pjb wrote:PS Totuan, how do you get the eliminations -8 r9c7and -8 r7c9?

Thanks for noticing that and more...for r1c7, r3c9. I corrected.

totuan

71 posts
• Page **5** of **5** • 1, 2, 3, 4, **5**

pjb wrote:PS Totuan, how do you get the eliminations -8 r9c7and -8 r7c9?

Thanks for noticing that and more...for r1c7, r3c9. I corrected.

totuan

- totuan
**Posts:**33**Joined:**25 May 2010**Location:**vietnam

David

You're perfectly correct (as usual). With this puzzle they each produce the same 46 eliminations after their follow-ons. However, I'm not convinced from experience that this is always the case. For starters I can produce examples where I can find an SK loop but not MSLS or MF, and same for each. The basic Base 4 4x4 MSLS's usually have an SK loop, but others (Base 4, 4x5,5x4, 4x3, etc and Base 3) usually don't. The reverse is rarer (eg ..3.....1.2...4.7.6.....8.......7.9....26.....5.3....7..1.....6.9.5...4.8.....3.. has an SK loop and MF, but not MSLS). Maybe my implementation of MSLS's is lacking. Puzzles having a Variant SK loop usually do not have MSLS's but occasionally have an MF's. Once we stray from the "vanilla" examples of these strategies, it's not so simple.

Phil

You're perfectly correct (as usual). With this puzzle they each produce the same 46 eliminations after their follow-ons. However, I'm not convinced from experience that this is always the case. For starters I can produce examples where I can find an SK loop but not MSLS or MF, and same for each. The basic Base 4 4x4 MSLS's usually have an SK loop, but others (Base 4, 4x5,5x4, 4x3, etc and Base 3) usually don't. The reverse is rarer (eg ..3.....1.2...4.7.6.....8.......7.9....26.....5.3....7..1.....6.9.5...4.8.....3.. has an SK loop and MF, but not MSLS). Maybe my implementation of MSLS's is lacking. Puzzles having a Variant SK loop usually do not have MSLS's but occasionally have an MF's. Once we stray from the "vanilla" examples of these strategies, it's not so simple.

Phil

- pjb
- 2014 Supporter
**Posts:**2106**Joined:**11 September 2011**Location:**Sydney, Australia

pjb wrote:The reverse is rarer (eg ..3.....1.2...4.7.6.....8.......7.9....26.....5.3....7..1.....6.9.5...4.8.....3.. has an SK loop and MF, but not MSLS).

Phil

Hi phil,

I did not check your example, but for me, a SK loop must have the 16 cells base rank 0 logic. It is exactly the same logic.

- champagne
- 2017 Supporter
**Posts:**7019**Joined:**02 August 2007**Location:**France Brittany

Phil, something must be adrift in your procedure. Turning the SK Loop into a MSLS produces this:

..3.....1.2...4.7.6.....8.......7.9....26.....5.3....7..1.....6.9.5...4.8.....3..

MS-NS: 16 digits, 16 cell covers (59)r2, (27)r8, (47)c2, (25)c8, (18)b1, (36)b3, (36)b7, (18)b9

Eliminations 15 digits in 12 cells 6r1c7, 9r2c4, 59r2c5, 3r3c9, 4r4c2, 47r5c2, 5r5c8, 2r6c8, 3r7c1, 27r8c5, 2r8c6, 6r9c3

If you build a collection of your funnies (where one method works and the other doesn't) and copy them to me in a PM, I can look into them.

David

..3.....1.2...4.7.6.....8.......7.9....26.....5.3....7..1.....6.9.5...4.8.....3..

MS-NS: 16 digits, 16 cell covers (59)r2, (27)r8, (47)c2, (25)c8, (18)b1, (36)b3, (36)b7, (18)b9

Eliminations 15 digits in 12 cells 6r1c7, 9r2c4, 59r2c5, 3r3c9, 4r4c2, 47r5c2, 5r5c8, 2r6c8, 3r7c1, 27r8c5, 2r8c6, 6r9c3

If you build a collection of your funnies (where one method works and the other doesn't) and copy them to me in a PM, I can look into them.

David

- David P Bird
- 2010 Supporter
**Posts:**1042**Joined:**16 September 2008**Location:**Middle England

Thanks David

I obviously have a relatively limited implementation of MSLS. What I do have one can see on my web site help file. I checked a large number of puzzles with standard SK loops and they all have an MSLS with 16 links in 4 rows and 4 columns and 16 cell truths. There must be something different about the puzzle in question.

Phil

I obviously have a relatively limited implementation of MSLS. What I do have one can see on my web site help file. I checked a large number of puzzles with standard SK loops and they all have an MSLS with 16 links in 4 rows and 4 columns and 16 cell truths. There must be something different about the puzzle in question.

Phil

- pjb
- 2014 Supporter
**Posts:**2106**Joined:**11 September 2011**Location:**Sydney, Australia

Since receiving a set of workgrids from Phil where the follow-on eliminations are not always equivalent I have a chance to analyse them. From these I find Phil has proved his point, and so I have re-worded my statement in my post of Jul 21st to read:

As usual, the reasons are not simple but seem to reduce to two:

1. Unless there is one house that holds unsolved digits retricted to either the Home or Away sets, it is impossible to transform a cover pattern with an even number of house covers to one that has an odd number and vice versa. The Obi-Whan trasformation rules don't allow this. Although I haven't explored this for a large number of puzzles, experience suggests that many SK-Loops do have such houses.

Multifish and MSLS are directly equivalent to each other as the MSLS logic simply uses the compliment of the strong cover set as a weak cover set. This then forces the cells to be considered as the strong sets. Therefore in the absence of an SK loop there is no problem.

2. It is possible for alternative rank 0 patterns to overlap. If an attempt is made to combine them, some eliminations may be lost because cells that external to one locked set (where eliminations can be made) are internal to the other (where the digits are locked). In such cases the two rank 0 patterns must be run consecutively. Depending on which one is run first, the results may appear to differ.

This may not immediately be obvious, as some follow-on eliminations are not usually thought of as rank O patterns.

This was an interesting exercise for me, as although on one hand it has been dissapointing to be corrected, on the other I have found something new in what I considered a dead subject.

I may post more on this in due course to provide some illustrative examples.

David PB

.

However when the eliminations from any follow-on tuples are made, they will~~always~~usually produce the same result as some eliminations will simply switch categories.

As usual, the reasons are not simple but seem to reduce to two:

1. Unless there is one house that holds unsolved digits retricted to either the Home or Away sets, it is impossible to transform a cover pattern with an even number of house covers to one that has an odd number and vice versa. The Obi-Whan trasformation rules don't allow this. Although I haven't explored this for a large number of puzzles, experience suggests that many SK-Loops do have such houses.

Multifish and MSLS are directly equivalent to each other as the MSLS logic simply uses the compliment of the strong cover set as a weak cover set. This then forces the cells to be considered as the strong sets. Therefore in the absence of an SK loop there is no problem.

2. It is possible for alternative rank 0 patterns to overlap. If an attempt is made to combine them, some eliminations may be lost because cells that external to one locked set (where eliminations can be made) are internal to the other (where the digits are locked). In such cases the two rank 0 patterns must be run consecutively. Depending on which one is run first, the results may appear to differ.

This may not immediately be obvious, as some follow-on eliminations are not usually thought of as rank O patterns.

This was an interesting exercise for me, as although on one hand it has been dissapointing to be corrected, on the other I have found something new in what I considered a dead subject.

I may post more on this in due course to provide some illustrative examples.

David PB

.

- David P Bird
- 2010 Supporter
**Posts:**1042**Joined:**16 September 2008**Location:**Middle England

If I understand the bulk of this thread, one follow up might be that there may be puzzles that require [with current known solving tools] both a JE and an MSLS. For example, perhaps a JE gives an initial set of exclusions and their implications. Then, after all the JE implications, an MSLS is revealed and a further set of new exclusions is identified.

I do not know of such a puzzle. There are certainly examples of puzzles with a JE and an MSLS, but only one of the two is actually needed to advance the puzzle to the same place in a path.

I do not know of such a puzzle. There are certainly examples of puzzles with a JE and an MSLS, but only one of the two is actually needed to advance the puzzle to the same place in a path.

- ghfick
**Posts:**52**Joined:**06 April 2016

here's a quick way of finishing off the position in platinum blonde after the wombo combo of jexocet+ and rectangular shaped multi fish. i don't remember seeing the puzzle solved from that point, and a search found nothing, after leren's pm grid here, so here's my hand-made offering

after exotic patterns we get to here

where the * and # candidates form a conjugate loop.

-4r4c2 seems to be the way to go, as it cracks the puzzle open. like space i also don't get david's argument that the ur threat in r67c89 after # cells are true immediately implies 4r6c3, but here's a contradiction net

assume # cells are true then

r4c2-4-r6c3-3-(r6c57)r8c3-6-r7c1=6=r7c7(-23)-6-r4c7=6=r4c5=3=r9c5-3-r9c78=3=r8c8(-3-r56c8=3=r4c7-3-r4c6)=2=r9c78-2-r9c45=2=r78c6-2-r4c6-4-r4c2 => r4c2=/=4

giving r4c6=4

box-line 4b4 in c3 => -4r12c3

ur2 79r12c37 => -6r123c1r8c3

r8c3=3, r7c1=6, r4c7=6, r6c4=6, r78c2=12

r4c5-3-r4c2-9|7-r7c6=3=r5c6-3-r4c5 => r4c5=/=3

r4c5=2, r2c6=2, r5c4=1

line-box 3r4 in b4

naked pair 49r5

hidden triple 479c8

hidden pair 23b6

r6c9=1

box-line 7b6 in c8

swordfish 9c258 (it's cool but useless)

r5c6-5-r1c6-8-r8c6-1-r8c2-2-r7c2=2=r7c7-2-r6c7-3-r6c5-5-r5c6 => r5c6=/=5 stte

after exotic patterns we get to here

- Code: Select all
`3568 3458 4679 |4679 568 458 |79 1 2`

1568 1458 4679 |4679 12568 12458 |79 568 3

1567*8 1589# 2 |3 15689* 157#8 |4 568 68

-------------------+---------------------+-------------------

237# 2349* 1 |8 236 234 |236 7*9# 5

235 6 349# |124 7 1235 |8 2349 149

2358 2358 347* |1246 1235 9 |123 23467 1467

-------------------+---------------------+-------------------

1236 123 8 |5 1239# 1237* |1236 479 479

9 123 36 |127# 4 1238 |5 2368 1678

4 7 5 |129* 1238 6 |123 238 189

where the * and # candidates form a conjugate loop.

-4r4c2 seems to be the way to go, as it cracks the puzzle open. like space i also don't get david's argument that the ur threat in r67c89 after # cells are true immediately implies 4r6c3, but here's a contradiction net

assume # cells are true then

r4c2-4-r6c3-3-(r6c57)r8c3-6-r7c1=6=r7c7(-23)-6-r4c7=6=r4c5=3=r9c5-3-r9c78=3=r8c8(-3-r56c8=3=r4c7-3-r4c6)=2=r9c78-2-r9c45=2=r78c6-2-r4c6-4-r4c2 => r4c2=/=4

giving r4c6=4

box-line 4b4 in c3 => -4r12c3

ur2 79r12c37 => -6r123c1r8c3

r8c3=3, r7c1=6, r4c7=6, r6c4=6, r78c2=12

- Code: Select all
`358 3458 679 |479 568 58 |79 1 2`

158 458 679 |479 12568 1258 |79 568 3

157*8 589# 2 |3 15689* 157#8 |4 568 68

------------------+---------------------+-------------------

237# 39* 1 |8 23 4 |6 7*9# 5

235 6 49# |12 7 1235 |8 2349 149

2358 358 47* |6 1235 9 |123 2347 147

------------------+---------------------+-------------------

6 12 8 |5 1239# 1237* |123 479 479

9 12 3 |127# 4 128 |5 268 1678

4 7 5 |129* 1238 6 |123 238 189

r4c5-3-r4c2-9|7-r7c6=3=r5c6-3-r4c5 => r4c5=/=3

r4c5=2, r2c6=2, r5c4=1

line-box 3r4 in b4

naked pair 49r5

hidden triple 479c8

hidden pair 23b6

r6c9=1

box-line 7b6 in c8

swordfish 9c258 (it's cool but useless)

- Code: Select all
`358 3458 679 |479 568 58 |79 1 2`

158 458 679 |479 1568 2 |79 568 3

1578 589 2 |3 15689 1578 |4 568 68

------------------+---------------------+-------------------

237 39 1 |8 2 4 |6 79 5

25 6 49 |1 7 35 |8 23 49

258 58 47 |6 35 9 |23 47 1

------------------+---------------------+-------------------

6 12 8 |5 139 137 |123 49 47

9 12 3 |27 4 18 |5 268 678

4 7 5 |29 138 6 |123 238 89

r5c6-5-r1c6-8-r8c6-1-r8c2-2-r7c2=2=r7c7-2-r6c7-3-r6c5-5-r5c6 => r5c6=/=5 stte

Once upon a time I was a teenager who was active on here 2007-2011

ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven

- 999_Springs
**Posts:**487**Joined:**27 January 2007**Location:**In the toilet, flushing down springs, one by one.

With trial and error

Combination B7=146 and D9=127

************************************************************

B7=1 D9=1 Wrong, Undo calculation

All reset to initial position

************************************************************

B7=1 D9=2 Wrong, Undo calculation

All reset to initial position

************************************************************

B7=1 D9=7 No solution, Fixed

Combination 2-digits cells

A9=2 No solution, Undo calculation

A9=3 No solution, Undo calculation

C7=6 No solution, Undo calculation

C7=7 No solution, Undo calculation

D5=2 Wrong, Undo calculation

D5=3 Wrong, Undo calculation

All reset to initial position

************************************************************

B7=4 D9=1 Wrong, Undo calculation

All reset to initial position

************************************************************

B7=4 D9=2 No solution, Fixed

Combination 2-digits cells

A9=1 Wrong, Undo calculation

A9=3 ( C5=3 ) Solved,

--------------------------------Solution

980 760 500-------------982 764 513

700 800 090-------------731 852 496

005 009 008-------------645 139 728

590 006 080-------------593 476 182

004 000 300-------------824 591 367

000 000 005-------------176 283 945

460 007 050-------------469 327 851

200 010 004-------------257 918 634

000 000 200-------------318 645 279

Total solving time is: 153 sec.

There are several Sudoku solvers. I wanted to program a Sudoku solver myself. I was not interested in the solution, but the program had to show you how to solve a Sudoku. I finally succeeded. But then I discovered the Andrew Stuart site. Although I could also solve these difficult Sudokus, it was a lot of work. So I programmed further to make this simpler. After much testing and programming, the program is ready. Adrew thanks for your difficult Sudoku's. I make the program available for anyone who wants it. It is Free-Ware. It can be downloaded from my OneDrive. It only works under Windows. because the program is new, some virus scanners will not recognize this. If you scan with Virus Total on the web you can see that it is safe.

Set before the link: h t t p s : / /

1drv.ms/f/s!AqqUaBdOy4dli1_qv5pnup-l7DUz

Combination B7=146 and D9=127

************************************************************

B7=1 D9=1 Wrong, Undo calculation

All reset to initial position

************************************************************

B7=1 D9=2 Wrong, Undo calculation

All reset to initial position

************************************************************

B7=1 D9=7 No solution, Fixed

Combination 2-digits cells

A9=2 No solution, Undo calculation

A9=3 No solution, Undo calculation

C7=6 No solution, Undo calculation

C7=7 No solution, Undo calculation

D5=2 Wrong, Undo calculation

D5=3 Wrong, Undo calculation

All reset to initial position

************************************************************

B7=4 D9=1 Wrong, Undo calculation

All reset to initial position

************************************************************

B7=4 D9=2 No solution, Fixed

Combination 2-digits cells

A9=1 Wrong, Undo calculation

A9=3 ( C5=3 ) Solved,

--------------------------------Solution

980 760 500-------------982 764 513

700 800 090-------------731 852 496

005 009 008-------------645 139 728

590 006 080-------------593 476 182

004 000 300-------------824 591 367

000 000 005-------------176 283 945

460 007 050-------------469 327 851

200 010 004-------------257 918 634

000 000 200-------------318 645 279

Total solving time is: 153 sec.

There are several Sudoku solvers. I wanted to program a Sudoku solver myself. I was not interested in the solution, but the program had to show you how to solve a Sudoku. I finally succeeded. But then I discovered the Andrew Stuart site. Although I could also solve these difficult Sudokus, it was a lot of work. So I programmed further to make this simpler. After much testing and programming, the program is ready. Adrew thanks for your difficult Sudoku's. I make the program available for anyone who wants it. It is Free-Ware. It can be downloaded from my OneDrive. It only works under Windows. because the program is new, some virus scanners will not recognize this. If you scan with Virus Total on the web you can see that it is safe.

Set before the link: h t t p s : / /

1drv.ms/f/s!AqqUaBdOy4dli1_qv5pnup-l7DUz

- Frans
**Posts:**2**Joined:**28 September 2018

pjb wrote:David

You're perfectly correct (as usual). With this puzzle they each produce the same 46 eliminations after their follow-ons. However, I'm not convinced from experience that this is always the case. For starters I can produce examples where I can find an SK loop but not MSLS or MF, and same for each. The basic Base 4 4x4 MSLS's usually have an SK loop, but others (Base 4, 4x5,5x4, 4x3, etc and Base 3) usually don't. The reverse is rarer (eg ..3.....1.2...4.7.6.....8.......7.9....26.....5.3....7..1.....6.9.5...4.8.....3.. has an SK loop and MF, but not MSLS). Maybe my implementation of MSLS's is lacking. Puzzles having a Variant SK loop usually do not have MSLS's but occasionally have an MF's. Once we stray from the "vanilla" examples of these strategies, it's not so simple.

Phil

Hello Phil, I am a new member of this forum, because I plan to exhibit my work in France on sudoku.

Your application (solver) is well done and I use it regularly.

Sincerely

Robert

Excuse my English, I use a French/English translator.

- Mauriès Robert
**Posts:**215**Joined:**07 November 2019**Location:**France

Hi,

Totuan used the following puzzle as an example in the discussion SK-Loops and MSLS's, a particularly difficult puzzle since neither Sk-loop nor MSLS can be detected without first simplifying the puzzle through AALS.

Here is another approach with a resolution by TDP of this puzzle whose unique solution is assumed.

- Step 1.

We build P(4r5c46) using extensions. (see puzzle1)

P(4r5c46).P(4r7c5).P(6r46c7).P(6r46c7) = {4r5c46,..., 4r7c5, 4r9c7, 14r46c9,..., 6r46c7, 6r3c9, 6r46c5, 6r5c1, 48r5c46, 8r2c9, 8r8c5, 68r1c46, 4r1c3,...} -> contradiction on c1.

P(4r5c46).P(4r7c5).P(6r5c79) = {4r5c46,..., 4r7c5, 4r9c7, 14r46c9,..., 6r5c79, 48r5c46, 8r2c9, 8r8c5, 357r578c1, 4r2c1, UI(48r15c46),...} -> contradiction with uniqueness.

=> P(4r5c46) = {4r5c46, 4r2c5, ...}

**puzzle1: **Show

P(4r5c46).P(8r5c46) = {4r5c46, 4r2c5,..., 8r5c46, 8r8c5, 357r238c1, 6r7c1,...} -> contradiction in r5c1. (see puzzle2)

=> P(4r5c46) = {4r5c46, 4r2c5, 6r5c46,...}

P(4r5c46).P(6r9c2) = {4r5c46, 4r2c5, 6r5c46,..., 357r237c1, 8r8c1, ...} -> contradiction in r5c1.

P(4r5c46).P(4r9c7) = {4r5c46, 4r2c5, 6r5c46,...4r9c7, 6r46c7, 6r3c9, 6r7c5, 57r237c1, 8r8c1,...} -> contradiction in r5c1.

=> P(4r5c46) = {4r5c46, 4r2c5, 6r5c46, 46r9c46, ...} = {4r2c5, UI(46r49c46, ...}-> contradiction with uniqueness.

=> - 4r5c46 and 14 eliminations by basic techniques.

**puzzle2: **Show

- Step 2 :

We study the track P(8r8c5) and its anti-track P'(8r8c5)=P(8r2c5). (see puzzle3)

P(8r8c5)= {8r8c5, ..., UI(16r46c29), ...} contradiction with uniqueness.

=> P(8r2c5)={8r2c5, ...} solution -> 9 placements (see puzzle3)

**puzzle3: **Show

- Step 3 :

The puzzle then ends well simplified, for example with the 3c9, like this where I let you check the results announced:

P(3r9c3).P(4r9c7) -> contradiction.

P(3r9c3).P(4r7c9) -> contradiction.

P(3r9c7) -> contradiction

P(3r9c46) -> puzzle solution. (see puzzle4)

**puzzle4: **Show

Totuan used the following puzzle as an example in the discussion SK-Loops and MSLS's, a particularly difficult puzzle since neither Sk-loop nor MSLS can be detected without first simplifying the puzzle through AALS.

Here is another approach with a resolution by TDP of this puzzle whose unique solution is assumed.

- Step 1.

We build P(4r5c46) using extensions. (see puzzle1)

P(4r5c46).P(4r7c5).P(6r46c7).P(6r46c7) = {4r5c46,..., 4r7c5, 4r9c7, 14r46c9,..., 6r46c7, 6r3c9, 6r46c5, 6r5c1, 48r5c46, 8r2c9, 8r8c5, 68r1c46, 4r1c3,...} -> contradiction on c1.

P(4r5c46).P(4r7c5).P(6r5c79) = {4r5c46,..., 4r7c5, 4r9c7, 14r46c9,..., 6r5c79, 48r5c46, 8r2c9, 8r8c5, 357r578c1, 4r2c1, UI(48r15c46),...} -> contradiction with uniqueness.

=> P(4r5c46) = {4r5c46, 4r2c5, ...}

P(4r5c46).P(8r5c46) = {4r5c46, 4r2c5,..., 8r5c46, 8r8c5, 357r238c1, 6r7c1,...} -> contradiction in r5c1. (see puzzle2)

=> P(4r5c46) = {4r5c46, 4r2c5, 6r5c46,...}

P(4r5c46).P(6r9c2) = {4r5c46, 4r2c5, 6r5c46,..., 357r237c1, 8r8c1, ...} -> contradiction in r5c1.

P(4r5c46).P(4r9c7) = {4r5c46, 4r2c5, 6r5c46,...4r9c7, 6r46c7, 6r3c9, 6r7c5, 57r237c1, 8r8c1,...} -> contradiction in r5c1.

=> P(4r5c46) = {4r5c46, 4r2c5, 6r5c46, 46r9c46, ...} = {4r2c5, UI(46r49c46, ...}-> contradiction with uniqueness.

=> - 4r5c46 and 14 eliminations by basic techniques.

- Step 2 :

We study the track P(8r8c5) and its anti-track P'(8r8c5)=P(8r2c5). (see puzzle3)

P(8r8c5)= {8r8c5, ..., UI(16r46c29), ...} contradiction with uniqueness.

=> P(8r2c5)={8r2c5, ...} solution -> 9 placements (see puzzle3)

- Step 3 :

The puzzle then ends well simplified, for example with the 3c9, like this where I let you check the results announced:

P(3r9c3).P(4r9c7) -> contradiction.

P(3r9c3).P(4r7c9) -> contradiction.

P(3r9c7) -> contradiction

P(3r9c46) -> puzzle solution. (see puzzle4)

- Mauriès Robert
**Posts:**215**Joined:**07 November 2019**Location:**France

71 posts
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