## Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

### Re: Exotic patterns a resume

The truth cells in box 1 are not contributing to exclusions and can be ignored. So you are left with a normal MSLS. If adding 3 cell truths from r357c1 you can get the same eliminations with Xsudo as with post "p38692 2 rows 2 columns". However these extra eliminations are within those truths.

My solver can like xsudo give those eliminations when entering the truths. (ignoring rank and currently 5ms, but can still be optimized to 1ms)
Xsudo also fails/is very slow in finding any rank 0.
Enumerating all combinations is unfeasible, hope you find something that can speed this up.

hello creint,
could you show your MSLS. As cells r3c123 are part of the logic in many cases, I would like to see your MSLS.

regarding Xsudo, I agree that the engine producing SLG's is not very rich;
My own old MSLS was not very efficient. I hope to build something much better adding the features described in the recent posts (and in the posts to come).
champagne
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### Re: conjecture : no valid logic negative rank

champagne wrote:Can we with a sudoku produce a truths/links logic of negative rank.
I have doubts for several reasons
...
let us assume that we have a 15 truths 14 links logic.
we can assign the right candidate in truths having no triple point. We then have a similar situation with less truths. At the end, we should find a pattern with 2 truths and one link. This should not happen in a sudoku

More on this post.

a pattern with 2 truths and one link, excluding solved cells and singles can not include cells. In the filed of basic sets, we have no set covering 2 cels truths.
The only solution, somehow artificial is to combine rows/columns sets with a box cover? This means that the rows and columns set are contained in the box.
A valid sudoku can not produce such a situation with 2 rows or 2 columns as set. This is possible

in a box

aaa
a..
a..

we can see this as a row set and a column set locked in a box and sharing one digit.
A manual player would immediately conclude that the common digit can be assigned.
If we use a computer, we have to assume that this simple rule has been applied before the search of a complex rank 0 logic.

I see so far no example of interleaved simple logic with 2 triple points both valid.

Note: starting the search of a complex logic after basic moves makes sense. In fact, in my current code, as I first try to locate interesting fields using a multi-floors brute force, I solve all "one floor" eliminations before the search.
Last edited by champagne on Wed Mar 11, 2020 3:19 am, edited 1 time in total.
champagne
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### Re: Exotic patterns a resume

Hi champagne

Despite the multiple MSLS's offered so far, my solver manages to come up with a different one:

16 cell Truths: c5689 r1257
16 links: 14c5, 23c6, 12c8, 34c9, 6r1, 9r2, 578r5, 78r7, 5b3
19 eliminations: r1c7<>6, r5c1<>5, r5c1<>8, r5c3<>5, r5c3<>7, r5c3<>8, r5c7<>7, r7c1<>8, r7c3<>7, r7c3<>8, r4c5<>1, r9c5<>4, r3c6<>2, r3c6<>3, r8c6<>2, r3c8<>1, r3c8<>2, r3c9<>3, r3c9<>4
Apologies if I missed this solution somewhere above.

Phil
pjb
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### Re: Exotic patterns a resume

pjb wrote:Hi champagne

16 cell Truths: c5689 r1257
16 links: 14c5, 23c6, 12c8, 34c9, 6r1, 9r2, 578r5, 78r7, 5b3
19 eliminations: r1c7<>6, r5c1<>5, r5c1<>8, r5c3<>5, r5c3<>7, r5c3<>8, r5c7<>7, r7c1<>8, r7c3<>7, r7c3<>8, r4c5<>1, r9c5<>4, r3c6<>2, r3c6<>3, r8c6<>2, r3c8<>1, r3c8<>2, r3c9<>3, r3c9<>4

Phil

perfect, with one box link and no triple point.
creint proposal is likely similar
champagne
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### Re: Exotic patterns a resume

Champagne, good luck with your analysis. Here is yet another way to cover the MSLS.

Code: Select all
98.7.....7.6...8......5....4......3..9.6.........24..1.6.9..5......3..4......1..2;38692;GP;12_07
*-------------------------*-------------------------*-------------------------*
| <9>     <8>     12345   | <7>     146     236     | 1234-6  1256    3456    |
| <7>     12345   <6>     | 1234    149     239     | <8>     1259    3459    |
1234 | 123     1234    1234    | 12348   <5>     689-23  | 1234679 679-12  679-34  |
*-------------------------*-------------------------*-------------------------*
| <4>     1257    12578   | 158     789-1   5789    | 267     <3>     5678    |
578 | 123-58  <9>     123-578 | <6>     178     3578    | 24-7*   2578    4578    | b5 13
| 6       357     3578    | 358     <2>     <4>     | 79      5789    <1>     | b6 24
*-------------------------*-------------------------*-------------------------*
78 | 123-8   <6>     1234-78 | <9>     478     278     | <5>     178     378     |
| 1258    1257    125789  | 258     <3>     5678-2  | 1679    <4>     6789    | b8 24
| 358     3457    345789  | 458     678-4   <1>     | 3679    6789    <2>     | b9 13
*-------------------------*-------------------------*-------------------------*
58                        679

MS-NS: 22 digits (1234)r3, (578)r5, (78)r7, (58)c4, (679)c7, (13)b5, (24)b6, (24)b8, (13)b9
22 cell covers r1c12347, r46897c48, r57c5689, r5c7
Eliminations: 19 digits in 12 cells 6r1c7, 23r3c6, 12r3c8, 34r3c9, 1r4c5, 58r5c1, 578r5c3, 7r5c7, 8r7c1, 78r7c3, 2r8c6, 4r9c5

The puzzle has an almost SK Loop where the MSLS can be derived by setting covers for the 4 'home' digits in the pivot boxes and covers for remaining 'away' digits in the SK Loop rows and columns. However in this case this gives a misbalance of 1 between the digit count and the fully covered cell count. As I have mentioned before, adding an extra home cover to a row or column through the completely uncovered box (box1 here) will often rectify the balance. In this case it is r3 that works.

Note:(7*)r5c7 is eliminated because while (24) in that cell are covered once (7) is covered twice. If it were true it would reduce the cell count by one but the digit count by 2 creating a misbalance.

To demonstrate the use of Hobi-Wahn's transforms:
We can add home sets to r456 and away sets b456 as these offer two ways of covering the same cells.
When home and away sets are added they simply cancel out as together they will cover every digit.

Theoretically it is possible for cover sets to be doubled using these operations but I avoid doing this as it makes the counting more complicated.

This home and away set approach suits me as it makes exploring the possible options much quicker.
David P Bird
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### Re: Exotic patterns a resume

Well, its fun time again, so I put my MSLS into survey mode and found 45 for this puzzle. Many were trivial, but I suspect that all the ones with >= 15 Truths would produce the usual 19 eliminations.

Hidden Text: Show
MSLS 5 : Base 1234; r3489 c12347 + r6c7 & r6c234 : 23 Links; 1234r3 12r4 12r8 34r9 & 3r6 ; 8c1 7c2 789c3 58c4 679c7 ; 5b4 5b7 ;
MSLS 6 : Base 1234; r34689 c347 + r3c1 r3c2 & r4689c2 : 21 Links; 1234r3 12r4 3r6 12r8 34r9 & 7c2 ; 789c3 58c4 679c7 ; 5b4 ;
MSLS 7 : Base 1234; r34689 c1347 + r3c2 & r4689c2 : 23 Links; 1234r3 12r4 3r6 12r8 34r9 & 7c2 ; 58c1 789c3 58c4 679c7 ; 5b4 ;
MSLS 8 : Base 1234; r34689 c2347 + r3c1 : 21 Links; 1234r3 12r4 3r6 12r8 34r9 ; 7c2 789c3 58c4 679c7 ; 5b4 ;
MSLS 9 : Base 1234; r34689 c12347 : 23 Links; 1234r3 12r4 3r6 12r8 34r9 ; 8c1 7c2 789c3 58c4 679c7 ; 5b4 5b7 ;
MSLS 30 : Base 1234; c5689 r157 & r2c5689 : 16 Links; 14c5 23c6 12c8 34c9 & 9r2 ; 6r1 578r5 78r7 ; 5b3 ;
MSLS 31 : Base 1234; c5689 r1257 : 16 Links; 14c5 23c6 12c8 34c9 ; 6r1 9r2 578r5 78r7 ; 5b3 ;
MSLS 32 : Base 1234; c15689 r157 + r3c1 & r2c5689 : 19 Links; 123c1 14c5 23c6 12c8 34c9 & 9r2 ; 6r1 578r5 78r7 ; 5b3 ;
MSLS 33 : Base 1234; c15689 r1257 + r3c1 : 19 Links; 123c1 14c5 23c6 12c8 34c9 ; 6r1 9r2 578r5 78r7 ; 5b3 ;

I think my number 30 is the same as Phil's. Also the extra (19th) elimination is because JCVH played a non-basic move before the MSLS and there was already no 5 in r1c7.

Leren
Leren

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### Re: Exotic patterns a resume

Welcome back David, nice cross post, good to see you back now that things appear to be .... different ... to what they were !!! Do I see an MSLS Compendium in our future ? Leren
Leren

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### Re: Exotic patterns a resume

In the first posts, i posted an erroneous example giving this puzzle as having a pure 2 rows 2 columns rank 0 logic

.....67...5.1...3...9.2...42..........8.4...29.46..........7.6....3..1..8.......5;11.30;1.20;1.20;elev;318

It appears that the 2 rows 2 columns solution with one crossing occupied is very similar to the solution for the puzzle 38692.
The MSLS should be slightly different, but likely as common.
champagne
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### Re: Exotic patterns a resume

21 Eliminations as follow
MSLS.PNG (56.6 KiB) Viewed 295 times

23 Eliminations as follow
msls2.png (58.63 KiB) Viewed 295 times
yzfwsf

Posts: 313
Joined: 16 April 2019

### Re: Exotic patterns a resume

Hi yzjwsf,

First thank for your small example. It helped me to better understand some aspects of the rank 0 logix.

Here, you have similar MSLS. This is fine.
I am more in favour of the smallest possible MSLS in my investigations. The reason is very simple, the search of small MSLS is normally cheaper than for bigger ones.

So I could propose to you and other specialists to produce MSLS as small as possible.
champagne
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Location: France Brittany

### Re: Exotic patterns a resume

I can offer another 16 cell veersion with the 1 box link:

16 cell Truths: r1278 c1359
16 links: 13r1, 67r2, 13r7, 67r8, 4c1, 2c3, 589c5, 89c9, 5b7
20 eliminations: r1c2<>1, r1c2<>3, r1c8<>1, r2c7<>6, r7c2<>1, r7c2<>3, r7c7<>3, r8c2<>6, r8c2<>7, r8c8<>7, r9c3<>2, r4c5<>5, r4c5<>8, r4c5<>9, r6c5<>5, r6c5<>8, r9c5<>9, r4c9<>8, r4c9<>9, r6c9<>8,

Phil
pjb
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### Re: Exotic patterns a resume

For this puzzle rated 10.2, leren produced in this thread an interesting MSLS size 19

98.7..6......6.........5.4.8..3..7...2...1.6...3......7...1..5..9..4...6..82..9..;4;4;10.2;10.2;9.2;fl; 1456;tr; 15;

Code: Select all
truths {5N1 23578N47 19N5689}
links {2r1 3r19 4r5 5r5 7r9 89c4 238c7 1b239 4b29 5b38 6b8}
20 Eliminations -->
r5c359<>5, r2c89<>1, r5c39<>4, r6c47<>8, r9c12<>3, r1c3<>2,
r2c6<>4, r2c9<>5, r3c9<>1, r6c7<>2, r6c4<>9, r7c9<>4, r7c6<>6, r8c8<>1

Applying eliminations, the rating goes down aroud 9.6 still a hard puzzle.

This puzzle has a JExocet and 4 exocets sharing the same base and one target

Code: Select all
9     8     1245  |7     23    234    |6     123    1235
12345 13457 12457 |1489  6     23489  |12358 123789 1235789
1236  1367  1267  |189   2389  5      |1238  4      123789
-----------------------------------------------------------
8     1456  14569 |3     259   2469   |7     129    12459
45    2     4579  |4589  5789  1      |3458  6      34589
1456  14567 3     |45689 25789 246789 |12458 1289   124589
-----------------------------------------------------------
7     346   246   |689   1     3689   |2348  5      2348
1235  9     125   |58    4     378    |1238  12378  6
13456 13456 8     |2     357   367    |9     137    1347

Jexocet base r5c1 r6c1 targets r9c2 r1c3
exocets base r5c1 r6c1 targets r9c2 plus r2c4/r4c6/r7c2/r9c9

the four cells r2c4/r4c6/r7c2/r9c9 have the same assignment, one of the digits 1456
The only possibilty is 4

so
r2c4=r4c6=r7c2=r9c9=4
<34r9c2>
r56c1 contains 4.

This brings us with basic moves to this point

Code: Select all
9     8     4     |7     23    23     |6     1      5
25    357   1     |4     6     89     |238   2389   2789
26    367   267   |1     89    5      |238   4      2789
-----------------------------------------------------------
8     56    569   |3     259   4      |7     29     1
4     2     79    |89    789   1      |5     6      3
1     57    3     |569   2579  2679   |4     289    289
-----------------------------------------------------------
7     4     26    |689   1     3689   |238   5      28
235   9     25    |58    4     378    |1     2378   6
356   1     8     |2     357   367    |9     37     4

solved by basic moves after
5r4c5 - 5r4c3 = 5r8c3 - 5r8c4 = 5r6c4 - ~5r4c5 rating 6.6

This is another exemple of the power of satellites exocets easy to spot when a JE has been seen.

I picked up this puzzle for the MSLS pattern, this will come in the appropriate thread
And congratuaions to leren, he has a powerful MSLS engine
champagne
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### Re: Exotic patterns a resume

My Exocet take on this puzzle was :

r5c1 r6c1 r1c3 r9c2 145
r2c9 r3c9 r6c8 r9c8 2789
r6c4 r6c6 r4c2 r4c8 2569 &
r8c1 r8c3 r9c5 r7c9 235

with the last one solving the puzzle with stte

Code: Select all
*--------------------------------------------------*
| 9    8     4    | 7    23   23   | 6   1    5    |
| 125  1357  1257 | 4    6    89   | 238 239  279  |
| 26   367   267  | 1    89   5    | 238 4    2789 |
|-----------------+----------------+---------------|
| 8    56    1569 | 3    259  4    | 7   29   129  |
| 45   2     79   | 89   789  1    | 45  6    3    |
| 145  157   3    | 569  2579 269  | 45  289  1289 |
|-----------------+----------------+---------------|
| 7    4     26   | 689  1    3689 | 238 5   T2-8  |
|B235  9    B25   | 58   4    7    | 1   238  6    |
| 1356 156   8    | 2   T35   36   | 9   7    4    |
*--------------------------------------------------*

I wasn't able to reproduce the same MSLS you mentioned but came up with similar ones and a conventional Multifish for the same 20 eliminations. It's sure been a long time since those days.

Leren
Leren

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Joined: 03 June 2012

### Re: Exotic patterns a resume

Leren wrote:My Exocet take on this puzzle was :

r5c1 r6c1 r1c3 r9c2 145
r2c9 r3c9 r6c8 r9c8 2789
r6c4 r6c6 r4c2 r4c8 2569 &
r8c1 r8c3 r9c5 r7c9 235

with the last one solving the puzzle with stte

Code: Select all
*--------------------------------------------------*
| 9    8     4    | 7    23   23   | 6   1    5    |
| 125  1357  1257 | 4    6    89   | 238 239  279  |
| 26   367   267  | 1    89   5    | 238 4    2789 |
|-----------------+----------------+---------------|
| 8    56    1569 | 3    259  4    | 7   29   129  |
| 45   2     79   | 89   789  1    | 45  6    3    |
| 145  157   3    | 569  2579 269  | 45  289  1289 |
|-----------------+----------------+---------------|
| 7    4     26   | 689  1    3689 | 238 5   T2-8  |
|B235  9    B25   | 58   4    7    | 1   238  6    |
| 1356 156   8    | 2   T35   36   | 9   7    4    |
*--------------------------------------------------*

I wasn't able to reproduce the same MSLS you mentioned but came up with similar ones and a conventional Multifish for the same 20 eliminations. It's sure been a long time since those days.

Leren

Hi leren,

Your "start pm" seems more advanced than your's years ago and mine.

this is your start in my records
Code: Select all
+-----------------------+-----------------------+----------------------------+
| 9       8       145-2 | 7       (23)   (234)  | 6        (123)    (1235)   |
| 12345   13457   12457 | (1489)  6      2389-4 | (12358)  23789-1  23789-15 |
| 1236    1367    1267  | (189)   2389   5      | (1238)   4        23789-1  |
+-----------------------+-----------------------+----------------------------+
| 8       1456    14569 | 3       259    2469   | 7        129      12459    |
| (45)    2       79-45 | (4589)  789-5  1      | (3458)   6        389-45   |
| 1456    14567   3     | 456-89  25789  246789 | 145-28   1289     124589   |
+-----------------------+-----------------------+----------------------------+
| 7       346     246   | (689)   1      389-6  | (2348)   5        238-4    |
| 1235    9       125   | (58)    4      378    | (1238)   2378-1   6        |
| 1456-3  1456-3  8     | 2       (357)  (367)  | 9        (137)    (1347)   |
+-----------------------+-----------------------+----------------------------+

How did you reach your start point
champagne
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Location: France Brittany

### Re: Exotic patterns a resume

Hi Champagne, just a bit of misunderstanding, my PM related to the situation after the first 3 Exocets, not the MSLS.

Quick PM for my latest MSLS was this. I'll check it for typos tomorrow. <Edit> Checked - OK.

Code: Select all
*-----------------------------------------------------------------------*
| 9       8       145-2 | 7      23    234    | 6      123     1235     |
|*12345  *13457  *12457 |*1489   6     2389-4 |*12358  23789-1 23789-15 |
|*1236   *1367   *1267  |*189    2389  5      |*1238   4       23789-1  |
|-----------------------+---------------------+-------------------------|
| 8       1456    14569 | 3      259   2469   | 7      129     12459    |
|*45      2       79-45 |*4589   789-5 1      |*3458   6       389-45   |
| 1456    14567   3     | 456-89 25789 246789 | 145-28 1289    124589   |
|-----------------------+---------------------+-------------------------|
| 7      *346    *246   |*689    1     389-6  |*2348   5       238-4    |
|*1235    9      *125   |*58     4     378    |*1238   2378-1  6        |
| 1456-3  1456-3  8     | 2      357   367    | 9      137     1347     |
*-----------------------------------------------------------------------*

MSLS 1 : Base 1456; r23578 c1247 & r2378c3 : 21 Links; 145r2 16r3 45r5 46r7 15r8 & 2c3 ; 23c1 3c2 89c4 238c7 ; 7b1 ;

Leren
Leren

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