The New Sudoku Players' Forum

[David P Bird]

If the only premise is the existence of two almost 0-rank multi-fish, we don't even know if ... if ... if one of the PEs is an invalid exclusion in each case. What are your other premises?

I'm using the MSLSs produced by multi-fish for my analysis. This is one of the Almost MSLSs for the Golden Nugget:
.......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7..... 47 Golden Nugget

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     *-------------------------*-------------------------*-------------------------*
 568 | (25678) (14568) 1247-56 | (268)   247-6   (4678)  | 1247    3       9       |
     | 689-27  689-4   2467    | 3689-2  23467   1       | 247     2467    5       |
 69  | (2679)  (1469)  3       | (269)   5       (4679)  | 8       1247-6  1247    |
     *-------------------------*-------------------------*-------------------------*
 35  | (235)   (345)   8       | (135)   9       (357)   | 1247-35 1247    6       |
     | 3569    7       456     | 3568-1  136     2       | 13459   1489    1348    |
     | 1       3569    256     | 4       367     3568-7  | 23579   2789    2378    |
     *-------------------------*-------------------------*-------------------------*
 36  | (367)   (136)   9       | (1236)  8       (346)   | 1247-3  5       1247-3  |
     | 358-7   2       157     | 359-1   134     359-4   | 6       14789   13478   |
     | 4       3568-1  156     | 7       1236    3569    | 1239    1289    1238    |
     *-------------------------*-------------------------*-------------------------*
       27      14                12              47

Almost MSLS: (568)r1,(69)r3,(35)r4,(36)r7,(27)c1,(14)c2,(12)c4,(47)c6 = 17 Constrained candidates in 16 available cells
PEs = 18 candidates in 14 cells

The 16 A-MSLS cells are shown bracketed. 16 out of the 17 constrained candidates must be true in these cells and the one that isn't must be true in just one of the PE cells. This means that 17 out of the 18 PEs are valid eliminations.

Now here's the extra premise you might be considering: for this inference to be sound none of the candidates in the pattern can be covered more than once. (The way I work this is always the case.) I haven't analysed the more exotic almost 0-rank scenarios that can be reached using Xsudo.

[Edit] references to "1-rank" patterns changed to "almost 0-rank" patterns at ronk's request.

[champagne]

Hi leren

comments on the puzzle 1819

98.7.....7.6...8......5.....7.4..6....4..3.2.....1...4.6.9..5......4..3......2..1;1819;GP;H364

Having applied

Jexocet r3c1 r3c3 r2c4 r1c7 1234

16 Truths = {1C1247 2C1247 3C1247 4C127 3N3 }
16 Links = {1r358 2r368 3r369 4r39 1n7 2n24 4n1 7n1 }

The solver comes to that PM

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A     B     C      |D     E    F     |G      H     I     
9     8     5      |7     236  146   |1234   146   236 
7     1234  6      |123   239  149   |8      1459  2359 
1234  1234  123    |12368 5    689   |123479 679   679
--------------------------------------------------------
123   7     123    |4     289  589   |6      1589  3589 
1568  159   4      |568   6789 3     |179    2     5789 
23568 2359  89     |2568  1    56789 |379    5789  4     
--------------------------------------------------------
1234  6     123    |9     378  178   |5      478   278   
1258  1259  789    |1568  4    5678  |279    3     6789
3458  3459  789    |3568  678  2     |479    6789  1   

the same reduced to floors 1234

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X     X     X     |X     23+   14+   |1234  14+   23+ 
X     1234  X     |123   23+   14+   |X     14+   23+   
1234  1234  123   |123+  X     X     |1234+ X     X   

123   X     123   |4g    2+    X     |X     1+    3+   
1+    1+    4g    |X     X     3g    |1+    2g    X     1
23+   23+   X     |2+    1g    X     |3+    X     4g    23

1234  X     123   |X     3+    1+    |X     4+    2+     
12+   12+   X     |1+    4g    1+    |2+    3g    2+    12
34+   34+   X     |3+    3+    2g    |4+    4+    1g    34 
==============     ==                 ==


What I want to test is that we have usually a rank 1 logic using the crossing band where is located the base plus the crossing rows/columns of the targets

Here we look for a rank 1 logic with sets made of columns 12347, it works

18 Truths = {1C12347 2C12347 3C12347 4C127 }
19 Links = {1r58 2r68 3r69 4r9 1n7 2n4 3n47 4n13 7n13 1234b1}


And we have potential eliminations
1r8c6 2r8c9 3r9c5 4r9c8
Plus extra digits in cells r3c47


The solver found the “abi loop” for pairs 12 23
I tried to clean the last possibility with digit2, the pair 24
We are quickly in that position

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X     X     X     |X     3     x     |4     1     2 
X     1     X     |2     x     4     |X     x     3     
2     4     3     |1     X     X     |+     X     X   

3     X     1     |4g    2     X     |X     x     x   
X     x     4g    |X     X     3g    |1     2g    X     1
X     2     X     |x     1g    X     |3     X     4g    23

14    X     2     |X     x     1+    |X     4+    x     
1+    x     X     |x     4g    1+    |2     3g    x     12
4+    3     X     |3     x     2g    |x     4+    1g    34 
==============     ==                 ==


one extra digit in r3c7 is true, so the other are false
<1>r8c6 + <4>r9c8 creates a conflict in r789c1

[Leren]

Champagne wrote:

The solver found the “abi loop” for pairs 12 23
I tried to clean the last possibility with digit2, the pair 24
We are quickly in that position

Hi Champagne,

I still can't follow your Almost Multifish argument for puzzle 1819.

Your logic set is OK but your box cover should read Box 1.

I can't understand your last diagram. Aren't you testing your Jexocet for 24 ?

In that case I would have thought you'd have r1c1 = 2 or 4 and r3c3 = 4 or 2.

Leren

[champagne]

Your logic set is OK but your box cover should read Box 1.
Leren

ok I edited the post

I still can't follow your Almost Multifish argument for puzzle 1819.

I can't understand your last diagram. Aren't you testing your Jexocet for 24 ?

In that case I would have thought you'd have r1c1 = 2 or 4 and r3c3 = 4 or 2.

Leren

yes if you mean r3c1= 2 or 4 and r3c2 = 2 or 4

But during expansion, this has been solved in r3c1=2 and r3c2=4

I hope the expansion is correct, if you do it (not more than several pair effect if my memory is correct), you should reach the final position.

For sure, an optimised expansion would be shorter, but in such studies, I don't try to find the shortest expression of the contradiction

[JasonLion]

An off topic side conversation about forum moderation has been removed.

[champagne]

I implemented in my solver the rank1 logic as shown by leren for Golden Nugget with the following restrictions:

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Sets made of
2 or 3 rows/columns in the cross band/stack containing the exocet base
The cross rows/columns containing the target.


I got the following results for the file of puzzles having an exocet

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31528 puzzles analysed
 2712 unsolved puzzles before rank 1 logic
 1737 unsolved puzzles with rank1 logic using the full cross band
 1685 unsolved puzzles with the 3 options for the rank 1 logic

Golden Nugget remains unsolved on my side.

The main difference with Leren, (as for puzzles having the “V loop”) is that I lock my solver to a process equivalent to serate dynamic plus extended to UR’s kites and skyscrapers while leren’s expansion is equivalent to serate’s nested level (to be confirmed by leren for Golden Nugget)

This rank1 logic of non overlapping sets/links (no triple point) seems to have a high potential.
A blind search is not very attractive. As for Jexocets, specific patterns could be searched, but up to now, I don’t see on which criteria.

[pjb]

Hi Leren

I found your post regarding 'Almost multi-fish' very interesting. In a similar vein, I've had an interest in 'Almost SK loops' with posts here and here. In my case the logic goes that with 3 rather than 2 linking digits, 17 digits have to be placed into 16 cells which of course doesn't work, and one digit is squeezed out and occupies a cell that would otherwise been an elimination. Thus of the potential eliminations that would occur if it was a normal SK loop, one digit is true rather than false, and all the other potential eliminations hold true.

I have now also enacted the strategy of trialing one of the potential eliminations as true and the rest false, and looking to see if a contradiction ensures. In every case I've tested, just one combination proves to be correct. Thus for puzzles such as golden nugget and champagne dry, following the procedure the puzzle greatly simplifies and can be solved with standard moves. This is up and running on my on-line solver if anyone is interested.

pjb

[Leren]

Champagne wrote: Regarding the "V loop", here is the list of puzzles resisting to the current code.

They have similarities, so it's likely the same reason (and it can be a bug in my code).
I have not yet studied the path proposed by the solver

..8...5...6...3.7.4.......1.7..32......9.5......67..2.5.......4.2.3...6...1...8..;7654;TkP;3138
9.......1.3...4.7...6...2...5.3.2.......6........78.5...2...6...4.7...3.1.......9;8400;tax;tarek-ultra-0204
98.7.....7.6.......54...7..4..6..9......5..3......2..1..94..6......1..5......3..2;8402;GP;H2040
1....6.8....7....2....3.5.....5....7.6...4.1.....2.3...14..8...6.2....4.89.......;8405;elev;H235
1.....9...3...7.4...5.....2.....6.7.....1.....4.3.8...9.......5.7.8...3...2...1..;8668;tax;tarek071223170000- 95895
..7...9...3...5.4.6.......8.4..51......7.2......34..1.9.......6.1.5...3...8...7..;9712;TkP;3164
..2...3...7...1.5.6.......8.4...5......43.......1.7.4.8.......2.5.7...1...3...6..;9717;TkP;3101
..9...7...4...1.2.8.......5.2...3......9.6.......12.3.7.......8.3.1...4...5...9..;9762;TkP;3715
..1...2...3...4.5.6.......7.....3.8.....1.....4.9.8...7.......1.5.8...4...2...6..;38022;ig;champagne

Hi all, Ive extended the code for clearance of SK/V loops to include finned XWings and Swordfishes plus W and M wings. All the above puzzles reported by Champagne can now be fully cleared without the need for Nishio, except for no 8405 for which there is only a partial clearance.

Champagne wrote:

Thinking on how to implement the rank 1 logic shown by Leren, I looked in my data base for examples of puzzles having both an exocet and a rank 0 logic.

Usually, these are combining an exocet and a “V loop” or an “almost “V loop”.

That one is much more in line with Leren work

98.7.....7.6...8......5.....7.4..6....4..3.2.....1...4.6.9..5......4..3......2..1;1819;GP;H364

I've applied the same code to the clearance of exocets. Puzzle 1819 exocet is now fully cleared without the need for Nishio, which removes the need for Almost Multifish or Forcing chain moves.

On the same basis the Golden Nugget exocet is almost cleared, with just one false case resistent to my current code (without Nishio). A full clearance without Nishio would require the addition of XY chains to my clearance code.

[champagne]

Hi all, Ive extended the code for clearance of SK/V loops to include finned XWings and Swordfishes plus W and M wings. All the above puzzles reported by Champagne can now be fully cleared without the need for Nishio, except for no 8405 for which there is only a partial clearance.

I have nothing against using the full set of rules in a scenario. Having to explore a limited number of situations remains in difficulty far below the exploration of 200_250 candidates.
One missing information in that case is "how hard and long has it been to achieve that".

Limiting the set or rules usually means shorter paths. As I have not implemented a full scenario study, I have limitations in nested possibilities. It's good to have another program lay out to do more.

I've applied the same code to the clearance of exocets. Puzzle 1819 exocet is now fully cleared without the need for Nishio, which removes the need for Almost Multifish or Forcing chain moves.

In that specific case, my new solver solves it as well with it's limited set of rules, but using exocet sub scenarios (one for each couple of target).


extended file of potential hardest

I loaded in the google skfr project the last update of my file of potential hardest.

here

I am revising the analysis of exotic patterns, a separate upload will come with the corresponding files

[dobrichev]

Hi champagne,

Thank you for the updated collection. It saved me lots of duplicate work.
I didn't expect the file is growing so rapidly.
It seems there is still plenty of low-hanging fruits.

[ronk]

I didn't expect the file is growing so rapidly.

It certainly grows faster when sub-puzzles are included.

[tarek]

I will be updating the list of hardest puzzles according to the criteria specified in the hardest sudoku thread (last update was almost a year and a half ago). In the second post of that thread there will be a link to champagne's page where his potential hardest can be found. My update will not add anything to what you already know & have but it brings the the title post & related lists closer to the present day.

[champagne]

I will be updating the list of hardest puzzles according to the criteria specified in the hardest sudoku thread (last update was almost a year and a half ago). In the second post of that thread there will be a link to champagne's page where his potential hardest can be found. My update will not add anything to what you already know & have but it brings the the title post & related lists closer to the present day.

the google skfr project that is supposed to be the most reliable place is the final location for that file. (and also the place where I can load the 7 millions puzzles file)

The current file will be replaced in the next days by a file without the 329 non minimal puzzles I added by mistake. I keep in the file 2 previous non minimal puzzles included for historical reasons.

The separate file with analysis of exotic patterns should be ready within one or 2 days

[tarek]

You have been more active than most on these topics & I can say that you keep your lists up-to-date more frequently than I have. If your most up-to-date files are going to be on the project page then the link will be to that.

[champagne]

just a warning to users of the last update of potential hardest.
puzzles rated using skfr can be identified in the "01 file " by an '*' at the end of the line.
This is written in the readme file, but in the last line.