The New Sudoku Players' Forum

by **blue** » Tue Aug 20, 2019 11:33 pm

From another thread:

blue wrote:
denis_berthier wrote:A more interesting question for me would now be: can one find a Sukaku not in B7B?

Tarek's "singles backdoor size 6" puzzles are all "TE[singles](4)" -- "in BBBB, but not in BBB".
There were two more puzzles of interest, mentioned here:

RuudLeft4: in BBB, but not in BB
tareknasty1: in BBB, but not in BB
The others (with high SE ratings) were "TE[singles](2)", and so in BB.
I can't say whether they're in B7B.

I should have added that if locked candidate and locked set eliminations are added to the techniques that are employed (initially, and after each guess or elimination), then the "singles backdoor size 6" puzzles become "T&E(3)", and "tareknasty1" becomes T&E(2).

Something else worth mentioning:

Sudoku Explainer's "Cell/Region Forcing chains" eliminations, cover Denis Berthier's "(singles) braids" eliminations.
Sudoku Explainer's methods cover all T&E[singles](1) eliminations; some part of the T&E[singles](2) eliminations, and some part of T&E[?](2) eliminations involving naked/hidden pairs and X-wings, and (I think) small chains.
(*) Sudoku Explainer's "Dynamic Cell/Region Forcing chains" cover something that, doesn't correspond to anything in the category of "T&E" eliminations -- common outcomes produced (in a complex way) from any one of a short list of possible guesses, one of which is inevitably "correct" (assuming the puzzle actually has a solution).

Aligned Pair and Aligned Triple eliminations, I don't really understand, but it's likely that they fall outside the scope of T&E eliminations too.

Disregard what follows.
The differences were due to a bug in by code. Thanks tarek.

@Dobrichev: referring to your latest post; for the first of the BDS 6 puzzles SE+ "failed" 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

T&E[singles](2), T&E[singles + locked candidates](2), T&E[singles + locked candidates + locked sets](2), and T&E[singles + locked candidates + locked sets + basic fish](2) ... all "fail" at this point:

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 | +--------------------------------+--------------------------------+------------------------------+ | 123456789 156789 1246789 | 123456789 12345678 1245678 | 236789 3456789 12346789 | | 12356789 179 1245789 | 123689 12346789 12478 | 2356789 379 12345789 | | 12369 12345679 12346789 | 12345689 12346 12345678 | 123456789 2345679 12347 | +--------------------------------+--------------------------------+------------------------------+

Interestingly(?), nothing happens at level 2, except in the T&E[singles] case.

The difference between the two final states, is that SE has two additional eliminations: 5r7c1 and 5r9c7.
Is it an easy job to plug the PM state from just above, into SE, and "ask it" if it can still eliminate those two candidates, and if so, how ?

BTW: I'm only asking out of curiosity.
You guys are on you own here.
Good luck, and have fun

by **tarek** » Wed Aug 21, 2019 7:47 am

I had a go at the Sukaku Explainer GUI which accepts parsing the Pencilmark grid as you posted it
Pressing Solve Step would give 1st this step with difficulty rating of 9.2

Double Forcing Chain: I2.5 on & off ==> G9.5 off
Dynamic Double Forcing Chain
With this solving technique, we will prove the two following assertions:
If I2 contains the value 5, then G9 cannot contain the value 5
If I2 does not contain the value 5, then G9 cannot contain the value 5
Because the two assumptions are complementary, and the results are the same, we can conclude that G9 cannot contain the value 5.
Each assertion is proved by a different chain of simple rules. The chains can be dynamic, which means that the conclusions of multiple sub-chains must be combined in some cases.
The details of each chain are given below. Use the view selector below the grid to switch between the graphical illustrations of the two different chains.

chain 1 with image: Show

chain 2 with image: Show

by **blue** » Wed Aug 21, 2019 10:29 am

Thank you tarek,

I had a stupid bug in my code ...

Code: Select all: if (solution[9 * r + c] == d) continue; // impossible elimination

should have been:

Code: Select all: if (solution[9 * r + c] == d + 1) continue; // impossible elimination

SE has its particular way of explaining things.
The two eliminations can be done with (simple) "grouped candidate" AICs, too ... starting from that PM state.
(Something else, that has been missing in SE).

BTW: After fixing the bug, nothing had changed in the T&E depth(s) that were required to solve the puzzles.

by **tarek** » Wed Aug 21, 2019 12:45 pm

Explainer indeed has a language of its own. It remains a valuable tool nevertheless.

The future release(s) of Sukaku explainer will show more efficient and faster solving in general. The GUI also would accept pasting pencilmarked grids like the one you posted with explainer continuing solution from that point as I demonstrated.

by **m_b_metcalf** » Tue Sep 03, 2019 10:40 am

This type of puzzle has somehow escaped my notice until now. For program testing I found the 729-digit string the most convenient format, so here are five published puzzles in that form for other adventurers:

Code: Select all: 123456789123456789023456789123406789123456789120406789123406789123406780123456789123456789103050000023056700023056789123456789123456789123456789023000700123456789123456789123456789123456789120056789123456789120450789123456789123406789123456789123456789123456789123456789020056789123456789123456789123456789123456789123456789123456789100400000123456789120450789123456789123456789000450000123456789123456789123456789123456789123456789123056789123456789123456789123456789123456789123456789123456789123456789023456789123456789123456009123406789123456789020000700123456789123456789123456789123456789123456789103450009100406009123456789123456789123456789123456789123456789020050000123456789123456709123456709123456789020000700020050700 dobrichev 637 120050700023400709120400709020406080120456709100456080000050709003050700103450080103056709123456789000456700003056780023056000020056789020456009023400000003056709023400080120056000123056780120400780003450789100400709000456709103400000120006789123056789000456709003056000103000080020456000123400089120456700103000080120406700123406080103406709003406709020406080100056780123406789123406789000000780123456000020050780120006080003406789000056089123456780000450080123456700000006709120450789023456700020406780120450080100000009103456789123406089023050080023450089120006709003000780100006089100456089123456789123406780020050780120006000123456089003050089103056080103400709103400089103000789003456080003056089123400780000006700023056780 ruud's first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ruud 13.10.2006 000000009000000080123450000000000700003406000120406000123400000100450000023050000000000700123050000123450000123400080003400089120400089000006000100450089023050089123400000123000000000006000123400080000050000120400089123400780100400789023000789120006080000400000120000009100006080000006780000050000020000780003000000020006789123006080123006000000000700000000009003406080100406080000050000000406080020006080003056080003056009003050009003406080020000000000406780000400780000406789100000000123456000123056700000000080000056000000406700020406700000000009100056700003056700023056000023056709023050009020056080100000000020006789003000780000056780000400000100456000100056709100450009000456080000406789003000000100000780020000000000056780 champagne dry with r7c4 changed to 56 000400009120000000023000000003050000020050000100000080003006000000400700100000009000056000003400000000000709000000780020400000000400700100000700000000089000450000100000080003000700000050080000006009003006000100000009000406000020050000023000000020050000000406000100006000100000080003000700003000080020000009020000009103000000103000000020050000000000709000400700000050009020006000003006000000450000000050080003400000000000089000000780020400000100006000003050000000400700100006000000400080020000700000406000003050000100050000020400000000000709000006080100050000000400700000006009000000089103000000000006080003400000000006700020050000000400700120000000000000780020050000100400000100050000003000080020000009000050009003000080003006000 81 pairs

by **m_b_metcalf** » Fri Sep 13, 2019 11:46 am

tarek wrote:Here are the original 11 puzzles in the 729 line format

After much huffing and puffing, my solver finally solved the second version:

Hidden Text: Show

and I'd be grateful for confirmation that that result is correct.

Thanks,

Mike

by **creint** » Fri Sep 13, 2019 4:20 pm

Result is correct, easy with minisat in 0.12 seconds. Did your solver use logic or DLX?

by **m_b_metcalf** » Fri Sep 13, 2019 4:50 pm

creint wrote:Result is correct, easy with minisat in 0.12 seconds. Did your solver use logic or DLX?

17 candidates were eliminated by logic, the rest was brute force.

by **creint** » Fri Sep 13, 2019 6:12 pm

m_b_metcalf wrote:17 candidates were eliminated by logic, the rest was brute force.

So 5 in all corners from the corner boxes + 9r1c7. And how long did the solver take to find those?
With my current logic it took 0.6 seconds to reach that state.

by **m_b_metcalf** » Fri Sep 13, 2019 6:38 pm

creint wrote:
m_b_metcalf wrote:17 candidates were eliminated by logic, the rest was brute force.

So 5 in all corners from the corner boxes + 9r1c7. And how long did the solver take to find those?
With my current logic it took 0.6 seconds to reach that state.

Code: Select all: At 7 1 cannot have 5 At 7 9 cannot have 5 At 9 1 cannot have 5 At 9 9 cannot have 5 At 1 1 cannot have 5 At 1 3 cannot have 5 At 1 7 cannot have 5 At 1 7 cannot have 9 At 1 9 cannot have 5 At 3 1 cannot have 5 At 3 3 cannot have 5 At 3 7 cannot have 5 At 3 9 cannot have 5 At 7 3 cannot have 5 At 7 7 cannot have 5 At 9 3 cannot have 5 At 9 7 cannot have 5 phase 1 took .30 seconds

by **tarek** » Mon Sep 16, 2019 10:56 am

Here on the hardest sudokus thread there was also a discussion on how convoluted some of these pencilmark sudokus (sukakus) can get

by **dobrichev** » Sun Sep 22, 2019 3:18 pm

This is the distribution by rating for puzzles having 637 unresolved pencilmarks.

#puzzles, ER, EP, ED

Code: Select all: 86226 2.8 2.3 2.3 32314 3.0 2.3 2.3 10568 3.0 3.0 3.0 1444 3.4 2.3 2.3 266 3.4 3.0 3.0 7528 3.6 2.3 2.3 3256 3.6 3.6 3.6 1224 7.3 2.3 2.3 24 7.3 3.0 3.0 426 8.3 2.3 2.3 90 8.3 8.3 3.0 180 8.3 8.3 4.4 342 8.9 2.3 2.3 90 8.9 8.9 3.0 90 8.9 8.9 8.4 84 9.0 2.3 2.3 90 9.0 9.0 8.4

The greatest common divisor is 2.

by **tarek** » Sun Sep 22, 2019 7:38 pm

2 months and 2 weeks since you posted your 637 puzzle and look where we are now!!! Great work!

by **dobrichev** » Sun Sep 22, 2019 8:06 pm

Actually all they appeared in the first 2 weeks, while I still experimented with the software.
They are close to each other and share small number of solution grids. [Edit: exactly 2 solutions, one of them has valid vanilla 17-clue puzzle, other has not.]
My attempt to reproduce them or find other island by starting from independent seed failed. So either I was lucky and this is the absolute minimum and complete list (which is very unlikely but still possible if the whole pencilmark space is well connected), or this is just one local minimum and the global can be much deeper.

by **dobrichev** » Thu Oct 03, 2019 4:47 pm

This puzzle is minimal and has 272 restrictions - i.e. it is high-clue.
Its first move is rated by SE as ED=10.3 Contradiction Forcing Chain: r7c3.1 on ==> r5c4.9 both on & off, followed by similar chains rated 12.6, 12.7, 12.8.
Its solution grid is the most-canonical grid.

Code: Select all: +-------------------------------+-------------------------------+-------------------------------+ | 139 236789 23456789 | 123456789 2345689 123567 | 3789 123458 4589 | | 12459 23579 2356789 | 12456 123458 369 | 1245678 23457 13689 | | 1234567 123456789 135789 | 145679 134589 12345789 | 134579 345679 147 | +-------------------------------+-------------------------------+-------------------------------+ | 1248 2789 12456 | 23567 1234689 12789 | 12358 2345678 3456 | | 123456789 23457 1247 | 2489 34 123456 | 236789 123569 2349 | | 2567 2345689 24678 | 13589 234678 124678 | 3457 23689 12356 | +-------------------------------+-------------------------------+-------------------------------+ | 1246789 3469 123456789 | 36789 1345678 123468 | 1489 134568 457 | | 1245678 1239 145689 | 239 345689 356 | 12345679 12345689 12789 | | 12456789 145679 1245678 | 1345678 234789 134569 | 1234579 2457 1345678 | +-------------------------------+-------------------------------+-------------------------------+

It has backdoor of size 4 in both singles and singles+locked, lower compared to tarek's hardest puzzles above in this thread which have backdoor 6 in singles and 4 in singles+locked.

SE rating of 12.8 isn't very uncommon for pencilmark-only puzzles. By frequency maybe it is equivalent to something below 10.0 or even 9.0 for vanilla puzzles.
The low diamond rating for the minimized derivatives of vanilla puzzles is explainable. Randomly generated pencilmark puzzles also trend to have low ED, and from this perspective the above puzzle is exceptional.

The puzzle in 729-char format and the first SE solution steps.

Hidden Text: Show

Code: Select all: 1.3.....9.23..6789.23456789123456789.23456.89123.567....3...78912345..8....45..8912.45...9.23.5.7.9.23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..1234567891.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8..2345678...3456...123456789.2345.7..12.4..7...2.4...89..34.....123456....23..6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56...12.4.6789..34.6..9123456789..3..67891.345678.1234.6.8.1..4...891.3456.8....45.7..12.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.912.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 10.3 Contradiction Forcing Chain: r7c3.1 on ==> r5c4.9 both on & off 1.3.....9.23..6789.23456789123456789.23456.89123.567....3...78912345..8....45..8912.45...9.23.5.7.9.23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..1234567891.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8..2345678...3456...123456789.2345.7..12.4..7...2.4...89..34.....123456....23..6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56...12.4.6789..34.6..9.23456789..3..67891.345678.1234.6.8.1..4...891.3456.8....45.7..12.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.912.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.6 Contradiction Forcing Chain: r5c1.2 on ==> r9c5.7 both on & off 1.3.....9.23..6789.23456789123456789.23456.89123.567....3...78912345..8....45..8912.45...9.23.5.7.9.23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..1234567891.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8..2345678...3456...1.3456789.2345.7..12.4..7...2.4...89..34.....123456....23..6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56...12.4.6789..34.6..9.23456789..3..67891.345678.1234.6.8.1..4...891.3456.8....45.7..12.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.912.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.7 Contradiction Forcing Chain: r3c2.9 on ==> r3c7.1 both on & off 1.3.....9.23..6789.23456789123456789.23456.89123.567....3...78912345..8....45..8912.45...9.23.5.7.9.23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8..2345678...3456...1.3456789.2345.7..12.4..7...2.4...89..34.....123456....23..6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56...12.4.6789..34.6..9.23456789..3..67891.345678.1234.6.8.1..4...891.3456.8....45.7..12.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.912.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.7 Contradiction Forcing Chain: r7c5.3 on ==> r8c8.1 both on & off 1.3.....9.23..6789.23456789123456789.23456.89123.567....3...78912345..8....45..8912.45...9.23.5.7.9.23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8..2345678...3456...1.3456789.2345.7..12.4..7...2.4...89..34.....123456....23..6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56...12.4.6789..34.6..9.23456789..3..67891..45678.1234.6.8.1..4...891.3456.8....45.7..12.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.912.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.8 Contradiction Forcing Chain: r7c6.3 on ==> r2c5.8 both on & off 1.3.....9.23..6789.23456789123456789.23456.89123.567....3...78912345..8....45..8912.45...9.23.5.7.9.23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8..2345678...3456...1.3456789.2345.7..12.4..7...2.4...89..34.....123456....23..6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56...12.4.6789..34.6..9.23456789..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7..12.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.912.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.8 Contradiction Forcing Chain: r5c7.3 on ==> r6c9.1 both on & off 1.3.....9.23..6789.23456789123456789.23456.89123.567....3...78912345..8....45..8912.45...9.23.5.7.9.23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8..2345678...3456...1.3456789.2345.7..12.4..7...2.4...89..34.....123456....2...6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56...12.4.6789..34.6..9.23456789..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7..12.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.912.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.8 Contradiction Forcing Chain: r8c1.1 on ==> r4c2.8 both on & off 1.3.....9.23..6789.23456789123456789.23456.89123.567....3...78912345..8....45..8912.45...9.23.5.7.9.23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8..2345678...3456...1.3456789.2345.7..12.4..7...2.4...89..34.....123456....2...6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56...12.4.6789..34.6..9.23456789..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.912.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.8 Contradiction Forcing Chain: r1c2.9 on ==> r7c4.7 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..8912.45...9.23.5.7.9.23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8..2345678...3456...1.3456789.2345.7..12.4..7...2.4...89..34.....123456....2...6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56...12.4.6789..34.6..9.23456789..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.912.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.8 Contradiction Forcing Chain: r2c1.2 on ==> r3c8.9 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7.9.23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8..2345678...3456...1.3456789.2345.7..12.4..7...2.4...89..34.....123456....2...6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56...12.4.6789..34.6..9.23456789..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.912.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.8 Contradiction Forcing Chain: r4c8.2 on ==> r8c8.4 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7.9.23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3456789.2345.7..12.4..7...2.4...89..34.....123456....2...6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56...12.4.6789..34.6..9.23456789..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.912.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.8 Contradiction Forcing Chain: r7c1.1 on ==> r1c1.9 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7.9.23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3456789.2345.7..12.4..7...2.4...89..34.....123456....2...6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23456789..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.912.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.9 Contradiction Forcing Chain: r7c3.7 on ==> r4c7.1 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7.9.23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3456789.2345.7..12.4..7...2.4...89..34.....123456....2...6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23456.89..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.912.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.9 Contradiction Forcing Chain: r5c1.4 on ==> r9c8.4 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7.9.23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3.56789.2345.7..12.4..7...2.4...89..34.....123456....2...6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23456.89..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.912.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.9 Contradiction Forcing Chain: r2c2.9 on ==> r5c8.1 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7...23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3.56789.2345.7..12.4..7...2.4...89..34.....123456....2...6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23456.89..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.912.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.9 Contradiction Forcing Chain: r9c3.1 on ==> r5c6.4 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7...23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3.56789.2345.7..12.4..7...2.4...89..34.....123456....2...6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23456.89..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.9.2.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.9 Contradiction Forcing Chain: r8c2.9 on ==> r4c1.4 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7...23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3.56789.2345.7..12.4..7...2.4...89..34.....123456....2...6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23456.89..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123......1..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.9.2.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.9 Contradiction Forcing Chain: r5c6.3 on ==> r9c8.7 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7...23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3.56789.2345.7..12.4..7...2.4...89..34.....12.456....2...6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23456.89..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123......1..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.9.2.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.9 Contradiction Forcing Chain: r5c8.3 on ==> r5c1.8 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7...23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3.56789.2345.7..12.4..7...2.4...89..34.....12.456....2...678912..56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23456.89..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123......1..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.9.2.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 13.0 Contradiction Forcing Chain: r9c1.1 on ==> r7c1.6 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7...23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3.56789.2345.7..12.4..7...2.4...89..34.....12.456....2...678912..56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23456.89..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123......1..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....789.2.4567891..4567.9.2.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 13.0 Contradiction Forcing Chain: r7c3.8 on ==> r8c5.5 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7...23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3.56789.2345.7..12.4..7...2.4...89..34.....12.456....2...678912..56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23456..9..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123......1..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....789.2.4567891..4567.9.2.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 13.0 Contradiction Forcing Chain: r8c3.1 on ==> r2c4.1 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7...23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3.56789.2345.7..12.4..7...2.4...89..34.....12.456....2...678912..56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23456..9..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123.........456.89.23.....9..3456.89..3.56...1234567.9123456.8912....789.2.4567891..4567.9.2.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 13.0 Contradiction Forcing Chain: r5c8.2 on ==> r9c8.5 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7...23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3.56789.2345.7..12.4..7...2.4...89..34.....12.456....2...67891...56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23456..9..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123.........456.89.23.....9..3456.89..3.56...1234567.9123456.8912....789.2.4567891..4567.9.2.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 13.0 Contradiction Forcing Chain: r5c2.4 on ==> r5c1.5 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7...23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3.56789.23.5.7..12.4..7...2.4...89..34.....12.456....2...67891...56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23456..9..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123.........456.89.23.....9..3456.89..3.56...1234567.9123456.8912....789.2.4567891..4567.9.2.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 13.0 Contradiction Forcing Chain: r7c3.4 on ==> r7c4.6 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7...23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..12345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3.56789.23.5.7..12.4..7...2.4...89..34.....12.456....2...67891...56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23.56..9..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123.........456.89.23.....9..3456.89..3.56...1234567.9123456.8912....789.2.4567891..4567.9.2.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 2.6 Pointing: Cells r8c2,r9c2: 1 in block and column 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7...23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567...2345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3.56789.23.5.7..12.4..7...2.4...89..34.....12.456....2...67891...56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23.56..9..3..67891..45678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123.........456.89.23.....9..3456.89..3.56...1234567.9123456.8912....789.2.4567891..4567.9.2.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.8 Contradiction Forcing Chain: r7c5.4 on ==> r2c7.2 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7...23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567...2345678.1.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3.56789.23.5.7..12.4..7...2.4...89..34.....12.456....2...67891...56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23.56..9..3..67891...5678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123.........456.89.23.....9..3456.89..3.56...1234567.9123456.8912....789.2.4567891..4567.9.2.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 12.9 Contradiction Forcing Chain: r3c5.4 on ==> r1c7.9 both on & off 1.3.....9.23..678..23456789123456789.23456.89123.567....3...78912345..8....45..891..45...9.23.5.7...23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567...2345678.1.3.5.7891..4567.91.3.5..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8...345678...3456...1.3.56789.23.5.7..12.4..7...2.4...89..34.....12.456....2...67891...56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56....2.4.6789..34.6..9.23.56..9..3..67891...5678.12.4.6.8.1..4...891.3456.8....45.7...2.45678.123.........456.89.23.....9..3456.89..3.56...1234567.9123456.8912....789.2.4567891..4567.9.2.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 1.3.....9.23..6789.23456789123456789.23456.89123.567....3...78912345..8....45..8912.45...9.23.5.7.9.23.5678912.456...12345..8...3..6..912.45678..2345.7..1.3..6.891234567..1234567891.3.5.7891..4567.91.345..8912345.7891.345.7.9..34567.91..4..7..12.4...8..2....78912.456....23.567..1234.6.8912....789123.5..8..2345678...3456...123456789.2345.7..12.4..7...2.4...89..34.....123456....23..6789123.56..9.234....9.2..567...23456.89.2.4.678.1.3.5..89.234.678.12.4.678...345.7...23..6.89123.56...12.4.6789..34.6..9123456789..3..67891.345678.1234.6.8.1..4...891.3456.8....45.7..12.45678.123.....91..456.89.23.....9..3456.89..3.56...1234567.9123456.8912....78912.4567891..4567.912.45678.1.345678..234..7891.3456..912345.7.9.2.45.7..1.345678. 272 20.0/0.0/10.3 xx

Edit: serate 1.4.1 (Sudoku Explainer) 2019-09-22 can't solve it giving up after processing for

Code: Select all: real 1541m37.897s user 5670m23.368s sys 24m51.504s

Highest rating steps are 6 x 13.0.
All steps are added to the solution path in the hidden section above.
The first solving step is fast in SE GUI mode and shows two spectacular chain diagrams.

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