## Help to solve hardest puzzles

Post the puzzle or solving technique that's causing you trouble and someone will help

### Re: Help to solve hardest puzzles

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

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Location: vietnam

### Re: Help to solve hardest puzzles

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
pjb
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Location: Sydney, Australia

### Re: Help to solve hardest puzzles

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
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Location: France Brittany

### Re: Help to solve hardest puzzles

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
David P Bird
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### Re: Help to solve hardest puzzles

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
pjb
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Location: Sydney, Australia

### Re: Help to solve hardest puzzles

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:

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
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Location: Middle England

### Re: Help to solve hardest puzzles

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.
ghfick

Posts: 102
Joined: 06 April 2016

### Re: Help to solve hardest puzzles

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
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    4799      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    4799     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     479     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
Pat wrote:prenyast
999_Springs

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### Re: Help to solve hardest puzzles

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
Frans

Posts: 2
Joined: 28 September 2018

### First Contact

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: 343
Joined: 07 November 2019
Location: France

### Re: Help to solve hardest puzzles

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

puzzle4: Show
Mauriès Robert

Posts: 343
Joined: 07 November 2019
Location: France

### Re: Help to solve hardest puzzles

So I elect to leave many puzzles unfinished. Maybe I will return to them as new methods emerge.

Zitmet

Posts: 2
Joined: 08 March 2020

### Re: Help to solve hardest puzzles

I am very big on a program called "Hodoku" for learning new advanced techniques. There is a way to enter your own givens for any puzzle. And then let Hodoku solve it for you. Or, even better, as you are trying to solve it and you get stuck Hodoku has a "Vague Hint" command which tells you the technique to use next but not where it is. If it's not one you know, then you can go out and learn it, come back and continue solving the puzzle.

I did an instructional video on how to download and install Hodoku. I also did a videos on how to use "Vague Hint" and enter your own givens. Here is the playlist of the videos: