Pencilmark only Sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

Re: Pencilmark only Sudoku

Postby tarek » Wed Jul 10, 2019 8:07 pm

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
User avatar
tarek
 
Posts: 2917
Joined: 05 January 2006

Re: Pencilmark only Sudoku

Postby 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
dobrichev
2016 Supporter
 
Posts: 1677
Joined: 24 May 2010

Re: Pencilmark only Sudoku

Postby 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? :?
User avatar
Mathimagics
2017 Supporter
 
Posts: 1200
Joined: 27 May 2015
Location: Canberra

Re: Pencilmark only Sudoku

Postby 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.
dobrichev
2016 Supporter
 
Posts: 1677
Joined: 24 May 2010

Re: Pencilmark only Sudoku

Postby tarek » Fri Jul 12, 2019 6:02 pm

Hi Mladen and Mathimagics,
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 :oops:

Minimal singles backdoor size 6 puzzles: Show
tarek wrote:Minimal singles backdoor size 6 puzzles

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..
..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..
..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..
..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..
..345678.1.3456789123456789.23456789...4.678912.4567891234567891.34567891..45.7891234567891.3...7..1.34..7..123..6.891234.678912.4..78.123..6.891........12345.7891234567891234567..12345678.123456.8912345678912345678.123.56.89123456.89123456789.23456789...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...5678912.45678912345678912345678.12.45678..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..
..3.567891.3456789123456789.23456789...4.678912.4567891234567891.34567891..45.789123.567891.3...7..12345.7..123..6.891234.678912.4..78.123..6.891........12345.7891234567891234567..12345678.123456.8912.45678912345678.123.56.89123456.89123456789.23456789...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.....7.912.45.789.23..6.891234.678912.4..78..23.567891.3...7.912345.789123.56..91234567.9123456789123456.891234.6...12345678.1234567891234567.912345.7..
..3.567891.3456789123456789.23456789...4.678912.4567891234567891.34567891..45.789123.567891.3...7..12345.7..123..6.891234.678912.4..78.123..6.891........12345.7891234567891234567..12345678.123456.8912.45678912345678.123.56.89123456..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...12345678.123.56..91234567.91234..7..1234567891234.6...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..
..3.567891.3456789123456789.23456789...4.678912.4567891234567891.34567891..45.789123.567891.3...7..12345678.123..6.891234.678912.4..78.123..6.891........12345.7891234567891234567..12345678.123456.89.2345678912345678.123.56.89123456..9123456789.23456789...4.678912.456789..3.567891.34567891..45.789.234567891..4.678912.456789.23..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...5678912.45678912345678912345678.12.45678..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..
..3.5678.1.3456789123456789.23456789...4.678912.4567891234567891.34567891..45.789123.567891.3...7..12345.7..123..6.891234.678912.4..78.123.56.891........12345.7891234567891234567..12345678.123456.8912345678912345678.123.56.89123456.89123456789.23456789...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...12345678.123.56..91234567.912345.7..1234567891234.6...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..
..3.567891.3456789123456789.23456789...4.678912.4567891234567891.34567891..45.789123.567891.3...7..12345.7..12...6.891234.678912.4...8.123.56.891........12345.7891234567891234567..12345678.123456.8912345678912345678.123.56.89123456.89123456789.23456789...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...12345678.123.56..91234567.912345.7..1234567891234.6...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..
..3.567891.3456789123456789.23456789...4.678912.4567891234567891.34567891..45.789123.567891.3...7..12345.7..123..6.891234.678912.4...8.123..6.891........12345.7891234567891234567..12345678.123456.8912345678912345678.123.56.89123456..9123456789.234567891..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...12345678.123.56..91234567.91234..7..1234567891234.6...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..


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?!

dobrichev wrote:Too early. Follow the tradition and wait for 12 and a half years after my last posting on the subject.
I agree
User avatar
tarek
 
Posts: 2917
Joined: 05 January 2006

Re: Pencilmark only Sudoku

Postby 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.
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?
dobrichev
2016 Supporter
 
Posts: 1677
Joined: 24 May 2010

Re: Pencilmark only Sudoku

Postby 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
User avatar
tarek
 
Posts: 2917
Joined: 05 January 2006

Re: Pencilmark only Sudoku

Postby 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.
dobrichev
2016 Supporter
 
Posts: 1677
Joined: 24 May 2010

Previous

Return to Sudoku variants