  | S2359    7       6        | S128     128       1238    |  1459    1249   S129     | CH 12  |  8       29      129      |  5       1267      4       |  1679    12679   3       |  +---------------------------+----------------------------+--------------------------+ | S3567    3468    34578    | S1678    145678    9       |  2       14678  S167     | CH 1 67 | S25679   24689   245789   | S12678   1245678   12678   |  14679   3      S1679    | CH 1267 |  1       24689   24789    |  3       24678     2678    |  4679    46789   5       |  +---------------------------+----------------------------+--------------------------+ | S2679    1       2789     |  2678    3         5       |  679     2679    4       |  |  4      S268    S278      |  12678   9         12678   |  3       5      t1267    |  |  23679   5       2379     |  4      b1267     b1267    |  8       12679   12679   |  +---------------------------+----------------------------+--------------------------+    CL2                         CLB                                          CL1          b7: CH  267`

The end, once the Exocet property is demonstrated, is obvious (-35 r1c1; -2 r8c9, -2b89146, -2 r9c1389; lclste)
Note that the exocet property can be easily demonstrated digit per digit, with basics and X-wings, in that case, it is a General Exocet (can't be named Senior Exocet). The true difficult point in this puzzle is to find the second target cell r1c1 ! blue's post JE Compendium gives a hint, how to find it manually for the standard Senior Exocet (with aligned cover houses)
Last edited by Cenoman on Tue Sep 15, 2020 2:12 pm, edited 2 times in total.
Cenoman
Cenoman

Posts: 1665
Joined: 21 November 2016
Location: Paris, France

### Re: "Potential Hardest" 2

Code: Select all
`...9....8.76......8..5.4..3.....92.........3.1..3....5.1..3...44...9..5..5.4..8..`

Analysis results
Difficulty rating: 11.4 (Dynamic Contradiction Forcing Chains (+ Dynamic Forcing Chains))
This Sudoku can be solved using the following logical methods:
57 x Hidden Single
1 x Direct Hidden Pair
5 x Pointing
2 x Claiming
1 x Hidden Triplet
1 x Skyscraper
1 x VWXYZ-Wing 1410
2 x Nishio Forcing Chains
2 x Cell Forcing Chains
3 x Dynamic Cell Forcing Chains
14 x Dynamic Contradiction Forcing Chains
11 x Dynamic Contradiction Forcing Chains (+)
3 x Dynamic Region Forcing Chains (+)
2 x Dynamic Cell Forcing Chains (+)
1 x Dynamic Region Forcing Chains (+ Forcing Chains)
1 x Dynamic Contradiction Forcing Chains (+ Forcing Chains)
3 x Dynamic Cell Forcing Chains (+ Multiple Forcing Chains)
8 x Dynamic Contradiction Forcing Chains (+ Multiple Forcing Chains)
2 x Dynamic Cell Forcing Chains (+ Dynamic Forcing Chains)
1 x Dynamic Contradiction Forcing Chains (+ Dynamic Forcing Chains)
The most difficult technique (ER): Dynamic Contradiction Forcing Chains (+ Dynamic Forcing Chains)
Pupp

Posts: 157
Joined: 18 October 2019

### Re: "Potential Hardest" 2

Hi Cenoman,

Cenoman wrote:Many thanks for your long response. I have tried to deepen the pattern, and I get conclusions similar to yours.

Glad to hear it, as you certainly have much more experience with Exocets.

I'm not much fond of r8c46 as "S"-cells for digit 1. In none of David's or blue's diagrams, cells in sight of the base cells are used as "S"-cells.

True.

That's makes sense to me, as "S"-cells are part of a "fish" used to demonstrate: BD digit True in the base-cells => same BD True in one target cell.

Yes, but to me the actual fish also includes the unlisted S-line candidates that are implicitly covered by the base box and base line. Whether they're called S-cells or not, they're still part of the logic. After all, they're base candidates in the true meaning of the word. (I really hate the confusing overloading of "base" in the Exocet context.)

That approach allows the fish to be any size and shape, as long as it can be used to prove the Exocet property. In this case the digit 1 has a 1-fish in row 8 (or box 9), of which box 8 (or row 9) cover two candidates leaving just one to be covered by the target cell. To me row 8 is an S-line even if it doesn't have any official S-cells for digit 1. Similarly box 9 could be considered an S-box if we took that route.

It's admittedly a different point of view, because I don't particularly like David's abstractions and terminology. They might make simple things simpler (or not), but they definitely make hard things harder, which I don't consider a good trade-off. I think one generic POV that works for every situation is better than memorizing a bunch of special cases relying on awkward terminology and weird kludges. For example, the term "cross-line" is bad because it can't be logically used for S-lines that are parallel to the base band, much less boxes. A more generic term is needed for the non-basic variants.

Note: one could also consider r123456c78 as "S"-cells for digit 1; four CH's (r1234) vs four CL's (c4789)! (I'm kidding... but it works.)

Hmm. Can you elaborate? I count five covering rows (12345) for the four S-columns (4789). Even four covers would be one too many (and it could be done with the boxes, or we could add c3 to get 5x5). What am I missing?

As regards BD 2,6,7, the "standard" Senior Exocet would be there, w/o the spoiler candidates 267r7c1.

Indeed. That was one thing that threw me off.

There is a need for one more CH, the additional "S"-cells of which shall see the second target r8c9; r8c23 only are compliant, and the additional CH is box 7.
Code: Select all
` +---------------------------+----------------------------+--------------------------+ | t235     234     12345    |  9       1267      12367   |  1567    1267    8       |  | S2359    7       6        | S128     128       1238    |  1459    1249   S129     | CH 12  |  8       29      129      |  5       1267      4       |  1679    12679   3       |  +---------------------------+----------------------------+--------------------------+ | S3567    3468    34578    | S1678    145678    9       |  2       14678  S167     | CH 1 67 | S25679   24689   245789   | S12678   1245678   12678   |  14679   3      S1679    | CH 1267 |  1       24689   24789    |  3       24678     2678    |  4679    46789   5       |  +---------------------------+----------------------------+--------------------------+ | S2679    1       2789     |  2678    3         5       |  679     2679    4       |  |  4      S268    S278      |  12678   9         12678   |  3       5      t1267    |  |  23679   5       2379     |  4      b1267     b1267    |  8       12679   12679   |  +---------------------------+----------------------------+--------------------------+    CL2                         CLB                                          CL1          b7: CH  267`

I mostly agree with that. However, like I said above, I don't see how those row covers for digit 1 can work. Also, I think the extra S-cells in r8c23 need to be associated with a house (because it's a truth) -- just like the normal cross-lines are associated with their columns. There we have the terminology problem I mentioned. That house is obviously row 8, but it can't be logically called a cross-line (any more than a box could be). Thus we need a more generic name for the S-cell houses. I've used S-line (could be S-box, too), and that seems to be somewhat in line with blue's terminology.

For example, in this case we have three S-columns and one S-row. No need to talk about confusing cross-lines which only make sense for the basic shape. (I already got confused when I wrote the previous post, because I thought cross-lines were cover houses crossing the S-lines -- but they're actually crossing the base band and are thus synonyms for (normal) S-lines). Then again, 'S' is associated with Swordfishes (though no longer officially), and as we've seen, they're not the only fish size we can have. 'F' would be better. This is how I might personally mark it (keeping the 'S' for now), using the same style I use for MSLS:

my grid markup: Show
Code: Select all
` +----------------------------+-----------------------------+---------------------------+ | \t235     234     12345    |  9        1267      12367   |  1567    1267     8       |  |  s2359    7       6        | s128      128       1238    |  1459    1249    s129     | \2  |   8       29      129      |  5        1267      4       |  1679    12679    3       |  +----------------------------+-----------------------------+---------------------------+ |  s3567    3468    34578    | s1678     145678    9       |  2       14678   s167     | \67 |  s25679   24689   245789   | s12678    1245678   12678   |  14679   3       s1679    | \267 |   1       24689   24789    |  3        24678     2678    |  4679    46789    5       |  +----------------------------+-----------------------------+---------------------------+ |  s2679    1       2789     | ?2678     3         5       |  679     2679     4       |  |   4      s268    s278      | ?12678    9        ?12678   |  3       5      \t1267    | *S4:1267 |  ?23679   5       2379     |  4      *b1267    *b1267    |  8       12679   ?12679   | \267 +----------------------------+-----------------------------+---------------------------+   *S2:267    \b7:267           *S1:267    \b8:1267                           *S3:267`

'*' : bases (truths)
'?' : cells I would logically consider S-cells in addition to the standard ones

The true difficult point in this puzzle is to find the second target cell r1c1 !

Indeed, especially since it can only hold one base candidate! Very hard to see as a target. That, together with the extra complexity of r7c1, made me go a completely different route.

blue's post gives a hint, how to find it manually.

Which post/part do you mean? (I don't think the basic case is nearly this hard to see anyway. This one had several additional challenges, which made if very interesting.)
Last edited by SpAce on Tue Sep 15, 2020 1:18 am, edited 1 time in total.

SpAce

Posts: 2672
Joined: 22 May 2017

### Re: "Potential Hardest" 2

mith wrote:
Code: Select all
`+-------+-------+-------+| . . . | 9 . . | . . 8 || . 7 6 | . . . | . . . || 8 . . | 5 . 4 | . . 3 |+-------+-------+-------+| . . . | . . 9 | 2 . . || . . . | . . . | . 3 . || 1 . . | 3 . . | . . 5 |+-------+-------+-------+| . 1 . | . 3 . | . . 4 || 4 . . | . 9 . | . 5 . || . 5 . | 4 . . | 8 . . |+-------+-------+-------+...9....8.76......8..5.4..3.....92.........3.1..3....5.1..3...44...9..5..5.4..8..`

(As a reminder, these are puzzles which are rated 11+ by SE, but fall to some advanced technique not implemented by SE.)

In Sudoku Explorer, are you turning on all the solving techniques? It defaults to certain things being turned off, and resets when you exit SE. So you need to turn on the techniques again when you start up SE. I only turn on the optional techniques if SE say's it can't analyze a puzzle.
Pupp

Posts: 157
Joined: 18 October 2019

### Re: "Potential Hardest" 2

Provide another puzzle:
Code: Select all
`........1..2..1.34.1.34.5.....2..6...2...3..77...8.....3.....9..5.8.....2.1..4..5`
yzfwsf

Posts: 363
Joined: 16 April 2019

### Re: "Potential Hardest" 2

yzfwsf wrote:Provide another puzzle:
Code: Select all
`........1..2..1.34.1.34.5.....2..6...2...3..77...8.....3.....9..5.8.....2.1..4..5`

No idea for an elegant solution, so here's an ugly one:

Code: Select all
`.------------------------.-----------------------.--------------------.| 345689  46789  3456789 | 5679   25679   256789 | 2789   2678   1    || 5689    6789   2       | 5679   5679    1      | 789    3      4    || 689     1      6789    | 3      4       26789  | 5      2678   2689 |:------------------------+-----------------------+--------------------:| 134589  49-8   34589   | 2      1579    579    | 6      1458   389  || 145689  2      45689   | 14569  1569    3      | 1489   1458   7    || 7       49-6   34569   | 14569  8       569    | 12349  1245   239  |:------------------------+-----------------------+--------------------:| 468     3      4678    | 1567   12567   2567   | 12478  9      268  || 469     5      4679    | 8      123679  2679   | 12347  12467  236  || 2       6789   1       | 679    3679    4      | 378    678    5    |'------------------------'-----------------------'--------------------'`

Step 1. T&E (1): 8r4c2 ->[basics, Finned Swordfish *]-> ! => -8 r4c2

(*): Show
Code: Select all
`       \              \       \.-------------------.-----------------------.------------------.| 35    4     35    |  679     2679    8    | 279    267   1   || 8    *679   2     | *5679   *5679    1    | 79     3     4   | *| 69    1     679   |  3       4       2679 | 5      267   8   |:-------------------+-----------------------+------------------:| 135  ^8     3459  |  2       1579    579  | 6      145   39  || 15    2    #4569  | *14569  *1569    3    | 148    1458  7   | *| 7     9-6   34569 |  14569   8       569  | 1234   1245  239 |:-------------------+-----------------------+------------------:| 46    3     8     |  1567    12567   2567 | 1247   9     26  || 469   5     679   |  8       123679  2679 | 12347  1247  236 || 2    *679   1     | *679    *3679    4    | 378    78    5   | *'-------------------'-----------------------'------------------'          \#b4`

[(6)r259\c245b4 => -6 r6c2]

Step 2. T&E (1): 6r6c2 ->[basics, Finned Mutant Jellyfish **]-> ! => -6 r6c2; btte

(**): Show
Code: Select all
`        \#b1                     \b2         *                        *.-------------------------.--------------------------.----------------------.|  345689  4789   3456789 |  5679    25679   *256789 | 2789    2678    1    || #5689    789    2       | *5679   *5679     1      | 789     3       4    | *|  89-6    1      789-6   |  3       4       *26789  | 5       2678   *2689 | \:-------------------------+--------------------------+----------------------:|  134589  49     34589   |  2       1579     579    | 6       1458    389  ||  14589   2      4589    |  14569   1569     3      | 1489    1458    7    ||  7      ^6      3459    |  1459    8        59     | 12349   1245    239  |:-------------------------+--------------------------+----------------------:|  468     3      4678    |  1567    12567   *2567   | 12478   9      *268  ||  469     5      4679    |  8       123679  *2679   | 12347   12467  *236  ||  2       789    1       | *679    *3679     4      | 378    *678     5    | *'-------------------------'--------------------------'----------------------'                                          \b8                       \b9`

[(6)r29c69\r3b1289 => -6 r3c13]

As a Grouped X-Chain:

[(6)r2c1 = r2c45 - r13c6 = r78c6 - r9c45 = r9c8 - r13c8 = (6)r3c9 => -6 r3c13]

Perhaps those fishes indicate some pattern there, but I can't see it. No time to look for one either, so I'll be expecting someone else to reveal the secrets of this evil puzzle.
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2672
Joined: 22 May 2017

### Re: "Potential Hardest" 2

SpAce wrote:
Note: one could also consider r123456c78 as "S"-cells for digit 1; four CH's (r1234) vs four CL's (c4789)! (I'm kidding... but it works.)

Hmm. Can you elaborate? I count five covering rows (12345) for the four S-columns (4789). Even four covers would be one too many (and it could be done with the boxes, or we could add c3 to get 5x5). What am I missing?

Tried to find something funny, but failed !
SpAce wrote:
blue's post gives a hint, how to find it manually.

Which post/part do you mean? (I don't think the basic case is nearly this hard to see anyway...

One more failure: I confused blue's post and David's Compendium.

Fixed in my previous post.
Cenoman
Cenoman

Posts: 1665
Joined: 21 November 2016
Location: Paris, France

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