I can see that you kept your interest here too dobrichev!
Well done!
The Pencilmark sudoku has many uncharted areas where records can be broken. I've already had a play with "Most difficult" and "biggest singles backdoor". I'm sure with better techniques and faster, more powerful machines these records can be easily broken
tarek
Pencilmark only Sudoku
Re: Pencilmark only Sudoku
by tarek » Wed Jul 10, 2019 8:07 pm
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Re: Pencilmark only Sudoku
by dobrichev » Thu Jul 11, 2019 9:11 pm
Hi Tarek,
IMO Pencilmark sudoku is maybe the most natural extension of the standard rules. All solvers in one or another way use pencilmarks, and I have no explanation why it isn't deeply investigated.
Аt the low-clue end, puzzles with 92 disallowed candidates + 637 allowed are maybe low-hanging fruits. At the moment my cache has 133488 such puzzles, living on at least 3 islands not connected by {-1,+1}.
For 93/636 the count is 454813 and growing, again on at least 3 islands.
This was collected form scratch for about one week, using 2 old home PC and unstable software.
High-clue end is entirely unexplored.
For the "Most difficult" I know you are far ahead and expect some high serate ratings from you. Is there something above ER 11+? Is ER applicable at all for Penclimark sudoku?
The preliminary observations show that low-clue puzzles are easier to solve, just like in the ordinary game.
Finally, if there is such animal as "biggest singles backdoor required to ensure that puzzle has multiple solutions", then records are possible.
Cheers,
MD
IMO Pencilmark sudoku is maybe the most natural extension of the standard rules. All solvers in one or another way use pencilmarks, and I have no explanation why it isn't deeply investigated.
Аt the low-clue end, puzzles with 92 disallowed candidates + 637 allowed are maybe low-hanging fruits. At the moment my cache has 133488 such puzzles, living on at least 3 islands not connected by {-1,+1}.
For 93/636 the count is 454813 and growing, again on at least 3 islands.
This was collected form scratch for about one week, using 2 old home PC and unstable software.
High-clue end is entirely unexplored.
For the "Most difficult" I know you are far ahead and expect some high serate ratings from you. Is there something above ER 11+? Is ER applicable at all for Penclimark sudoku?
The preliminary observations show that low-clue puzzles are easier to solve, just like in the ordinary game.
Finally, if there is such animal as "biggest singles backdoor required to ensure that puzzle has multiple solutions", then records are possible.
Cheers,
MD
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Re: Pencilmark only Sudoku
by Mathimagics » Fri Jul 12, 2019 1:42 pm
dobrichev wrote:IMO Pencilmark sudoku is maybe the most natural extension of the standard rules. All solvers in one or another way use pencilmarks, and I have no explanation why it isn't deeply investigated.
I agree 100%.
It's just an alternate form of presenting the puzzle, and rich with possibilities that the standard method doesn't cover …
I'd like to delve into it more, just as soon as I have some spare time .. . perhaps in 2023? 2025?
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Re: Pencilmark only Sudoku
by dobrichev » Fri Jul 12, 2019 3:08 pm
Too early. Follow the tradition and wait for 12 and a half years after my last posting on the subject.
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Re: Pencilmark only Sudoku
by tarek » Fri Jul 12, 2019 6:02 pm
Hi Mladen and Mathimagics,
1to9only has kindly contributed to an SE version that handles the Sukaku. You will need to use the 729 character format. You can follow that discussion by following this link http://forum.enjoysudoku.com/help-with-sudoku-explainer-t6677-60.html?hilit=sukaku#p271963
Sadly I didn't have time dedicated to this task since although I was initially enthusiastic about it. The slow SE had a role. The idea is to have an SE defeating puzzle (i.e. 12+) but I didn't even test my Singles backdoor size 6 puzzles
Now then ... You'll love this.. Your Minimum clue puzzle is not necessarily a locally minimal one. If adding any one possible candidate to your puzzle results in multiple solutions then that is a locally minimal puzzle. So your record can be for the Minimum clue locally minimal Pencil-mark sudoku ... Interesting isn't it?!
dobrichev wrote:Is there something above ER 11+? Is ER applicable at all for Penclimark sudoku?
1to9only has kindly contributed to an SE version that handles the Sukaku. You will need to use the 729 character format. You can follow that discussion by following this link http://forum.enjoysudoku.com/help-with-sudoku-explainer-t6677-60.html?hilit=sukaku#p271963
Sadly I didn't have time dedicated to this task since although I was initially enthusiastic about it. The slow SE had a role. The idea is to have an SE defeating puzzle (i.e. 12+) but I didn't even test my Singles backdoor size 6 puzzles
Minimal singles backdoor size 6 puzzles: Show
dobrichev wrote:if there is such animal as "biggest singles backdoor required to ensure that puzzle has multiple solutions", then records are possible.
Now then ... You'll love this.. Your Minimum clue puzzle is not necessarily a locally minimal one. If adding any one possible candidate to your puzzle results in multiple solutions then that is a locally minimal puzzle. So your record can be for the Minimum clue locally minimal Pencil-mark sudoku ... Interesting isn't it?!
I agreedobrichev wrote:Too early. Follow the tradition and wait for 12 and a half years after my last posting on the subject.
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Re: Pencilmark only Sudoku
by dobrichev » Fri Jul 12, 2019 7:33 pm
I used 1to9only's extension of serate in GUI mode just to verify independently that the published puzzle has single solution. I will try it in batch mode.
If this is a joke, I did not get it. Of course the published puzzle, as well as other 133487 ED puzzles of the same size, ARE locally minimal.
My point was that while doing {-1, +1} at pencilmarks level, some puzzles required more than ten millions guesses before finding a secondary solution. In singles. Changing guessing strategy reduced the guessing 50 times, but only after including the line-block eliminations the guesses were reduced to a practical value of hundreds. Locked candidates aren't considered singles, right?
tarek wrote:dobrichev wrote:if there is such animal as "biggest singles backdoor required to ensure that puzzle has multiple solutions", then records are possible.
Now then ... You'll love this.. Your Minimum clue puzzle is not necessarily a locally minimal one. If adding any one possible candidate to your puzzle results in multiple solutions then that is a locally minimal puzzle. So your record can be for the Minimum clue locally minimal Pencil-mark sudoku ... Interesting isn't it?!
If this is a joke, I did not get it. Of course the published puzzle, as well as other 133487 ED puzzles of the same size, ARE locally minimal.
My point was that while doing {-1, +1} at pencilmarks level, some puzzles required more than ten millions guesses before finding a secondary solution. In singles. Changing guessing strategy reduced the guessing 50 times, but only after including the line-block eliminations the guesses were reduced to a practical value of hundreds. Locked candidates aren't considered singles, right?
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Re: Pencilmark only Sudoku
by tarek » Sat Jul 13, 2019 9:51 am
dobrichev wrote:I used 1to9only's extension of serate in GUI mode just to verify independently that the published puzzle has single solution. I will try it in batch mode.tarek wrote:dobrichev wrote:if there is such animal as "biggest singles backdoor required to ensure that puzzle has multiple solutions", then records are possible.
Now then ... You'll love this.. Your Minimum clue puzzle is not necessarily a locally minimal one. If adding any one possible candidate to your puzzle results in multiple solutions then that is a locally minimal puzzle. So your record can be for the Minimum clue locally minimal Pencil-mark sudoku ... Interesting isn't it?!
If this is a joke, I did not get it. Of course the published puzzle, as well as other 133487 ED puzzles of the same size, ARE locally minimal.
My point was that while doing {-1, +1} at pencilmarks level, some puzzles required more than ten millions guesses before finding a secondary solution. In singles. Changing guessing strategy reduced the guessing 50 times, but only after including the line-block eliminations the guesses were reduced to a practical value of hundreds. Locked candidates aren't considered singles, right?
No joke intended but I also didn't mean YOUR puzzles either. It is the concept of minimality which I found easier to understand with our regular vanilla sudokus. With Pencilmark sudokus you can see how minimal means more candidates not less.
With the candidate space getting closer to 729, vicinity searches even at {-1 +1} level is tedious ... I'm hoping that you, Mathimagics and others will optimise and find quicker ways of doing this.
tarek
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Re: Pencilmark only Sudoku
by dobrichev » Sat Jul 13, 2019 10:17 am
Yes, minimal and maximal are confusing. Don't ask me how many times I renamed the variables, functions, and parameters in my code.
In my current process a combined {-1,+1} and {-2,+1} mutation takes in average a bit more than one second per puzzle. Rarely some puzzles require 15+ seconds. Puzzles with more restrictions (farther from the low-end) take 1.5 seconds or more.
In my current process a combined {-1,+1} and {-2,+1} mutation takes in average a bit more than one second per puzzle. Rarely some puzzles require 15+ seconds. Puzzles with more restrictions (farther from the low-end) take 1.5 seconds or more.
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Re: Pencilmark only Sudoku
by HATMAN » Mon Jul 29, 2019 9:00 am
On Dobrichev's
"why it isn't deeply investigated"
I would surmise that while they are interesting mathematically (combinatorics and group theory I guess) or computationally, they are a long way from what people want to solve hence naturally of less interest.
To deal with this by avoiding piles of raw pencil-marks, various ways have been tried. Early on there were Phrrhon's double clue ones, I've done a few myself and I recently did negative clue ones posted here.
A while ago para did a killer with adjacent cage totals i.e. they were wrong by +/-1. So here is a vanilla (not plain) on the same basis:
The actual cell values are adjacent to the number given. This cried out to me to be NC, so it is. It is also X.
Not too difficult: one small fish and some NC moves of similar level.
I'll post more if anyone likes them.
"why it isn't deeply investigated"
I would surmise that while they are interesting mathematically (combinatorics and group theory I guess) or computationally, they are a long way from what people want to solve hence naturally of less interest.
To deal with this by avoiding piles of raw pencil-marks, various ways have been tried. Early on there were Phrrhon's double clue ones, I've done a few myself and I recently did negative clue ones posted here.
A while ago para did a killer with adjacent cage totals i.e. they were wrong by +/-1. So here is a vanilla (not plain) on the same basis:
The actual cell values are adjacent to the number given. This cried out to me to be NC, so it is. It is also X.
Not too difficult: one small fish and some NC moves of similar level.
I'll post more if anyone likes them.
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Re: Pencilmark only Sudoku
by HATMAN » Wed Jul 31, 2019 8:03 am
Sukaku Twins 2
Another Twins Sukaku: NC and X and the givens are wrong by one.
I'm posting this because it is unique with just the three red 2 clues. I knew that the solution space was restrained* as for some reason X and NC interfere with each other, but I was surprised to find it unique with just three clues.
* this word usage is from Ruud long ago which I have kept up - tariq will no doubt remember.
Another Twins Sukaku: NC and X and the givens are wrong by one.
I'm posting this because it is unique with just the three red 2 clues. I knew that the solution space was restrained* as for some reason X and NC interfere with each other, but I was surprised to find it unique with just three clues.
* this word usage is from Ruud long ago which I have kept up - tariq will no doubt remember.
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Re: Pencilmark only Sudoku
by tarek » Mon Aug 05, 2019 9:06 am
Yes and we had a play at finding these 8 clue puzzles at one stage!HATMAN wrote:* this word usage is from Ruud long ago which I have kept up - tariq will no doubt remember.
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Re: Pencilmark only Sudoku
by tarek » Tue Aug 13, 2019 8:14 am
Just adding here that a group of us (I'm hoping this group grows with time) are working on improving Sudoku Explainer code from the "Serate" modification that is currently being used in the Patterns game - This modification would allow rating Pencilmark sudokus in addition to improving rating performance of vanilla sudokus.
The Repository of the work can be found here:
https://github.com/SudokuMonster/SukakuExplainer
There are some early releases but the work still continues. Let me know if anyone is interested in joining forces & collaborating. The most recent work has been done by 1to9only and dobrichev which can be found on this thread from this point:
http://forum.enjoysudoku.com/help-with-sudoku-explainer-t6677-80.html
I also started a small off-topic debate (off-topic there but not here) about the Proper naming of this variant where I supported dropping the word "only" from "Pencilmark only Sudoku" and therefore Sukakus should be considered as a normal extension of vanilla sudoku where your ordinary sudoku is actually a Pencilmark sudoku with a restriction:
The Repository of the work can be found here:
https://github.com/SudokuMonster/SukakuExplainer
There are some early releases but the work still continues. Let me know if anyone is interested in joining forces & collaborating. The most recent work has been done by 1to9only and dobrichev which can be found on this thread from this point:
http://forum.enjoysudoku.com/help-with-sudoku-explainer-t6677-80.html
I also started a small off-topic debate (off-topic there but not here) about the Proper naming of this variant where I supported dropping the word "only" from "Pencilmark only Sudoku" and therefore Sukakus should be considered as a normal extension of vanilla sudoku where your ordinary sudoku is actually a Pencilmark sudoku with a restriction:
tarek wrote:The debate about what constitutes a sukaku or not is a debate I like to take part in. (But it is a can of worms, who doesn't like worms)
I (initially) agree that excluding vanilla sudokus from sukakus is silly because vanilla sudokus are a small set within Sukakus. in that sense it is vanilla that is the restriction (or variant) to Sukaku and not the opposite.
Here is my definition of vanilla sudokus:
Vanilla sudoku:
is a sukaku puzzle where Only a known set of Naked singles is needed to determine puzzle validity/uniqueness.
Now to the fun part (and the reason why a small part of me favours a restriction):
Can we therefore divide Sukaku puzzles into 2 separate groups; vanilla sudokus and Sukaku puzzles that are non-vanilla sudokus?
The answer should be yes (for that it requires some proper definitions) but currently the answer is no!!
Look at the definition of vanilla sudoku that I provided above: Looking at a cell that has a solved naked single (one candidate in a cell) will look like a solved hidden single (unique candidate per sector). If a vanilla sudoku clue is a naked single then you can substitute that known clue with a hidden singles (through adding that candidate to all other cells in a shared sector then adding other candidates to that cell). With our current definitions; this means that a vanilla puzzle has several equivalent non-vanilla forms (And Yes: each known vanilla puzzle can be transformed into a Pencilmark-only version in that way)
One way to guarantee that we don't have several versions of essentially the same puzzle appearing is to restrict the definition of non-vanilla further:
Desired non-vanilla: Minimal Sukaku with no hidden singles at the start (Minimal guarantees a single version of the puzzle that has cells with 1 candidate (naked singles), No hidden singles will guarantee that we don't have minimal puzzles appearing in a different form). This may need to extend to hidden doubles and hidden triples that are in more than one sector!
unDesired non-vanilla: All other Sukakus that are not vanilla sudokus nor Desired sukakus.
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Re: Pencilmark only Sudoku
by 1to9only » Sun Aug 18, 2019 7:57 am
I collected some (most!) of the sukakus in this thread, rated them using a slightly modified version of the Aug 5 SE posted here, with the following results:
The naming is mine, and it should be easy to find the sukaku in this thread.
.
- Code: Select all
Post1 ED=9.9/2.6/2.6
SudoCue70070 ED=11.2/9.4/2.8
RuudLeft4 unrated, Ctrl-C'd
Pyrrhon2 ED=1.2/1.2/1.2
Ruud450 ED=9.5/1.2/1.2
Ruud512 ED=12.2/12.2/2.8
Ruud554 ED=11.7/1.5/1.5
Ruud590 ED=9.4/1.2/1.2
Ruud592 ED=9.5/1.5/1.5
Ruud598 ED=9.9/1.5/1.5
Pyrrhon622 ED=4.4/1.5/1.5
Ruud623 ED=4.4/1.5/1.5
Ruud628a ED=2.8/1.2/1.2
Ruud625 ED=2.8/1.5/1.5
Ruud628b ED=2.6/1.2/1.2
Ruud633 ED=2.8/1.2/1.2
tareknasty1 at least ED=12.6, Ctrl-C'd
tareknasty2 not rated
tarekbackdoor5 not rated
dobrichev637 ED=3.0/3.0/3.0
The naming is mine, and it should be easy to find the sukaku in this thread.
.
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Re: Pencilmark only Sudoku
by tarek » Sun Aug 18, 2019 1:21 pm
That puzzle Ruud512 should be interesting to analyze as it solves completely and exceeds 12 even with our current solver state.
Tarek
Tarek
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Re: Pencilmark only Sudoku
by dobrichev » Sun Aug 18, 2019 3:06 pm
As of current state of the solver, this puzzle (first from the tarek's bd6)
fails here:
This puzzle (second from the tarek's bd6)
fails here
This one (third from tarek's bd6)
does some progress to here
and is candidate for Ctrl-C.
Edit: not a candidate, compare to the pencilmarks below.
The fourth from tarek's bd6
fails here
- Code: Select all
..3.5678.1.3456789123456789.23456789...4.678912.4567891234567891.34567891..45.789123.567891.3...7..12345.7..123....891234.678912.4...8.123..6.891........12345.7891234567891234567..12345678.123456.8912345678912345678.123.56.89123456..9123456789.23456789...4.678912.4567891.3.567891.34567891..45.789.234567891..4.678912.456789.23..6.891234.6789123456789123.567891.3...7.912345.789123.567891234.678912.4..78.123456.891234.6...123456789123.56..91234567.91234..7..123456.891234.6...12345678.1234567891...5678912.45678912345678912345678.12.45678..23.567891.3456789123456789123.567891.....7.912.45.789123..6.891234.678912.4..78..23.567891.3...7.912345.789123.56..91234567.9123456789123456.891234.6...12345678.1234567891234567.912345.7..
+-------------------------------+-------------------------------+-------------------------------+
| 35678 13456789 123456789 | 23456789 46789 12456789 | 123456789 13456789 145789 |
| 12356789 137 123457 | 12389 12346789 1248 | 123689 1 12345789 |
| 123456789 1234567 12345678 | 12345689 123456789 12345678 | 1235689 1234569 123456789 |
+-------------------------------+-------------------------------+-------------------------------+
| 23456789 46789 12456789 | 1356789 13456789 145789 | 23456789 146789 12456789 |
| 23689 12346789 123456789 | 12356789 1379 12345789 | 12356789 12346789 12478 |
| 12345689 12346 123456789 | 123569 12345679 12347 | 12345689 12346 12345678 |
+-------------------------------+-------------------------------+-------------------------------+
| 123456789 156789 12456789 | 123456789 12345678 1245678 | 2356789 13456789 123456789 |
| 12356789 179 1245789 | 123689 12346789 12478 | 2356789 1379 12345789 |
| 123569 12345679 123456789 | 12345689 12346 12345678 | 123456789 12345679 123457 |
+-------------------------------+-------------------------------+-------------------------------+
fails here:
- Code: Select all
+-------------------------------+-------------------------------+-------------------------------+
| 3678 13456789 12346789 | 23456789 46789 12456789 | 2346789 3456789 4789 |
| 2356789 37 23457 | 2389 2346789 248 | 23689 1 2345789 |
| 12346789 1234567 1234678 | 12345689 123456789 12345678 | 23689 234569 2346789 |
+-------------------------------+-------------------------------+-------------------------------+
| 23456789 46789 12456789 | 1356789 13456789 145789 | 23456789 46789 12456789 |
| 23689 12346789 123456789 | 12356789 1379 12345789 | 12356789 2346789 12478 |
| 12345689 12346 123456789 | 123569 12345679 12347 | 12345689 2346 12345678 |
+-------------------------------+-------------------------------+-------------------------------+
| 12346789 156789 1246789 | 123456789 12345678 1245678 | 236789 3456789 12346789 |
| 12356789 179 1245789 | 123689 12346789 12478 | 2356789 379 12345789 |
| 12369 12345679 12346789 | 12345689 12346 12345678 | 12346789 2345679 12347 |
+-------------------------------+-------------------------------+-------------------------------+
ED=20.0/2.3/2.3
This puzzle (second from the tarek's bd6)
- Code: Select all
..3.5678.1.3456789123456789.23456789...4.678912.4567891234567891.34567891..45.7891234567891.3...7..1234..78.123..6.891234.678912.4...8.123..6.891........12345.7891234567891234567..12345678.123456.89.2345678912345678.123.56.89123456..9123456789.23456789...4.678912.456789..3.567891.34567891..45.789.234567891..4.678912.456789123..6.891234.6789123456789123.567891.3...7.912345.789123.567891234.678912.4..78.123456.891234.6...12345678.123.56..91234567.91234..7..1234567891234.6...12345678.1234567891...5678912.456789.2345678912345678.12.45678..23.567891.3456789123456789123.567891.....7.912.456789.23..6.891234.678912.4..78..23.567891.3...7.912345.789123.56..91234567.9123456789123456.891234.6...12345678.1234567891234567.912345.7..
+-------------------------------+-------------------------------+-------------------------------+
| 35678 13456789 123456789 | 23456789 46789 12456789 | 123456789 13456789 145789 |
| 123456789 137 123478 | 123689 12346789 1248 | 123689 1 12345789 |
| 123456789 1234567 12345678 | 12345689 23456789 12345678 | 1235689 1234569 123456789 |
+-------------------------------+-------------------------------+-------------------------------+
| 23456789 46789 12456789 | 356789 13456789 145789 | 23456789 146789 12456789 |
| 123689 12346789 123456789 | 12356789 1379 12345789 | 12356789 12346789 12478 |
| 12345689 12346 12345678 | 123569 12345679 12347 | 123456789 12346 12345678 |
+-------------------------------+-------------------------------+-------------------------------+
| 123456789 156789 12456789 | 23456789 12345678 1245678 | 2356789 13456789 123456789 |
| 12356789 179 12456789 | 23689 12346789 12478 | 2356789 1379 12345789 |
| 123569 12345679 123456789 | 12345689 12346 12345678 | 123456789 12345679 123457 |
+-------------------------------+-------------------------------+-------------------------------+
fails here
- Code: Select all
+-------------------------------+-------------------------------+-------------------------------+
| 3678 13456789 12346789 | 23456789 46789 12456789 | 234678 3456789 4789 |
| 23456789 37 23478 | 23689 2346789 248 | 23689 1 2345789 |
| 12346789 1234567 1234678 | 12345689 23456789 12345678 | 23689 234569 2346789 |
+-------------------------------+-------------------------------+-------------------------------+
| 23456789 46789 12456789 | 356789 13456789 145789 | 23456789 46789 12456789 |
| 123689 12346789 123456789 | 12356789 1379 12345789 | 12356789 2346789 12478 |
| 12345689 12346 12345678 | 123569 12345679 12347 | 123456789 2346 12345678 |
+-------------------------------+-------------------------------+-------------------------------+
| 12346789 156789 1246789 | 23456789 12345678 1245678 | 236789 3456789 12346789 |
| 12356789 179 12456789 | 23689 12346789 12478 | 2356789 379 12345789 |
| 12369 12345679 12346789 | 12345689 12346 12345678 | 12346789 2345679 12347 |
+-------------------------------+-------------------------------+-------------------------------+
ED=20.0/2.3/2.3
This one (third from tarek's bd6)
- Code: Select all
..3.5678.1.3456789123456789.23456789...4.678912.4567891234567891.34567891..45.789123.567891.3...7..12345.78.123....891234.678912.4..78.123..6.891........12345.7891234567891234567..12345678.123456.89.2345678912345678.123.56.89123456..9123456789.234567891..4.678912.456789..3.567891.34567891..45.789.234567891..4.678912.456789.23..6.891234.6789123456789123.567891.3...7.912345.789123.567891234.678912.4..78.123456.891234.6...123456789123.56..91234567.91234..7..123456.891234.6...12345678.1234567891...5678912.45678912345678912345678.12.45678..23.567891.3456789123456789123.567891.....7.912.45.789.23..6.891234.678912.4..78..23.567891.3...7.912345.789123.56..91234567.9123456789123456.891234.6...12345678.1234567891234567.912345.7..
+-------------------------------+-------------------------------+-------------------------------+
| 35678 13456789 123456789 | 23456789 46789 12456789 | 123456789 13456789 145789 |
| 12356789 137 1234578 | 12389 12346789 12478 | 123689 1 12345789 |
| 123456789 1234567 12345678 | 12345689 23456789 12345678 | 1235689 1234569 123456789 |
+-------------------------------+-------------------------------+-------------------------------+
| 23456789 146789 12456789 | 356789 13456789 145789 | 23456789 146789 12456789 |
| 23689 12346789 123456789 | 12356789 1379 12345789 | 12356789 12346789 12478 |
| 12345689 12346 123456789 | 123569 12345679 12347 | 12345689 12346 12345678 |
+-------------------------------+-------------------------------+-------------------------------+
| 123456789 156789 12456789 | 123456789 12345678 1245678 | 2356789 13456789 123456789 |
| 12356789 179 1245789 | 23689 12346789 12478 | 2356789 1379 12345789 |
| 123569 12345679 123456789 | 12345689 12346 12345678 | 123456789 12345679 123457 |
+-------------------------------+-------------------------------+-------------------------------+
does some progress to here
- Code: Select all
+-------------------------------+-------------------------------+-------------------------------+
| 3678 13456789 12346789 | 23456789 46789 12456789 | 2346789 3456789 4789 |
| 23456789 37 2347 | 289 234689 248 | 23689 1 2345789 |
| 12346789 1234567 1234678 | 12345689 123456789 123456789 | 23689 2345689 2346789 |
+-------------------------------+-------------------------------+-------------------------------+
| 23456789 146789 12456789 | 356789 13456789 145789 | 23456789 46789 12456789 |
| 23689 12346789 123456789 | 12356789 1379 12345789 | 12356789 2346789 12478 |
| 12345689 12346 123456789 | 123569 12345679 123457 | 12345689 2346 12345678 |
+-------------------------------+-------------------------------+-------------------------------+
| 12346789 156789 1246789 | 23456789 12345678 1245678 | 236789 3456789 12346789 |
| 12356789 179 1245789 | 23689 12346789 12478 | 2356789 379 12345789 |
| 123689 12345679 12346789 | 12345689 12346 12345678 | 12346789 2345679 12347 |
+-------------------------------+-------------------------------+-------------------------------+
................1................................................................ 12.8, Contradiction Forcing Chain: C1.7 on ==> H8.3 both on & off
+-------------------------------+-------------------------------+-------------------------------+
| 3678 13456789 1234689 | 23456789 46789 12456789 | 2346789 3456789 4789 |
| 23456789 37 2347 | 289 234689 248 | 23689 1 2345789 |
| 12346789 1234567 1234678 | 12345689 123456789 123456789 | 23689 2345689 2346789 |
+-------------------------------+-------------------------------+-------------------------------+
| 23456789 146789 12456789 | 356789 13456789 145789 | 23456789 46789 12456789 |
| 23689 12346789 123456789 | 12356789 1379 12345789 | 12356789 2346789 12478 |
| 12345689 12346 123456789 | 123569 12345679 123457 | 12345689 2346 12345678 |
+-------------------------------+-------------------------------+-------------------------------+
| 12346789 156789 1246789 | 23456789 12345678 1245678 | 236789 3456789 12346789 |
| 12356789 179 1245789 | 23689 12346789 12478 | 2356789 379 12345789 |
| 123689 12345679 12346789 | 12345689 12346 12345678 | 12346789 2345679 12347 |
+-------------------------------+-------------------------------+-------------------------------+
and is candidate for Ctrl-C.
Edit: not a candidate, compare to the pencilmarks below.
The fourth from tarek's bd6
- Code: Select all
..3.5678.1.3456789123456789.23456789...4.678912.4567891234567891.34567891..45.7891234567891.3...7..1234..7..12.....891234.6.8912.4...8.123..6.891........12345.7891234567891234567..12345678.123456.89123456789123456789123.56.89123456.89123456789.234567891..4.678912.456789..3.567891.34567891..45.789.234567891..4.678912.456789.23..6.891234.6789123456789123.567891.3...7.912345.789123.567891234.678912.4..78.123456.891234.6...123456789123.56..91234567.912345.7..123456.891234.6...12345678.1234567891...5678912.456789.2345678912345678.12.45678..23.567891.3456789123456789123.567891.....7.912.45.789.23..6.891234.678912.4..78..23.567891.3...7.912345.789123.56.891234567.9123456789123456.891234.6...12345678.1234567891234567.912345.7..
+-------------------------------+-------------------------------+-------------------------------+
| 35678 13456789 123456789 | 23456789 46789 12456789 | 123456789 13456789 145789 |
| 123456789 137 12347 | 1289 1234689 1248 | 123689 1 12345789 |
| 123456789 1234567 12345678 | 12345689 123456789 123456789 | 1235689 12345689 123456789 |
+-------------------------------+-------------------------------+-------------------------------+
| 23456789 146789 12456789 | 356789 13456789 145789 | 23456789 146789 12456789 |
| 23689 12346789 123456789 | 12356789 1379 12345789 | 12356789 12346789 12478 |
| 12345689 12346 123456789 | 123569 12345679 123457 | 12345689 12346 12345678 |
+-------------------------------+-------------------------------+-------------------------------+
| 123456789 156789 12456789 | 23456789 12345678 1245678 | 2356789 13456789 123456789 |
| 12356789 179 1245789 | 23689 12346789 12478 | 2356789 1379 12345789 |
| 1235689 12345679 123456789 | 12345689 12346 12345678 | 123456789 12345679 123457 |
+-------------------------------+-------------------------------+-------------------------------+
fails here
- Code: Select all
+-------------------------------+-------------------------------+-------------------------------+
| 3678 13456789 12346789 | 23456789 46789 12456789 | 2346789 3456789 4789 |
| 23456789 37 2347 | 289 234689 248 | 23689 1 2345789 |
| 12346789 1234567 1234678 | 12345689 123456789 123456789 | 23689 2345689 2346789 |
+-------------------------------+-------------------------------+-------------------------------+
| 23456789 146789 12456789 | 356789 13456789 145789 | 23456789 46789 12456789 |
| 23689 12346789 123456789 | 12356789 1379 12345789 | 12356789 2346789 12478 |
| 12345689 12346 123456789 | 123569 12345679 123457 | 12345689 2346 12345678 |
+-------------------------------+-------------------------------+-------------------------------+
| 12346789 156789 1246789 | 23456789 12345678 1245678 | 236789 3456789 12346789 |
| 12356789 179 1245789 | 23689 12346789 12478 | 2356789 379 12345789 |
| 123689 12345679 12346789 | 12345689 12346 12345678 | 12346789 2345679 12347 |
+-------------------------------+-------------------------------+-------------------------------+
................1................................................................ 12.8, Contradiction Forcing Chain: C1.7 on ==> H8.3 both on & off
+-------------------------------+-------------------------------+-------------------------------+
| 3678 13456789 1234689 | 23456789 46789 12456789 | 2346789 3456789 4789 |
| 23456789 37 2347 | 289 234689 248 | 23689 1 2345789 |
| 12346789 1234567 1234678 | 12345689 123456789 123456789 | 23689 2345689 2346789 |
+-------------------------------+-------------------------------+-------------------------------+
| 23456789 146789 12456789 | 356789 13456789 145789 | 23456789 46789 12456789 |
| 23689 12346789 123456789 | 12356789 1379 12345789 | 12356789 2346789 12478 |
| 12345689 12346 123456789 | 123569 12345679 123457 | 12345689 2346 12345678 |
+-------------------------------+-------------------------------+-------------------------------+
| 12346789 156789 1246789 | 23456789 12345678 1245678 | 236789 3456789 12346789 |
| 12356789 179 1245789 | 23689 12346789 12478 | 2356789 379 12345789 |
| 123689 12345679 12346789 | 12345689 12346 12345678 | 12346789 2345679 12347 |
+-------------------------------+-------------------------------+-------------------------------+
ED=20.0/2.3/2.3
- dobrichev
- 2016 Supporter
- Posts: 1850
- Joined: 24 May 2010
