X Sudoku (extreme)

For fans of Killer Sudoku, Samurai Sudoku and other variants

Re: X Sudoku (extreme)

Postby m_b_metcalf » Sun Dec 29, 2019 12:28 pm

tarek wrote:Andrew Sturat's Sudoku X solver doesn't like your puzzle at all because it couldn't advance even a single elimination and gave up!!!

When I'm home again in the New Year I hope to be able to find an elusive high diamond. Watch this space.

Mike
User avatar
m_b_metcalf
2017 Supporter
 
Posts: 11128
Joined: 15 May 2006
Location: Berlin

Re: X Sudoku (extreme)

Postby m_b_metcalf » Mon Jan 06, 2020 7:54 pm

m_b_metcalf wrote:When I'm home again in the New Year I hope to be able to find an elusive high diamond. Watch this space.

I'm back, and production is running excruciatingly slowly, SE taking an average of seven minutes per rating. Nevertheless, some new records, including a new highest rating and a new highest ED (7.9). I'll start a search for mid-range diamonds when the current run's finished.

Regards,

Mike
Code: Select all
 . . 1 . . . 2 . .
 . . 2 1 . . . . 3
 3 . . . . . . . .
 4 . 5 . . . . 6 .
 . 6 . . . . . . 4
 . . 7 . . . . . .
 . . . . 8 5 . . .
 . . 4 . 9 . . . .
 . 8 . . . 7 . 9 .   ED=11.4/11.4/7.7

Code: Select all
.............1...2.345.67....2......4..8.72.9......8....86.234.3...8.............   ED=6.4/4.1/4..   
......1....23....44........5.3....4..6......5..1..........73.....5.8.....7...1.8.   ED=7.6/4.3/2.9   
.............1...2..34.56....2......7.89.62.3......9....95.387.8...6.............   ED=7.8/4.3/4.3   
.............1...2..32.45....4......3.67.54.8......3....79.268.6...5.............   ED=8.0/8.0/4.3   
.............1...2.3.2.45....3......6.78.53.9......8....84.297.7...5.............   ED=8.3/4.3/4.3   
.............1...2.3.2.45....6......7.38.56.9......8....84.296.9...5.............   ED=8.4/7.9/4.3   
.............1...2.342.5.....6......4.71.86.3......1....15.274.6...8.............   ED=9.0/9.0/4.3   
.............1...2..34.56....4......7.89.63.4......9....95.287.8...6.............   ED=9.1/9.1/7.7   
.............1...2.342.56....7......4..8.69.7......8....89.235.3...6.............   ED=9.2/9.2/7.8   
.............1...2.34..56....6......4.37.68.5......7....75.234.3...8.............   ED=9.3/9.3/7.7   
.............1...2.34..56....3......7.18.63.4......8....85.297.9...6.............   ED=9.4/9.4/7.8   
.............1...2..34.56....4......3.78.64.5......8....59.273.7...6.............   ED=9.5/9.5/7.8   
.............1...2..32.45....6......3.78.96.5......8....85.273.7...6.............   ED=9.6/9.6/7.8   
.............1...2.345.67....8......4..9.58.7......9....56.234.3...5.............   ED=9.7/9.7/7.8   
.............1...2.3.2.45....3......6.78.53.9......8....84.296.4...5.............   ED=9.8/9.8/7.9   <<---------------
..1...2....34....55........6.4....1..2......6..7..........34.....6.8.....9...7.8.   ED=10.0/10.0/2.9
..1...2....23....14........1.3....4..5......6..7..........83.....6.9.....8...7.9.   ED=10.1/10.1/7.7
.............1...2.342.5.....6......4.37.86.9......7....75.234.3...8.............   ED=10.4/10.4/4.3
.............1...2.342.56....6......4..7.68.9......7....75.238.3...8.............   ED=10.5/10.5/7.8
..1...2....23....44........2.5....1..6......7..8..........95.....7.3.....9...8.3.   ED=10.7/10.7/7.7
..1...2....23....14........5.6....3..7......5.............86.....5.9.....8...4.9.   ED=10.8/10.8/7.7
..1...2....23....44........1.3....5..6......1..7..........83.....5.9.....8...7.6.   ED=10.9/10.9/2.9
..1...2....34....55........2.4....1..6......7..8..........34.....7.9.....3...8.9.   ED=11.0/11.0/4.3
..1...2....23....44........5.6....1..7......5..8..........97.....5.3.....9...8.3.   ED=11.1/11.1/2.9
User avatar
m_b_metcalf
2017 Supporter
 
Posts: 11128
Joined: 15 May 2006
Location: Berlin

ED=12.0/12.0/7.8!!!!!!!!!!!!!!!!!

Postby m_b_metcalf » Tue Jan 07, 2020 2:01 pm

Using ever-higher seeds, SE now takes an hour to rate four puzzles, on average. This monster took an hour and twenty minutes :D . I have a backlog of 400!

Regards,

Mike

Code: Select all
 . . 1 . . . 2 . .
 . . 2 3 . . . . 4
 5 . . . . . . . .
 4 . 6 . . . . 1 .
 . 5 . . . . . . 7
 . . 8 . . . . . .
 . . . . 9 6 . . .
 . . 5 . 3 . . . .
 . 9 . . . 8 . 3 . ED=12.0/12.0/7.8

001000200002300004500000000406000010050000007008000000000096000005030000090008030 ED=12.0/12.0/7.8
User avatar
m_b_metcalf
2017 Supporter
 
Posts: 11128
Joined: 15 May 2006
Location: Berlin

Re: ED=12.0/12.0/7.8

Postby tarek » Tue Jan 07, 2020 11:08 pm

I will need to double check this one as the GUI failed to solve it with techniques available

tarek
User avatar
tarek
 
Posts: 3745
Joined: 05 January 2006

Re: ED=12.0/12.0/7.8

Postby m_b_metcalf » Wed Jan 08, 2020 7:19 am

tarek wrote:I will need to double check this one as the GUI failed to solve it with techniques available


Overnight I've found a yet higher rating, and another puzzle is still being rated after nearly four hours.

More later.

Mike
User avatar
m_b_metcalf
2017 Supporter
 
Posts: 11128
Joined: 15 May 2006
Location: Berlin

Re: X Sudoku (extreme)

Postby tarek » Wed Jan 08, 2020 12:54 pm

You are obviously using the command line solver …
Can you give me the parameters to emulate. if you use the -S option then it would display all the parameters needed as well to your preferred output.

tarek
User avatar
tarek
 
Posts: 3745
Joined: 05 January 2006

Re: X Sudoku (extreme)

Postby m_b_metcalf » Wed Jan 08, 2020 1:08 pm

tarek wrote:You are obviously using the command line solver …
Can you give me the parameters to emulate. if you use the -S option then it would display all the parameters needed as well to your preferred output.


This a sample command line. The supposed four-hour timing mentioned above was incorrect, it seems to have been an artefact of overnight runs.
Code: Select all
java -cp SukakuExplainer.jar diuf.sudoku.test.serate -X1 001000200002300004400000000503000060020000005006000000000078000005090000070001090 > c:\sudoku\res.txt                   1
User avatar
m_b_metcalf
2017 Supporter
 
Posts: 11128
Joined: 15 May 2006
Location: Berlin

Re: X Sudoku (extreme)

Postby tarek » Wed Jan 08, 2020 7:03 pm

The command line worked well without issues and rated it as you said. The GUI, however, appears to have gone out of sorts when it hit the high ratings of 11.9+ and just stopped. I'm wondering if it is a memory related issue or something similar as the IDE debug mode didn't report any problems.
The step that the GUI couldn't display: Show
--before
%g: ..1...2....23....45........4.6....1..5......7..8..........96.....5.3.....9...8.3.
%i: ..1...2....23....45........4.6....1..5......7..8..........96.....5.3.....9...8.3.
%m: ..3..6789..34.678.1...........456789...45678....45.7.9.2...........56789..3.56.89.....6789.....678..2.........3......1...5678.1...5.7.91...56789....56789...4.........5......34.678...34..7.912.4.678912.4.678.12.4..7.91.3..6789.....67891.3..6.89...4......23...7.......6....2..5.789.2..5.78..23.5.7.9..3.5..891.........23.5..89123.....9....5......3.....91..4.6.8912.4...8.1234....9...4.6.8..2.4.6.89......7..123...7.9123...7.........8.12.4567.91..4567..12345.7....3456..9.2.456..9.2..56...123...78.1234..78...34..7..12.45.7..........9.....6...1..45.78..2.45.78.12..5..8.12...678.12.4.678.....5....12.4..7....3......12.4..7..1..4.6789.2.4.678912...6.8912...67..........9...4..7..12.45.7..12.45.7.........8.1..4567....3......12..56...
%M:
+-------------------------+-------------------------+-------------------------+
| 36789 34678 1 | 456789 45678 4579 | 2 56789 35689 |
| 6789 678 2 | 3 15678 1579 | 156789 56789 4 |
| 5 34678 3479 | 1246789 124678 12479 | 136789 6789 13689 |
+-------------------------+-------------------------+-------------------------+
| 4 237 6 | 25789 2578 23579 | 3589 1 23589 |
| 1239 5 39 | 14689 1248 12349 | 468 24689 7 |
| 12379 1237 8 | 1245679 14567 123457 | 34569 24569 256 |
+-------------------------+-------------------------+-------------------------+
| 12378 123478 347 | 12457 9 6 | 14578 24578 1258 |
| 12678 124678 5 | 1247 3 1247 | 146789 246789 12689 |
| 1267 9 47 | 12457 12457 8 | 14567 3 1256 |
+-------------------------+-------------------------+-------------------------+
--- end of before section ---
--after
%e: 1m04s
%h:
<html>
<body>
<h2>Dynamic Contradiction Forcing Chains</h2>
<p>
With this solving technique, we will prove the two following assertions:
<ul>
<li>If r7c2 contains the value 4, then r8c6 must contain the value 4
<li>If r7c2 contains the value 4, then r8c6 cannot contain the value 4
</ul>
Because the same assumption yields to contradictory results, we can conclude that the
assumption is false, that is, <b><font color="#00AAAA">r7c2 cannot contain the value 4</font></b>.
</p><p>
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.
</p><p>
The details of each chain are given below. Use the view selector below the grid
to switch between the <font color="#E08000">graphical illustrations</font> of the two different chains.
</p><p>
Chain 1: <b>If r7c2 contains the value 4, then r8c6 cannot contain the value 4</b> (View 1):<br>
(1) If r7c2 contains the value 4, then r9c3 cannot contain the value 4 (the value can occur only once in the block)<br>(2) If r7c2 contains the value 4 (initial assumption), then r7c3 cannot contain the value 4 (the value can occur only once in the block)<br>(3) If r7c3 does not contain the value 4 and r9c3 does not contain the value 4 (1), then r3c3 must contain the value 4 (only remaining possible position in the column)<br>(4) If r3c3 contains the value 4, then r5c5 cannot contain the value 4 (the value can occur only once in the Main Diagonal)<br>(5) If r7c2 contains the value 4 (initial assumption), then r8c2 cannot contain the value 4 (the value can occur only once in the block)<br>(6) If r8c2 does not contain the value 4, r7c3 does not contain the value 4 (2) and r5c5 does not contain the value 4 (4), then r6c4 must contain the value 4 (only remaining possible position in the Anti Diagonal)<br>(7) If r6c4 contains the value 4, then r6c4 cannot contain the value 9 (the cell can contain only one value)<br>(8) If r3c3 contains the value 4 (3), then r3c3 cannot contain the value 9 (the cell can contain only one value)<br>(9) If r9c3 does not contain the value 4 (1), then r9c3 must contain the value 7 (only remaining possible value in the cell)<br>(10) If r9c3 contains the value 7, then r7c3 cannot contain the value 7 (the value can occur only once in the block)<br>(11) If r7c3 does not contain the value 4 (2) and r7c3 does not contain the value 7, then r7c3 must contain the value 3 (only remaining possible value in the cell)<br>(12) If r7c3 contains the value 3, then r3c7 cannot contain the value 3 (the value can occur only once in the Anti Diagonal)<br>(13) If r7c3 contains the value 3 (11), then r1c9 cannot contain the value 3 (the value can occur only once in the Anti Diagonal)<br>(14) If r1c9 does not contain the value 3 and r3c7 does not contain the value 3 (12), then r3c9 must contain the value 3 (only remaining possible position in the block)<br>(15) If r3c9 contains the value 3, then r3c9 cannot contain the value 9 (the cell can contain only one value)<br>(16) If r3c3 does not contain the value 9 (8), then r5c3 must contain the value 9 (only remaining possible position in the column)<br>(17) If r5c3 contains the value 9, then r5c4 cannot contain the value 9 (the value can occur only once in the row)<br>(18) If r5c3 contains the value 9 (16), then r5c6 cannot contain the value 9 (the value can occur only once in the row)<br>(19) If r6c4 does not contain the value 9 (7), r5c6 does not contain the value 9 and r5c4 does not contain the value 9 (17), then r4c9 cannot contain the value 9 (Cells r4c4,r4c6 on value 9 in block 5)<br>(20) If r4c9 does not contain the value 9, r3c9 does not contain the value 9 (15), r3c3 does not contain the value 9 (8) and r6c4 does not contain the value 9 (7), then r3c8 cannot contain the value 9 (Region Forcing Chains: 9 in Anti Diagonal ==> r3c8.9 off)<br>(21) If r6c4 does not contain the value 9 (7) and r3c3 does not contain the value 9 (8), then r1c8 cannot contain the value 9 (Contradiction Forcing Chain: r1c8.9 on ==> r4c4.9 both on & off)<br>(22) If r3c3 does not contain the value 9 (8), r6c4 does not contain the value 9 (7), r5c6 does not contain the value 9 (18) and r5c4 does not contain the value 9 (17), then r2c8 cannot contain the value 9 (Region Forcing Chains: 9 in block ==> r2c8.9 off)<br>(23) If r5c3 contains the value 9 (16), then r5c8 cannot contain the value 9 (the value can occur only once in the row)<br>(24) If r4c9 does not contain the value 9 (19), r3c9 does not contain the value 9 (15), r6c4 does not contain the value 9 (7), r5c6 does not contain the value 9 (18) and r5c4 does not contain the value 9 (17), then r8c8 cannot contain the value 9 (Region Forcing Chains: 9 in column ==> r8c8.9 off)<br>(25) If r8c8 does not contain the value 9, r5c8 does not contain the value 9 (23), r2c8 does not contain the value 9 (22), r1c8 does not contain the value 9 (21) and r3c8 does not contain the value 9 (20), then r6c8 must contain the value 9 (only remaining possible position in the column)<br>(26) If r6c8 contains the value 9, then r6c8 cannot contain the value 5 (the cell can contain only one value)<br>(27) If r6c4 contains the value 4 (6), then r6c4 cannot contain the value 2 (the cell can contain only one value)<br>(28) If r9c3 contains the value 7 (9), then r7c1 cannot contain the value 7 (the value can occur only once in the block)<br>(29) If r9c3 contains the value 7 (9), then r8c1 cannot contain the value 7 (the value can occur only once in the block)<br>(30) If r9c3 contains the value 7 (9), then r9c1 cannot contain the value 7 (the value can occur only once in the block)<br>(31) If r7c2 contains the value 4 (initial assumption), then r7c2 cannot contain the value 1 (the cell can contain only one value)<br>(32) If r3c3 contains the value 4 (3), then r3c3 cannot contain the value 3 (the cell can contain only one value)<br>(33) If r6c4 contains the value 4 (6), then r6c4 cannot contain the value 7 (the cell can contain only one value)<br>(34) If r9c3 contains the value 7 (9), then r8c2 cannot contain the value 7 (the value can occur only once in the block)<br>(35) If r3c9 contains the value 3 (14), then r3c9 cannot contain the value 1 (the cell can contain only one value)<br>(36) If r3c9 contains the value 3 (14), then r3c9 cannot contain the value 6 (the cell can contain only one value)<br>(37) If r6c4 contains the value 4 (6), then r6c4 cannot contain the value 5 (the cell can contain only one value)<br>(38) If r3c9 does not contain the value 1 (35), then r7c7 cannot contain the value 1 (Cells r2c7,r3c7 on value 1 in block 3)<br>(39) If r7c7 does not contain the value 1, r6c4 does not contain the value 5 (37), r3c9 does not contain the value 6 (36), r4c9 does not contain the value 9 (19), r3c9 does not contain the value 9 (15), r6c4 does not contain the value 9 (7), r5c6 does not contain the value 9 (18), r5c4 does not contain the value 9 (17), r3c9 does not contain the value 1 (35), r3c3 does not contain the value 9 (8), r8c2 does not contain the value 7 (34), r7c3 does not contain the value 7 (10), r6c4 does not contain the value 7 (33), r5c8 does not contain the value 9 (23), r3c3 does not contain the value 3 (32), r7c2 does not contain the value 1 (31), r9c1 does not contain the value 7 (30), r8c1 does not contain the value 7 (29), r7c1 does not contain the value 7 (28) and r6c4 does not contain the value 2 (27), then r4c4 cannot contain the value 5 (Contradiction Forcing Chain: r4c4.9 off ==> r6c9.2 both on & off)<br>(40) If r5c3 contains the value 9 (16), then r5c1 cannot contain the value 9 (the value can occur only once in the block)<br>(41) If r6c4 contains the value 4 (6), then r6c8 cannot contain the value 4 (the value can occur only once in the row)<br>(42) If r7c2 contains the value 4 (initial assumption), then r7c8 cannot contain the value 4 (the value can occur only once in the row)<br>(43) If r3c3 contains the value 4 (3), then r8c8 cannot contain the value 4 (the value can occur only once in the Main Diagonal)<br>(44) If r8c8 does not contain the value 4, r7c8 does not contain the value 4 (42) and r6c8 does not contain the value 4 (41), then r5c8 must contain the value 4 (only remaining possible position in the column)<br>(45) If r5c8 contains the value 4, then r5c8 cannot contain the value 2 (the cell can contain only one value)<br>(46) If r7c3 contains the value 3 (11), then r5c3 cannot contain the value 3 (the value can occur only once in the column)<br>(47) If r7c2 contains the value 4 (initial assumption), then r7c2 cannot contain the value 2 (the cell can contain only one value)<br>(48) If r6c4 does not contain the value 9 (7), r5c6 does not contain the value 9 (18) and r5c4 does not contain the value 9 (17), then r4c7 cannot contain the value 9 (Cells r4c4,r4c6 on value 9 in block 5)<br>(49) If r3c3 does not contain the value 3 (32), then r6c1 cannot contain the value 3 (Cells r1c1,r6c6 on value 3 in Main Diagonal)<br>(50) If r7c3 contains the value 3 (11), then r7c1 cannot contain the value 3 (the value can occur only once in the block)<br>(51) If r7c3 contains the value 3 (11), then r4c6 cannot contain the value 3 (the value can occur only once in the Anti Diagonal)<br>(52) If r4c6 does not contain the value 3, r7c1 does not contain the value 3 (50), r6c1 does not contain the value 3 (49), r5c8 does not contain the value 9 (23), r4c9 does not contain the value 9 (19), r4c7 does not contain the value 9 (48), r7c2 does not contain the value 2 (47), r3c3 does not contain the value 9 (8), r5c3 does not contain the value 3 (46), r5c8 does not contain the value 2 (45), r7c2 does not contain the value 1 (31), r5c1 does not contain the value 9 (40) and r3c9 does not contain the value 1 (35), then r6c6 cannot contain the value 5 (Cell Forcing Chains: r5c1 ==> r6c6.5 off)<br>(53) If r6c6 does not contain the value 5 and r4c4 does not contain the value 5 (39), then r7c8 cannot contain the value 5 (Cells r7c7,r9c9 on value 5 in Main Diagonal)<br>(54) If r7c8 does not contain the value 5 and r6c8 does not contain the value 5 (26), then r1c9 cannot contain the value 5 (Cells r1c8,r2c8 on value 5 in column 8)<br>(55) If r6c4 does not contain the value 5 (37) and r1c9 does not contain the value 5, then r2c6 cannot contain the value 5 (Cells r2c8,r4c6 on value 5 in Anti Diagonal)<br>(56) If r7c2 does not contain the value 1 (31), r7c7 does not contain the value 1 (38) and r3c9 does not contain the value 1 (35), then r2c6 cannot contain the value 1 (Region Forcing Chains: 1 in block ==> r2c6.1 off)<br>(57) If r3c3 does not contain the value 9 (8), r6c4 does not contain the value 9 (7), r5c6 does not contain the value 9 (18) and r5c4 does not contain the value 9 (17), then r2c6 cannot contain the value 9 (Region Forcing Chains: 9 in block ==> r2c6.9 off)<br>(58) If r2c6 does not contain the value 9, r2c6 does not contain the value 1 (56) and r2c6 does not contain the value 5 (55), then r2c6 must contain the value 7 (only remaining possible value in the cell)<br>(59) If r2c6 contains the value 7, then r4c6 cannot contain the value 7 (the value can occur only once in the column)<br>(60) If r2c6 contains the value 7 (58), then r2c8 cannot contain the value 7 (the value can occur only once in the row)<br>(61) If r9c1 does not contain the value 7 (30), r8c2 does not contain the value 7 (34), r7c3 does not contain the value 7 (10), r6c4 does not contain the value 7 (33), r2c8 does not contain the value 7 and r4c6 does not contain the value 7 (59), then r3c7 must contain the value 7 (only remaining possible position in the Anti Diagonal)<br>(62) If r3c7 contains the value 7, then r3c7 cannot contain the value 9 (the cell can contain only one value)<br>(63) If r7c7 does not contain the value 1 (38), r3c9 does not contain the value 9 (15), r6c4 does not contain the value 5 (37), r3c9 does not contain the value 6 (36), r6c4 does not contain the value 9 (7), r3c9 does not contain the value 1 (35), r3c3 does not contain the value 9 (8), r8c2 does not contain the value 7 (34), r7c3 does not contain the value 7 (10), r6c4 does not contain the value 7 (33), r5c8 does not contain the value 9 (23), r4c9 does not contain the value 9 (19), r4c7 does not contain the value 9 (48), r3c3 does not contain the value 3 (32), r7c2 does not contain the value 1 (31), r9c1 does not contain the value 7 (30), r8c1 does not contain the value 7 (29), r7c1 does not contain the value 7 (28) and r6c4 does not contain the value 2 (27), then r2c7 cannot contain the value 9 (Contradiction Forcing Chain: r2c7.9 on ==> r6c9.2 both on & off)<br>(64) If r6c8 contains the value 9 (25), then r6c7 cannot contain the value 9 (the value can occur only once in the block)<br>(65) If r6c7 does not contain the value 9, r4c7 does not contain the value 9 (48), r2c7 does not contain the value 9 (63) and r3c7 does not contain the value 9 (62), then r8c7 must contain the value 9 (only remaining possible position in the column)<br>(66) If r8c7 contains the value 9, then r8c7 cannot contain the value 4 (the cell can contain only one value)<br>(67) If r6c4 contains the value 4 (6), then r8c4 cannot contain the value 4 (the value can occur only once in the column)<br>(68) If r8c8 does not contain the value 4 (43), r8c4 does not contain the value 4, r8c2 does not contain the value 4 (5) and r8c7 does not contain the value 4 (66), then r8c6 must contain the value 4 (only remaining possible position in the row)<br>
</p><p>
Chain 2: <b>If r8c6 must contain the value 4, then r8c6 cannot contain the value 4</b> (View 2):<br>
(1) If r7c2 contains the value 4, then r9c3 cannot contain the value 4 (the value can occur only once in the block)<br>(2) If r7c2 contains the value 4 (initial assumption), then r7c3 cannot contain the value 4 (the value can occur only once in the block)<br>(3) If r7c3 does not contain the value 4 and r9c3 does not contain the value 4 (1), then r3c3 must contain the value 4 (only remaining possible position in the column)<br>(4) If r3c3 contains the value 4, then r5c5 cannot contain the value 4 (the value can occur only once in the Main Diagonal)<br>(5) If r7c2 contains the value 4 (initial assumption), then r8c2 cannot contain the value 4 (the value can occur only once in the block)<br>(6) If r8c2 does not contain the value 4, r7c3 does not contain the value 4 (2) and r5c5 does not contain the value 4 (4), then r6c4 must contain the value 4 (only remaining possible position in the Anti Diagonal)<br>(7) If r6c4 contains the value 4, then r6c4 cannot contain the value 9 (the cell can contain only one value)<br>(8) If r3c3 contains the value 4 (3), then r3c3 cannot contain the value 9 (the cell can contain only one value)<br>(9) If r9c3 does not contain the value 4 (1), then r9c3 must contain the value 7 (only remaining possible value in the cell)<br>(10) If r9c3 contains the value 7, then r7c3 cannot contain the value 7 (the value can occur only once in the block)<br>(11) If r7c3 does not contain the value 4 (2) and r7c3 does not contain the value 7, then r7c3 must contain the value 3 (only remaining possible value in the cell)<br>(12) If r7c3 contains the value 3, then r3c7 cannot contain the value 3 (the value can occur only once in the Anti Diagonal)<br>(13) If r7c3 contains the value 3 (11), then r1c9 cannot contain the value 3 (the value can occur only once in the Anti Diagonal)<br>(14) If r1c9 does not contain the value 3 and r3c7 does not contain the value 3 (12), then r3c9 must contain the value 3 (only remaining possible position in the block)<br>(15) If r3c9 contains the value 3, then r3c9 cannot contain the value 9 (the cell can contain only one value)<br>(16) If r3c3 does not contain the value 9 (8), then r5c3 must contain the value 9 (only remaining possible position in the column)<br>(17) If r5c3 contains the value 9, then r5c4 cannot contain the value 9 (the value can occur only once in the row)<br>(18) If r5c3 contains the value 9 (16), then r5c6 cannot contain the value 9 (the value can occur only once in the row)<br>(19) If r6c4 does not contain the value 9 (7), r5c6 does not contain the value 9 and r5c4 does not contain the value 9 (17), then r4c9 cannot contain the value 9 (Cells r4c4,r4c6 on value 9 in block 5)<br>(20) If r4c9 does not contain the value 9, r3c9 does not contain the value 9 (15), r3c3 does not contain the value 9 (8) and r6c4 does not contain the value 9 (7), then r3c8 cannot contain the value 9 (Region Forcing Chains: 9 in Anti Diagonal ==> r3c8.9 off)<br>(21) If r6c4 does not contain the value 9 (7) and r3c3 does not contain the value 9 (8), then r1c8 cannot contain the value 9 (Contradiction Forcing Chain: r1c8.9 on ==> r4c4.9 both on & off)<br>(22) If r3c3 does not contain the value 9 (8), r6c4 does not contain the value 9 (7), r5c6 does not contain the value 9 (18) and r5c4 does not contain the value 9 (17), then r2c8 cannot contain the value 9 (Region Forcing Chains: 9 in block ==> r2c8.9 off)<br>(23) If r5c3 contains the value 9 (16), then r5c8 cannot contain the value 9 (the value can occur only once in the row)<br>(24) If r4c9 does not contain the value 9 (19), r3c9 does not contain the value 9 (15), r6c4 does not contain the value 9 (7), r5c6 does not contain the value 9 (18) and r5c4 does not contain the value 9 (17), then r8c8 cannot contain the value 9 (Region Forcing Chains: 9 in column ==> r8c8.9 off)<br>(25) If r8c8 does not contain the value 9, r5c8 does not contain the value 9 (23), r2c8 does not contain the value 9 (22), r1c8 does not contain the value 9 (21) and r3c8 does not contain the value 9 (20), then r6c8 must contain the value 9 (only remaining possible position in the column)<br>(26) If r6c8 contains the value 9, then r6c8 cannot contain the value 5 (the cell can contain only one value)<br>(27) If r6c4 contains the value 4 (6), then r6c4 cannot contain the value 2 (the cell can contain only one value)<br>(28) If r9c3 contains the value 7 (9), then r7c1 cannot contain the value 7 (the value can occur only once in the block)<br>(29) If r9c3 contains the value 7 (9), then r8c1 cannot contain the value 7 (the value can occur only once in the block)<br>(30) If r9c3 contains the value 7 (9), then r9c1 cannot contain the value 7 (the value can occur only once in the block)<br>(31) If r7c2 contains the value 4 (initial assumption), then r7c2 cannot contain the value 1 (the cell can contain only one value)<br>(32) If r3c3 contains the value 4 (3), then r3c3 cannot contain the value 3 (the cell can contain only one value)<br>(33) If r6c4 contains the value 4 (6), then r6c4 cannot contain the value 7 (the cell can contain only one value)<br>(34) If r9c3 contains the value 7 (9), then r8c2 cannot contain the value 7 (the value can occur only once in the block)<br>(35) If r3c9 contains the value 3 (14), then r3c9 cannot contain the value 1 (the cell can contain only one value)<br>(36) If r3c9 contains the value 3 (14), then r3c9 cannot contain the value 6 (the cell can contain only one value)<br>(37) If r6c4 contains the value 4 (6), then r6c4 cannot contain the value 5 (the cell can contain only one value)<br>(38) If r3c9 does not contain the value 1 (35), then r7c7 cannot contain the value 1 (Cells r2c7,r3c7 on value 1 in block 3)<br>(39) If r7c7 does not contain the value 1, r6c4 does not contain the value 5 (37), r3c9 does not contain the value 6 (36), r4c9 does not contain the value 9 (19), r3c9 does not contain the value 9 (15), r6c4 does not contain the value 9 (7), r5c6 does not contain the value 9 (18), r5c4 does not contain the value 9 (17), r3c9 does not contain the value 1 (35), r3c3 does not contain the value 9 (8), r8c2 does not contain the value 7 (34), r7c3 does not contain the value 7 (10), r6c4 does not contain the value 7 (33), r5c8 does not contain the value 9 (23), r3c3 does not contain the value 3 (32), r7c2 does not contain the value 1 (31), r9c1 does not contain the value 7 (30), r8c1 does not contain the value 7 (29), r7c1 does not contain the value 7 (28) and r6c4 does not contain the value 2 (27), then r4c4 cannot contain the value 5 (Contradiction Forcing Chain: r4c4.9 off ==> r6c9.2 both on & off)<br>(40) If r5c3 contains the value 9 (16), then r5c1 cannot contain the value 9 (the value can occur only once in the block)<br>(41) If r6c4 contains the value 4 (6), then r6c8 cannot contain the value 4 (the value can occur only once in the row)<br>(42) If r7c2 contains the value 4 (initial assumption), then r7c8 cannot contain the value 4 (the value can occur only once in the row)<br>(43) If r3c3 contains the value 4 (3), then r8c8 cannot contain the value 4 (the value can occur only once in the Main Diagonal)<br>(44) If r8c8 does not contain the value 4, r7c8 does not contain the value 4 (42) and r6c8 does not contain the value 4 (41), then r5c8 must contain the value 4 (only remaining possible position in the column)<br>(45) If r5c8 contains the value 4, then r5c8 cannot contain the value 2 (the cell can contain only one value)<br>(46) If r7c3 contains the value 3 (11), then r5c3 cannot contain the value 3 (the value can occur only once in the column)<br>(47) If r7c2 contains the value 4 (initial assumption), then r7c2 cannot contain the value 2 (the cell can contain only one value)<br>(48) If r6c4 does not contain the value 9 (7), r5c6 does not contain the value 9 (18) and r5c4 does not contain the value 9 (17), then r4c7 cannot contain the value 9 (Cells r4c4,r4c6 on value 9 in block 5)<br>(49) If r3c3 does not contain the value 3 (32), then r6c1 cannot contain the value 3 (Cells r1c1,r6c6 on value 3 in Main Diagonal)<br>(50) If r7c3 contains the value 3 (11), then r7c1 cannot contain the value 3 (the value can occur only once in the block)<br>(51) If r7c3 contains the value 3 (11), then r4c6 cannot contain the value 3 (the value can occur only once in the Anti Diagonal)<br>(52) If r4c6 does not contain the value 3, r7c1 does not contain the value 3 (50), r6c1 does not contain the value 3 (49), r5c8 does not contain the value 9 (23), r4c9 does not contain the value 9 (19), r4c7 does not contain the value 9 (48), r7c2 does not contain the value 2 (47), r3c3 does not contain the value 9 (8), r5c3 does not contain the value 3 (46), r5c8 does not contain the value 2 (45), r7c2 does not contain the value 1 (31), r5c1 does not contain the value 9 (40) and r3c9 does not contain the value 1 (35), then r6c6 cannot contain the value 5 (Cell Forcing Chains: r5c1 ==> r6c6.5 off)<br>(53) If r6c6 does not contain the value 5 and r4c4 does not contain the value 5 (39), then r7c8 cannot contain the value 5 (Cells r7c7,r9c9 on value 5 in Main Diagonal)<br>(54) If r7c8 does not contain the value 5 and r6c8 does not contain the value 5 (26), then r1c9 cannot contain the value 5 (Cells r1c8,r2c8 on value 5 in column 8)<br>(55) If r6c4 does not contain the value 5 (37) and r1c9 does not contain the value 5, then r2c6 cannot contain the value 5 (Cells r2c8,r4c6 on value 5 in Anti Diagonal)<br>(56) If r7c2 does not contain the value 1 (31), r7c7 does not contain the value 1 (38) and r3c9 does not contain the value 1 (35), then r2c6 cannot contain the value 1 (Region Forcing Chains: 1 in block ==> r2c6.1 off)<br>(57) If r3c3 does not contain the value 9 (8), r6c4 does not contain the value 9 (7), r5c6 does not contain the value 9 (18) and r5c4 does not contain the value 9 (17), then r2c6 cannot contain the value 9 (Region Forcing Chains: 9 in block ==> r2c6.9 off)<br>(58) If r2c6 does not contain the value 9, r2c6 does not contain the value 1 (56) and r2c6 does not contain the value 5 (55), then r2c6 must contain the value 7 (only remaining possible value in the cell)<br>(59) If r2c6 contains the value 7, then r4c6 cannot contain the value 7 (the value can occur only once in the column)<br>(60) If r2c6 contains the value 7 (58), then r2c8 cannot contain the value 7 (the value can occur only once in the row)<br>(61) If r9c1 does not contain the value 7 (30), r8c2 does not contain the value 7 (34), r7c3 does not contain the value 7 (10), r6c4 does not contain the value 7 (33), r2c8 does not contain the value 7 and r4c6 does not contain the value 7 (59), then r3c7 must contain the value 7 (only remaining possible position in the Anti Diagonal)<br>(62) If r3c7 contains the value 7, then r3c7 cannot contain the value 9 (the cell can contain only one value)<br>(63) If r7c7 does not contain the value 1 (38), r3c9 does not contain the value 9 (15), r6c4 does not contain the value 5 (37), r3c9 does not contain the value 6 (36), r6c4 does not contain the value 9 (7), r3c9 does not contain the value 1 (35), r3c3 does not contain the value 9 (8), r8c2 does not contain the value 7 (34), r7c3 does not contain the value 7 (10), r6c4 does not contain the value 7 (33), r5c8 does not contain the value 9 (23), r4c9 does not contain the value 9 (19), r4c7 does not contain the value 9 (48), r3c3 does not contain the value 3 (32), r7c2 does not contain the value 1 (31), r9c1 does not contain the value 7 (30), r8c1 does not contain the value 7 (29), r7c1 does not contain the value 7 (28) and r6c4 does not contain the value 2 (27), then r2c7 cannot contain the value 9 (Contradiction Forcing Chain: r2c7.9 on ==> r6c9.2 both on & off)<br>(64) If r3c9 does not contain the value 9 (15), r3c8 does not contain the value 9 (20), r2c8 does not contain the value 9 (22), r2c7 does not contain the value 9, r1c8 does not contain the value 9 (21) and r3c7 does not contain the value 9 (62), then r1c9 must contain the value 9 (only remaining possible position in the block)<br>(65) If r1c9 contains the value 9, then r1c6 cannot contain the value 9 (the value can occur only once in the row)<br>(66) If r5c8 does not contain the value 2 (45) and r7c2 does not contain the value 2 (47), then r4c6 cannot contain the value 2 (Region Forcing Chains: 2 in column ==> r4c6.2 off)<br>(67) If r7c7 does not contain the value 1 (38), r6c4 does not contain the value 5 (37), r3c9 does not contain the value 6 (36), r4c9 does not contain the value 9 (19), r3c9 does not contain the value 9 (15), r3c9 does not contain the value 1 (35), r3c3 does not contain the value 9 (8), r8c2 does not contain the value 7 (34), r7c3 does not contain the value 7 (10), r6c4 does not contain the value 7 (33), r5c8 does not contain the value 9 (23), r3c3 does not contain the value 3 (32), r7c2 does not contain the value 1 (31), r9c1 does not contain the value 7 (30), r8c1 does not contain the value 7 (29), r7c1 does not contain the value 7 (28) and r6c4 does not contain the value 2 (27), then r4c6 cannot contain the value 9 (Contradiction Forcing Chain: r4c6.9 on ==> r6c9.2 both on & off)<br>(68) If r4c6 does not contain the value 9, r4c6 does not contain the value 3 (51), r4c6 does not contain the value 2 (66) and r4c6 does not contain the value 7 (59), then r4c6 must contain the value 5 (only remaining possible value in the cell)<br>(69) If r4c6 contains the value 5, then r1c6 cannot contain the value 5 (the value can occur only once in the column)<br>(70) If r2c6 contains the value 7 (58), then r1c6 cannot contain the value 7 (the value can occur only once in the block)<br>(71) If r1c6 does not contain the value 7, r1c6 does not contain the value 5 (69) and r1c6 does not contain the value 9 (65), then r1c6 must contain the value 4 (only remaining possible value in the cell)<br>(72) If r1c6 contains the value 4, then r8c6 cannot contain the value 4 (the value can occur only once in the column)<br>
</p>
<br><br>
<b>Nested Forcing Chains details</b> (Note that each Nested Forcing Chain relies on the fact that some <font color="blue">candidates</font> have been excluded by the main Forcing Chain): <br><br>
<i>Nested <b>Contradiction Forcing Chain: r2c7.9 on ==> r6c9.2 both on & off</b></i><br>
Chain 3: <b>If r2c7 contains the value 9, then r6c9 must contain the value 2</b> (View 3):<br>
(1) If r2c7 contains the value 9, then r3c7 cannot contain the value 9 (the value can occur only once in the block)<br>(2) If r2c7 contains the value 9 (initial assumption), then r1c9 cannot contain the value 9 (the value can occur only once in the block)<br>(3) If r2c7 contains the value 9 (initial assumption), then r2c8 cannot contain the value 9 (the value can occur only once in the block)<br>(4) If r2c8 does not contain the value 9, r1c9 does not contain the value 9 (2) and r3c7 does not contain the value 9 (1), then r4c6 must contain the value 9 (only remaining possible position in the Anti Diagonal)<br>(5) If r4c6 contains the value 9, then r4c6 cannot contain the value 7 (the cell can contain only one value)<br>(6) If r2c7 contains the value 9 (initial assumption), then r2c7 cannot contain the value 1 (the cell can contain only one value)<br>(7) If r2c7 does not contain the value 1, then r3c7 must contain the value 1 (only remaining possible position in the block)<br>(8) If r3c7 contains the value 1, then r3c7 cannot contain the value 7 (the cell can contain only one value)<br>(9) If r3c7 does not contain the value 7 and r4c6 does not contain the value 7 (5), then r2c8 must contain the value 7 (only remaining possible position in the Anti Diagonal)<br>(10) If r2c8 contains the value 7, then r2c1 cannot contain the value 7 (the value can occur only once in the row)<br>(11) If r2c7 contains the value 9 (initial assumption), then r2c1 cannot contain the value 9 (the value can occur only once in the row)<br>(12) If r2c1 does not contain the value 9, then r1c1 must contain the value 9 (only remaining possible position in the block)<br>(13) If r1c1 contains the value 9, then r1c1 cannot contain the value 7 (the cell can contain only one value)<br>(14) If r1c1 does not contain the value 7 and r2c1 does not contain the value 7 (10), then r6c1 must contain the value 7 (only remaining possible position in the column)<br>(15) If r6c1 contains the value 7, then r6c1 cannot contain the value 2 (the cell can contain only one value)<br>(16) If r3c7 contains the value 1 (7), then r8c2 cannot contain the value 1 (the value can occur only once in the Anti Diagonal)<br>(17) If r8c2 does not contain the value 1, then r6c2 must contain the value 1 (only remaining possible position in the column)<br>(18) If r6c2 contains the value 1, then r6c2 cannot contain the value 2 (the cell can contain only one value)<br>(19) If r1c1 contains the value 9 (12), then r1c1 cannot contain the value 3 (the cell can contain only one value)<br>(20) If r1c1 does not contain the value 3, then r6c6 must contain the value 3 (only remaining possible position in the Main Diagonal)<br>(21) If r6c6 contains the value 3, then r6c6 cannot contain the value 2 (the cell can contain only one value)<br>(22) If r2c7 contains the value 9 (initial assumption), then r6c7 cannot contain the value 9 (the value can occur only once in the column)<br>(23) If r6c7 does not contain the value 9, then r6c8 must contain the value 9 (only remaining possible position in the block)<br>(24) If r6c8 contains the value 9, then r6c8 cannot contain the value 2 (the cell can contain only one value)<br>(25) If r6c8 does not contain the value 2, r6c6 does not contain the value 2 (21), r6c2 does not contain the value 2 (18) and r6c1 does not contain the value 2 (15), then r6c9 must contain the value 2 (only remaining possible position in the row)<br><br>
Chain 4: <b>If r2c7 contains the value 9, then r6c9 cannot contain the value 2</b> (View 4):<br>
(1) If r2c7 contains the value 9, then r3c7 cannot contain the value 9 (the value can occur only once in the block)<br>(2) If r2c7 contains the value 9 (initial assumption), then r1c9 cannot contain the value 9 (the value can occur only once in the block)<br>(3) If r2c7 contains the value 9 (initial assumption), then r2c8 cannot contain the value 9 (the value can occur only once in the block)<br>(4) If r2c8 does not contain the value 9, r1c9 does not contain the value 9 (2) and r3c7 does not contain the value 9 (1), then r4c6 must contain the value 9 (only remaining possible position in the Anti Diagonal)<br>(5) If r4c6 contains the value 9, then r4c6 cannot contain the value 7 (the cell can contain only one value)<br>(6) If r2c7 contains the value 9 (initial assumption), then r2c7 cannot contain the value 1 (the cell can contain only one value)<br>(7) If r2c7 does not contain the value 1, then r3c7 must contain the value 1 (only remaining possible position in the block)<br>(8) If r3c7 contains the value 1, then r3c7 cannot contain the value 7 (the cell can contain only one value)<br>(9) If r3c7 does not contain the value 7 and r4c6 does not contain the value 7 (5), then r2c8 must contain the value 7 (only remaining possible position in the Anti Diagonal)<br>(10) If r2c8 contains the value 7, then r2c8 cannot contain the value 5 (the cell can contain only one value)<br>(11) If r4c6 contains the value 9 (4), then r4c6 cannot contain the value 5 (the cell can contain only one value)<br>(12) If r4c6 does not contain the value 5 and r2c8 does not contain the value 5 (10), then r1c9 must contain the value 5 (only remaining possible position in the Anti Diagonal)<br>(13) If r1c9 contains the value 5, then r1c9 cannot contain the value 6 (the cell can contain only one value)<br>(14) If r1c9 does not contain the value 9 (2), then r8c9 must contain the value 9 (only remaining possible position in the column)<br>(15) If r8c9 contains the value 9, then r8c9 cannot contain the value 6 (the cell can contain only one value)<br>(16) If r3c7 contains the value 1 (7), then r8c2 cannot contain the value 1 (the value can occur only once in the Anti Diagonal)<br>(17) If r8c2 does not contain the value 1, then r6c2 must contain the value 1 (only remaining possible position in the column)<br>(18) If r6c2 contains the value 1, then r6c6 cannot contain the value 1 (the value can occur only once in the row)<br>(19) If r3c7 contains the value 1 (7), then r5c5 cannot contain the value 1 (the value can occur only once in the Anti Diagonal)<br>(20) If r5c5 does not contain the value 1 and r6c6 does not contain the value 1 (18), then r9c9 must contain the value 1 (only remaining possible position in the Main Diagonal)<br>(21) If r9c9 contains the value 1, then r9c9 cannot contain the value 6 (the cell can contain only one value)<br>(22) If r9c9 does not contain the value 6, r8c9 does not contain the value 6 (15) and r1c9 does not contain the value 6 (13), then r6c9 must contain the value 6 (only remaining possible position in the column)<br>(23) If r6c9 contains the value 6, then r6c9 cannot contain the value 2 (the cell can contain only one value)<br><br>
<i>Nested <b>Region Forcing Chains: 9 in Anti Diagonal ==> r3c8.9 off</b></i><br>
Chain 5: <b>If r1c9 contains the value 9, then r3c8 cannot contain the value 9</b> (View 5):<br>
(1) If r1c9 contains the value 9, then r3c8 cannot contain the value 9 (the value can occur only once in the block)<br><br>
Chain 6: <b>If r2c8 contains the value 9, then r3c8 cannot contain the value 9</b> (View 6):<br>
(1) If r2c8 contains the value 9, then r3c8 cannot contain the value 9 (the value can occur only once in the block)<br><br>
Chain 7: <b>If r3c7 contains the value 9, then r3c8 cannot contain the value 9</b> (View 7):<br>
(1) If r3c7 contains the value 9, then r3c8 cannot contain the value 9 (the value can occur only once in the block)<br><br>
Chain 8: <b>If r4c6 contains the value 9, then r3c8 cannot contain the value 9</b> (View 8):<br>
(1) If r4c6 contains the value 9, then r1c9 cannot contain the value 9 (the value can occur only once in the Anti Diagonal)<br>(2) If r1c9 does not contain the value 9, then r8c9 must contain the value 9 (only remaining possible position in the column)<br>(3) If r8c9 contains the value 9, then r8c8 cannot contain the value 9 (the value can occur only once in the block)<br>(4) If r4c6 contains the value 9 (initial assumption), then r4c4 cannot contain the value 9 (the value can occur only once in the block)<br>(5) If r4c4 does not contain the value 9 and r8c8 does not contain the value 9 (3), then r1c1 must contain the value 9 (only remaining possible position in the Main Diagonal)<br>(6) If r1c1 contains the value 9, then r2c1 cannot contain the value 9 (the value can occur only once in the block)<br>(7) If r4c6 contains the value 9 (initial assumption), then r2c6 cannot contain the value 9 (the value can occur only once in the column)<br>(8) If r4c6 contains the value 9 (initial assumption), then r2c8 cannot contain the value 9 (the value can occur only once in the Anti Diagonal)<br>(9) If r2c8 does not contain the value 9, r2c6 does not contain the value 9 (7) and r2c1 does not contain the value 9 (6), then r2c7 must contain the value 9 (only remaining possible position in the row)<br>(10) If r2c7 contains the value 9, then r3c8 cannot contain the value 9 (the value can occur only once in the block)<br><br>
<i>Nested <b>Contradiction Forcing Chain: r1c8.9 on ==> r4c4.9 both on & off</b></i><br>
Chain 9: <b>If r1c8 contains the value 9, then r4c4 must contain the value 9</b> (View 9):<br>
(1) If r1c8 contains the value 9, then r8c8 cannot contain the value 9 (the value can occur only once in the column)<br>(2) If r1c8 contains the value 9 (initial assumption), then r1c1 cannot contain the value 9 (the value can occur only once in the row)<br>(3) If r1c1 does not contain the value 9 and r8c8 does not contain the value 9 (1), then r4c4 must contain the value 9 (only remaining possible position in the Main Diagonal)<br><br>
Chain 10: <b>If r1c8 contains the value 9, then r4c4 cannot contain the value 9</b> (View 10):<br>
(1) If r1c8 contains the value 9, then r3c7 cannot contain the value 9 (the value can occur only once in the block)<br>(2) If r1c8 contains the value 9 (initial assumption), then r1c9 cannot contain the value 9 (the value can occur only once in the block)<br>(3) If r1c8 contains the value 9 (initial assumption), then r2c8 cannot contain the value 9 (the value can occur only once in the block)<br>(4) If r2c8 does not contain the value 9, r1c9 does not contain the value 9 (2) and r3c7 does not contain the value 9 (1), then r4c6 must contain the value 9 (only remaining possible position in the Anti Diagonal)<br>(5) If r4c6 contains the value 9, then r4c4 cannot contain the value 9 (the value can occur only once in the block)<br><br>
<i>Nested <b>Region Forcing Chains: 9 in block ==> r2c8.9 off</b></i><br>
Chain 11: <b>If r1c1 contains the value 9, then r2c8 cannot contain the value 9</b> (View 11):<br>
(1) If r1c1 contains the value 9, then r4c4 cannot contain the value 9 (the value can occur only once in the Main Diagonal)<br>(2) If r4c4 does not contain the value 9, then r4c6 must contain the value 9 (only remaining possible position in the block)<br>(3) If r4c6 contains the value 9, then r2c8 cannot contain the value 9 (the value can occur only once in the Anti Diagonal)<br><br>
Chain 12: <b>If r2c1 contains the value 9, then r2c8 cannot contain the value 9</b> (View 12):<br>
(1) If r2c1 contains the value 9, then r2c8 cannot contain the value 9 (the value can occur only once in the row)<br><br>
<i>Nested <b>Region Forcing Chains: 9 in column ==> r8c8.9 off</b></i><br>
Chain 13: <b>If r1c9 contains the value 9, then r8c8 cannot contain the value 9</b> (View 13):<br>
(1) If r1c9 contains the value 9, then r4c6 cannot contain the value 9 (the value can occur only once in the Anti Diagonal)<br>(2) If r4c6 does not contain the value 9, then r4c4 must contain the value 9 (only remaining possible position in the block)<br>(3) If r4c4 contains the value 9, then r8c8 cannot contain the value 9 (the value can occur only once in the Main Diagonal)<br><br>
Chain 14: <b>If r8c9 contains the value 9, then r8c8 cannot contain the value 9</b> (View 14):<br>
(1) If r8c9 contains the value 9, then r8c8 cannot contain the value 9 (the value can occur only once in the block)<br><br>
<i>Nested <b>Region Forcing Chains: 1 in block ==> r2c6.1 off</b></i><br>
Chain 15: <b>If r2c7 contains the value 1, then r2c6 cannot contain the value 1</b> (View 15):<br>
(1) If r2c7 contains the value 1, then r2c6 cannot contain the value 1 (the value can occur only once in the row)<br><br>
Chain 16: <b>If r3c7 contains the value 1, then r2c6 cannot contain the value 1</b> (View 16):<br>
(1) If r3c7 contains the value 1, then r8c2 cannot contain the value 1 (the value can occur only once in the Anti Diagonal)<br>(2) If r8c2 does not contain the value 1, then r6c2 must contain the value 1 (only remaining possible position in the column)<br>(3) If r6c2 contains the value 1, then r6c6 cannot contain the value 1 (the value can occur only once in the row)<br>(4) If r3c7 contains the value 1 (initial assumption), then r5c5 cannot contain the value 1 (the value can occur only once in the Anti Diagonal)<br>(5) If r5c5 does not contain the value 1 and r6c6 does not contain the value 1 (3), then r9c9 must contain the value 1 (only remaining possible position in the Main Diagonal)<br>(6) If r9c9 contains the value 1, then r9c5 cannot contain the value 1 (the value can occur only once in the row)<br>(7) If r3c7 contains the value 1 (initial assumption), then r3c5 cannot contain the value 1 (the value can occur only once in the row)<br>(8) If r6c2 contains the value 1 (2), then r6c5 cannot contain the value 1 (the value can occur only once in the row)<br>(9) If r6c5 does not contain the value 1, r5c5 does not contain the value 1 (4), r3c5 does not contain the value 1 (7) and r9c5 does not contain the value 1 (6), then r2c5 must contain the value 1 (only remaining possible position in the column)<br>(10) If r2c5 contains the value 1, then r2c6 cannot contain the value 1 (the value can occur only once in the block)<br><br>
<i>Nested <b>Region Forcing Chains: 9 in block ==> r2c6.9 off</b></i><br>
Chain 17: <b>If r1c1 contains the value 9, then r2c6 cannot contain the value 9</b> (View 17):<br>
(1) If r1c1 contains the value 9, then r4c4 cannot contain the value 9 (the value can occur only once in the Main Diagonal)<br>(2) If r4c4 does not contain the value 9, then r4c6 must contain the value 9 (only remaining possible position in the block)<br>(3) If r4c6 contains the value 9, then r2c6 cannot contain the value 9 (the value can occur only once in the column)<br><br>
Chain 18: <b>If r2c1 contains the value 9, then r2c6 cannot contain the value 9</b> (View 18):<br>
(1) If r2c1 contains the value 9, then r2c6 cannot contain the value 9 (the value can occur only once in the row)<br><br>
<i>Nested <b>Contradiction Forcing Chain: r4c4.9 off ==> r6c9.2 both on & off</b></i><br>
Chain 19: <b>If r4c4 does not contain the value 9, then r6c9 must contain the value 2</b> (View 19):<br>
(1) If r4c4 does not contain the value 9, then r4c6 must contain the value 9 (only remaining possible position in the block)<br>(2) If r4c6 contains the value 9, then r1c9 cannot contain the value 9 (the value can occur only once in the Anti Diagonal)<br>(3) If r1c9 does not contain the value 9, then r8c9 must contain the value 9 (only remaining possible position in the column)<br>(4) If r8c9 contains the value 9, then r8c8 cannot contain the value 9 (the value can occur only once in the block)<br>(5) If r4c4 does not contain the value 9 (initial assumption) and r8c8 does not contain the value 9, then r1c1 must contain the value 9 (only remaining possible position in the Main Diagonal)<br>(6) If r1c1 contains the value 9, then r2c1 cannot contain the value 9 (the value can occur only once in the block)<br>(7) If r4c6 contains the value 9 (1), then r2c6 cannot contain the value 9 (the value can occur only once in the column)<br>(8) If r4c6 contains the value 9 (1), then r2c8 cannot contain the value 9 (the value can occur only once in the Anti Diagonal)<br>(9) If r2c8 does not contain the value 9, r2c6 does not contain the value 9 (7) and r2c1 does not contain the value 9 (6), then r2c7 must contain the value 9 (only remaining possible position in the row)<br>(10) If r2c7 contains the value 9, then r2c7 cannot contain the value 1 (the cell can contain only one value)<br>(11) If r2c7 does not contain the value 1, then r3c7 must contain the value 1 (only remaining possible position in the block)<br>(12) If r3c7 contains the value 1, then r3c7 cannot contain the value 7 (the cell can contain only one value)<br>(13) If r4c6 contains the value 9 (1), then r4c6 cannot contain the value 7 (the cell can contain only one value)<br>(14) If r4c6 does not contain the value 7 and r3c7 does not contain the value 7 (12), then r2c8 must contain the value 7 (only remaining possible position in the Anti Diagonal)<br>(15) If r2c8 contains the value 7, then r2c1 cannot contain the value 7 (the value can occur only once in the row)<br>(16) If r1c1 contains the value 9 (5), then r1c1 cannot contain the value 7 (the cell can contain only one value)<br>(17) If r1c1 does not contain the value 7 and r2c1 does not contain the value 7 (15), then r6c1 must contain the value 7 (only remaining possible position in the column)<br>(18) If r6c1 contains the value 7, then r6c1 cannot contain the value 2 (the cell can contain only one value)<br>(19) If r3c7 contains the value 1 (11), then r8c2 cannot contain the value 1 (the value can occur only once in the Anti Diagonal)<br>(20) If r8c2 does not contain the value 1, then r6c2 must contain the value 1 (only remaining possible position in the column)<br>(21) If r6c2 contains the value 1, then r6c2 cannot contain the value 2 (the cell can contain only one value)<br>(22) If r1c1 contains the value 9 (5), then r1c1 cannot contain the value 3 (the cell can contain only one value)<br>(23) If r1c1 does not contain the value 3, then r6c6 must contain the value 3 (only remaining possible position in the Main Diagonal)<br>(24) If r6c6 contains the value 3, then r6c6 cannot contain the value 2 (the cell can contain only one value)<br>(25) If r2c7 contains the value 9 (9), then r3c8 cannot contain the value 9 (the value can occur only once in the block)<br>(26) If r1c1 contains the value 9 (5), then r1c8 cannot contain the value 9 (the value can occur only once in the row)<br>(27) If r8c8 does not contain the value 9 (4), r2c8 does not contain the value 9 (8), r1c8 does not contain the value 9 and r3c8 does not contain the value 9 (25), then r6c8 must contain the value 9 (only remaining possible position in the column)<br>(28) If r6c8 contains the value 9, then r6c8 cannot contain the value 2 (the cell can contain only one value)<br>(29) If r6c8 does not contain the value 2, r6c6 does not contain the value 2 (24), r6c2 does not contain the value 2 (21) and r6c1 does not contain the value 2 (18), then r6c9 must contain the value 2 (only remaining possible position in the row)<br><br>
Chain 20: <b>If r4c4 does not contain the value 9, then r6c9 cannot contain the value 2</b> (View 20):<br>
(1) If r4c4 does not contain the value 9, then r4c6 must contain the value 9 (only remaining possible position in the block)<br>(2) If r4c6 contains the value 9, then r1c9 cannot contain the value 9 (the value can occur only once in the Anti Diagonal)<br>(3) If r1c9 does not contain the value 9, then r8c9 must contain the value 9 (only remaining possible position in the column)<br>(4) If r8c9 contains the value 9, then r8c8 cannot contain the value 9 (the value can occur only once in the block)<br>(5) If r4c4 does not contain the value 9 (initial assumption) and r8c8 does not contain the value 9, then r1c1 must contain the value 9 (only remaining possible position in the Main Diagonal)<br>(6) If r1c1 contains the value 9, then r2c1 cannot contain the value 9 (the value can occur only once in the block)<br>(7) If r4c6 contains the value 9 (1), then r2c6 cannot contain the value 9 (the value can occur only once in the column)<br>(8) If r4c6 contains the value 9 (1), then r2c8 cannot contain the value 9 (the value can occur only once in the Anti Diagonal)<br>(9) If r2c8 does not contain the value 9, r2c6 does not contain the value 9 (7) and r2c1 does not contain the value 9 (6), then r2c7 must contain the value 9 (only remaining possible position in the row)<br>(10) If r2c7 contains the value 9, then r2c7 cannot contain the value 1 (the cell can contain only one value)<br>(11) If r2c7 does not contain the value 1, then r3c7 must contain the value 1 (only remaining possible position in the block)<br>(12) If r3c7 contains the value 1, then r3c7 cannot contain the value 7 (the cell can contain only one value)<br>(13) If r4c6 contains the value 9 (1), then r4c6 cannot contain the value 7 (the cell can contain only one value)<br>(14) If r4c6 does not contain the value 7 and r3c7 does not contain the value 7 (12), then r2c8 must contain the value 7 (only remaining possible position in the Anti Diagonal)<br>(15) If r2c8 contains the value 7, then r2c8 cannot contain the value 5 (the cell can contain only one value)<br>(16) If r4c6 contains the value 9 (1), then r4c6 cannot contain the value 5 (the cell can contain only one value)<br>(17) If r4c6 does not contain the value 5 and r2c8 does not contain the value 5 (15), then r1c9 must contain the value 5 (only remaining possible position in the Anti Diagonal)<br>(18) If r1c9 contains the value 5, then r1c9 cannot contain the value 6 (the cell can contain only one value)<br>(19) If r8c9 contains the value 9 (3), then r8c9 cannot contain the value 6 (the cell can contain only one value)<br>(20) If r3c7 contains the value 1 (11), then r5c5 cannot contain the value 1 (the value can occur only once in the Anti Diagonal)<br>(21) If r1c1 contains the value 9 (5), then r1c1 cannot contain the value 3 (the cell can contain only one value)<br>(22) If r1c1 does not contain the value 3, then r6c6 must contain the value 3 (only remaining possible position in the Main Diagonal)<br>(23) If r6c6 contains the value 3, then r6c6 cannot contain the value 1 (the cell can contain only one value)<br>(24) If r6c6 does not contain the value 1 and r5c5 does not contain the value 1 (20), then r9c9 must contain the value 1 (only remaining possible position in the Main Diagonal)<br>(25) If r9c9 contains the value 1, then r9c9 cannot contain the value 6 (the cell can contain only one value)<br>(26) If r9c9 does not contain the value 6, r8c9 does not contain the value 6 (19) and r1c9 does not contain the value 6 (18), then r6c9 must contain the value 6 (only remaining possible position in the column)<br>(27) If r6c9 contains the value 6, then r6c9 cannot contain the value 2 (the cell can contain only one value)<br><br>
<i>Nested <b>Cell Forcing Chains: r5c1 ==> r6c6.5 off</b></i><br>
Chain 21: <b>If r5c1 contains the value 1, then r6c6 cannot contain the value 5</b> (View 21):<br>
(1) If r5c1 contains the value 1, then r5c1 cannot contain the value 3 (the cell can contain only one value)<br>(2) If r5c1 does not contain the value 3, then r5c6 must contain the value 3 (only remaining possible position in the row)<br>(3) If r5c6 contains the value 3, then r5c6 cannot contain the value 2 (the cell can contain only one value)<br>(4) If r5c1 contains the value 1 (initial assumption), then r5c1 cannot contain the value 2 (the cell can contain only one value)<br>(5) If r5c1 does not contain the value 2 and r5c6 does not contain the value 2 (3), then r5c5 must contain the value 2 (only remaining possible position in the row)<br>(6) If r5c5 contains the value 2, then r9c1 cannot contain the value 2 (the value can occur only once in the Anti Diagonal)<br>(7) If r5c5 contains the value 2 (5), then r9c5 cannot contain the value 2 (the value can occur only once in the column)<br>(8) If r5c5 contains the value 2 (5), then r9c9 cannot contain the value 2 (the value can occur only once in the Main Diagonal)<br>(9) If r9c9 does not contain the value 2, r9c5 does not contain the value 2 (7) and r9c1 does not contain the value 2 (6), then r9c4 must contain the value 2 (only remaining possible position in the row)<br>(10) If r9c4 contains the value 2, then r8c6 cannot contain the value 2 (the value can occur only once in the block)<br>(11) If r5c5 contains the value 2 (5), then r4c6 cannot contain the value 2 (the value can occur only once in the block)<br>(12) If r5c5 contains the value 2 (5), then r6c6 cannot contain the value 2 (the value can occur only once in the block)<br>(13) If r6c6 does not contain the value 2, r5c6 does not contain the value 2 (3), r4c6 does not contain the value 2 (11) and r8c6 does not contain the value 2 (10), then r3c6 must contain the value 2 (only remaining possible position in the column)<br>(14) If r3c6 contains the value 2, then r3c6 cannot contain the value 1 (the cell can contain only one value)<br>(15) If r5c1 contains the value 1 (initial assumption), then r6c2 cannot contain the value 1 (the value can occur only once in the block)<br>(16) If r6c2 does not contain the value 1, then r8c2 must contain the value 1 (only remaining possible position in the column)<br>(17) If r8c2 contains the value 1, then r3c7 cannot contain the value 1 (the value can occur only once in the Anti Diagonal)<br>(18) If r3c7 does not contain the value 1, then r2c7 must contain the value 1 (only remaining possible position in the block)<br>(19) If r2c7 contains the value 1, then r2c6 cannot contain the value 1 (the value can occur only once in the row)<br>(20) If r5c1 contains the value 1 (initial assumption), then r5c6 cannot contain the value 1 (the value can occur only once in the row)<br>(21) If r8c2 contains the value 1 (16), then r8c6 cannot contain the value 1 (the value can occur only once in the row)<br>(22) If r8c6 does not contain the value 1, r5c6 does not contain the value 1 (20), r2c6 does not contain the value 1 (19) and r3c6 does not contain the value 1 (14), then r6c6 must contain the value 1 (only remaining possible position in the column)<br>(23) If r6c6 contains the value 1, then r6c6 cannot contain the value 5 (the cell can contain only one value)<br><br>
Chain 22: <b>If r5c1 contains the value 2, then r6c6 cannot contain the value 5</b> (View 22):<br>
(1) If r5c1 contains the value 2, then r6c2 cannot contain the value 2 (the value can occur only once in the block)<br>(2) If r5c1 contains the value 2 (initial assumption), then r4c2 cannot contain the value 2 (the value can occur only once in the block)<br>(3) If r4c2 does not contain the value 2 and r6c2 does not contain the value 2 (1), then r8c2 must contain the value 2 (only remaining possible position in the column)<br>(4) If r8c2 contains the value 2, then r8c2 cannot contain the value 1 (the cell can contain only one value)<br>(5) If r8c2 does not contain the value 1, then r6c2 must contain the value 1 (only remaining possible position in the column)<br>(6) If r6c2 contains the value 1, then r6c2 cannot contain the value 3 (the cell can contain only one value)<br>(7) If r5c1 contains the value 2 (initial assumption), then r5c1 cannot contain the value 3 (the cell can contain only one value)<br>(8) If r5c1 does not contain the value 3, then r5c6 must contain the value 3 (only remaining possible position in the row)<br>(9) If r5c6 contains the value 3, then r6c6 cannot contain the value 3 (the value can occur only once in the block)<br>(10) If r6c6 does not contain the value 3 and r6c2 does not contain the value 3 (6), then r6c7 must contain the value 3 (only remaining possible position in the row)<br>(11) If r6c7 contains the value 3, then r6c7 cannot contain the value 9 (the cell can contain only one value)<br>(12) If r6c7 does not contain the value 9, then r6c8 must contain the value 9 (only remaining possible position in the block)<br>(13) If r6c8 contains the value 9, then r8c8 cannot contain the value 9 (the value can occur only once in the column)<br>(14) If r5c1 does not contain the value 3 (7), then r1c1 must contain the value 3 (only remaining possible position in the column)<br>(15) If r1c1 contains the value 3, then r1c1 cannot contain the value 9 (the cell can contain only one value)<br>(16) If r1c1 does not contain the value 9 and r8c8 does not contain the value 9 (13), then r4c4 must contain the value 9 (only remaining possible position in the Main Diagonal)<br>(17) If r4c4 contains the value 9, then r4c4 cannot contain the value 2 (the cell can contain only one value)<br>(18) If r5c1 contains the value 2 (initial assumption), then r5c5 cannot contain the value 2 (the value can occur only once in the row)<br>(19) If r8c2 contains the value 2 (3), then r8c8 cannot contain the value 2 (the value can occur only once in the row)<br>(20) If r6c8 contains the value 9 (12), then r6c8 cannot contain the value 2 (the cell can contain only one value)<br>(21) If r8c8 does not contain the value 2 (19) and r6c8 does not contain the value 2, then r7c8 must contain the value 2 (only remaining possible position in the column)<br>(22) If r7c8 contains the value 2, then r9c9 cannot contain the value 2 (the value can occur only once in the block)<br>(23) If r9c9 does not contain the value 2, r8c8 does not contain the value 2 (19), r5c5 does not contain the value 2 (18) and r4c4 does not contain the value 2 (17), then r6c6 must contain the value 2 (only remaining possible position in the Main Diagonal)<br>(24) If r6c6 contains the value 2, then r6c6 cannot contain the value 5 (the cell can contain only one value)<br><br>
Chain 23: <b>If r5c1 contains the value 3, then r6c6 cannot contain the value 5</b> (View 23):<br>
(1) If r5c1 contains the value 3, then r5c6 cannot contain the value 3 (the value can occur only once in the row)<br>(2) If r5c6 does not contain the value 3, then r6c6 must contain the value 3 (only remaining possible position in the block)<br>(3) If r6c6 contains the value 3, then r6c6 cannot contain the value 5 (the cell can contain only one value)<br><br>
<i>Nested <b>Region Forcing Chains: 2 in column ==> r4c6.2 off</b></i><br>
Chain 24: <b>If r4c2 contains the value 2, then r4c6 cannot contain the value 2</b> (View 24):<br>
(1) If r4c2 contains the value 2, then r4c6 cannot contain the value 2 (the value can occur only once in the row)<br><br>
Chain 25: <b>If r6c2 contains the value 2, then r4c6 cannot contain the value 2</b> (View 25):<br>
(1) If r6c2 contains the value 2, then r6c9 cannot contain the value 2 (the value can occur only once in the row)<br>(2) If r6c2 contains the value 2 (initial assumption), then r6c8 cannot contain the value 2 (the value can occur only once in the row)<br>(3) If r6c8 does not contain the value 2 and r6c9 does not contain the value 2 (1), then r4c9 must contain the value 2 (only remaining possible position in the block)<br>(4) If r4c9 contains the value 2, then r4c6 cannot contain the value 2 (the value can occur only once in the row)<br><br>
Chain 26: <b>If r8c2 contains the value 2, then r4c6 cannot contain the value 2</b> (View 26):<br>
(1) If r8c2 contains the value 2, then r4c6 cannot contain the value 2 (the value can occur only once in the Anti Diagonal)<br><br>
<i>Nested <b>Contradiction Forcing Chain: r4c6.9 on ==> r6c9.2 both on & off</b></i><br>
Chain 27: <b>If r4c6 contains the value 9, then r6c9 must contain the value 2</b> (View 27):<br>
(1) If r4c6 contains the value 9, then r1c9 cannot contain the value 9 (the value can occur only once in the Anti Diagonal)<br>(2) If r1c9 does not contain the value 9, then r8c9 must contain the value 9 (only remaining possible position in the column)<br>(3) If r8c9 contains the value 9, then r8c8 cannot contain the value 9 (the value can occur only once in the block)<br>(4) If r4c6 contains the value 9 (initial assumption), then r4c4 cannot contain the value 9 (the value can occur only once in the block)<br>(5) If r4c4 does not contain the value 9 and r8c8 does not contain the value 9 (3), then r1c1 must contain the value 9 (only remaining possible position in the Main Diagonal)<br>(6) If r1c1 contains the value 9, then r2c1 cannot contain the value 9 (the value can occur only once in the block)<br>(7) If r4c6 contains the value 9 (initial assumption), then r2c6 cannot contain the value 9 (the value can occur only once in the column)<br>(8) If r4c6 contains the value 9 (initial assumption), then r2c8 cannot contain the value 9 (the value can occur only once in the Anti Diagonal)<br>(9) If r2c8 does not contain the value 9, r2c6 does not contain the value 9 (7) and r2c1 does not contain the value 9 (6), then r2c7 must contain the value 9 (only remaining possible position in the row)<br>(10) If r2c7 contains the value 9, then r2c7 cannot contain the value 1 (the cell can contain only one value)<br>(11) If r2c7 does not contain the value 1, then r3c7 must contain the value 1 (only remaining possible position in the block)<br>(12) If r3c7 contains the value 1, then r3c7 cannot contain the value 7 (the cell can contain only one value)<br>(13) If r4c6 contains the value 9 (initial assumption), then r4c6 cannot contain the value 7 (the cell can contain only one value)<br>(14) If r4c6 does not contain the value 7 and r3c7 does not contain the value 7 (12), then r2c8 must contain the value 7 (only remaining possible position in the Anti Diagonal)<br>(15) If r2c8 contains the value 7, then r2c1 cannot contain the value 7 (the value can occur only once in the row)<br>(16) If r1c1 contains the value 9 (5), then r1c1 cannot contain the value 7 (the cell can contain only one value)<br>(17) If r1c1 does not contain the value 7 and r2c1 does not contain the value 7 (15), then r6c1 must contain the value 7 (only remaining possible position in the column)<br>(18) If r6c1 contains the value 7, then r6c1 cannot contain the value 2 (the cell can contain only one value)<br>(19) If r3c7 contains the value 1 (11), then r8c2 cannot contain the value 1 (the value can occur only once in the Anti Diagonal)<br>(20) If r8c2 does not contain the value 1, then r6c2 must contain the value 1 (only remaining possible position in the column)<br>(21) If r6c2 contains the value 1, then r6c2 cannot contain the value 2 (the cell can contain only one value)<br>(22) If r1c1 contains the value 9 (5), then r1c1 cannot contain the value 3 (the cell can contain only one value)<br>(23) If r1c1 does not contain the value 3, then r6c6 must contain the value 3 (only remaining possible position in the Main Diagonal)<br>(24) If r6c6 contains the value 3, then r6c6 cannot contain the value 2 (the cell can contain only one value)<br>(25) If r2c7 contains the value 9 (9), then r3c8 cannot contain the value 9 (the value can occur only once in the block)<br>(26) If r1c1 contains the value 9 (5), then r1c8 cannot contain the value 9 (the value can occur only once in the row)<br>(27) If r8c8 does not contain the value 9 (3), r2c8 does not contain the value 9 (8), r1c8 does not contain the value 9 and r3c8 does not contain the value 9 (25), then r6c8 must contain the value 9 (only remaining possible position in the column)<br>(28) If r6c8 contains the value 9, then r6c8 cannot contain the value 2 (the cell can contain only one value)<br>(29) If r6c8 does not contain the value 2, r6c6 does not contain the value 2 (24), r6c2 does not contain the value 2 (21) and r6c1 does not contain the value 2 (18), then r6c9 must contain the value 2 (only remaining possible position in the row)<br><br>
Chain 28: <b>If r4c6 contains the value 9, then r6c9 cannot contain the value 2</b> (View 28):<br>
(1) If r4c6 contains the value 9, then r1c9 cannot contain the value 9 (the value can occur only once in the Anti Diagonal)<br>(2) If r1c9 does not contain the value 9, then r8c9 must contain the value 9 (only remaining possible position in the column)<br>(3) If r8c9 contains the value 9, then r8c8 cannot contain the value 9 (the value can occur only once in the block)<br>(4) If r4c6 contains the value 9 (initial assumption), then r4c4 cannot contain the value 9 (the value can occur only once in the block)<br>(5) If r4c4 does not contain the value 9 and r8c8 does not contain the value 9 (3), then r1c1 must contain the value 9 (only remaining possible position in the Main Diagonal)<br>(6) If r1c1 contains the value 9, then r2c1 cannot contain the value 9 (the value can occur only once in the block)<br>(7) If r4c6 contains the value 9 (initial assumption), then r2c6 cannot contain the value 9 (the value can occur only once in the column)<br>(8) If r4c6 contains the value 9 (initial assumption), then r2c8 cannot contain the value 9 (the value can occur only once in the Anti Diagonal)<br>(9) If r2c8 does not contain the value 9, r2c6 does not contain the value 9 (7) and r2c1 does not contain the value 9 (6), then r2c7 must contain the value 9 (only remaining possible position in the row)<br>(10) If r2c7 contains the value 9, then r2c7 cannot contain the value 1 (the cell can contain only one value)<br>(11) If r2c7 does not contain the value 1, then r3c7 must contain the value 1 (only remaining possible position in the block)<br>(12) If r3c7 contains the value 1, then r3c7 cannot contain the value 7 (the cell can contain only one value)<br>(13) If r4c6 contains the value 9 (initial assumption), then r4c6 cannot contain the value 7 (the cell can contain only one value)<br>(14) If r4c6 does not contain the value 7 and r3c7 does not contain the value 7 (12), then r2c8 must contain the value 7 (only remaining possible position in the Anti Diagonal)<br>(15) If r2c8 contains the value 7, then r2c8 cannot contain the value 5 (the cell can contain only one value)<br>(16) If r4c6 contains the value 9 (initial assumption), then r4c6 cannot contain the value 5 (the cell can contain only one value)<br>(17) If r4c6 does not contain the value 5 and r2c8 does not contain the value 5 (15), then r1c9 must contain the value 5 (only remaining possible position in the Anti Diagonal)<br>(18) If r1c9 contains the value 5, then r1c9 cannot contain the value 6 (the cell can contain only one value)<br>(19) If r8c9 contains the value 9 (2), then r8c9 cannot contain the value 6 (the cell can contain only one value)<br>(20) If r3c7 contains the value 1 (11), then r5c5 cannot contain the value 1 (the value can occur only once in the Anti Diagonal)<br>(21) If r1c1 contains the value 9 (5), then r1c1 cannot contain the value 3 (the cell can contain only one value)<br>(22) If r1c1 does not contain the value 3, then r6c6 must contain the value 3 (only remaining possible position in the Main Diagonal)<br>(23) If r6c6 contains the value 3, then r6c6 cannot contain the value 1 (the cell can contain only one value)<br>(24) If r6c6 does not contain the value 1 and r5c5 does not contain the value 1 (20), then r9c9 must contain the value 1 (only remaining possible position in the Main Diagonal)<br>(25) If r9c9 contains the value 1, then r9c9 cannot contain the value 6 (the cell can contain only one value)<br>(26) If r9c9 does not contain the value 6, r8c9 does not contain the value 6 (19) and r1c9 does not contain the value 6 (18), then r6c9 must contain the value 6 (only remaining possible position in the column)<br>(27) If r6c9 contains the value 6, then r6c9 cannot contain the value 2 (the cell can contain only one value)<br><br>
</body>
</html>
%g: ..1...2....23....45........4.6....1..5......7..8..........96.....5.3.....9...8.3.
%i: ..1...2....23....45........4.6....1..5......7..8..........96.....5.3.....9...8.3.
%m: ..3..6789..34.678.1...........456789...45678....45.7.9.2...........56789..3.56.89.....6789.....678..2.........3......1...5678.1...5.7.91...56789....56789...4.........5......34.678...34..7.912.4.678912.4.678.12.4..7.91.3..6789.....67891.3..6.89...4......23...7.......6....2..5.789.2..5.78..23.5.7.9..3.5..891.........23.5..89123.....9....5......3.....91..4.6.8912.4...8.1234....9...4.6.8..2.4.6.89......7..123...7.9123...7.........8.12.4567.91..4567..12345.7....3456..9.2.456..9.2..56...123...78.123...78...34..7..12.45.7..........9.....6...1..45.78..2.45.78.12..5..8.12...678.12.4.678.....5....12.4..7....3......12.4..7..1..4.6789.2.4.678912...6.8912...67..........9...4..7..12.45.7..12.45.7.........8.1..4567....3......12..56...
%M:
+-------------------------+-------------------------+-------------------------+
| 36789 34678 1 | 456789 45678 4579 | 2 56789 35689 |
| 6789 678 2 | 3 15678 1579 | 156789 56789 4 |
| 5 34678 3479 | 1246789 124678 12479 | 136789 6789 13689 |
+-------------------------+-------------------------+-------------------------+
| 4 237 6 | 25789 2578 23579 | 3589 1 23589 |
| 1239 5 39 | 14689 1248 12349 | 468 24689 7 |
| 12379 1237 8 | 1245679 14567 123457 | 34569 24569 256 |
+-------------------------+-------------------------+-------------------------+
| 12378 12378 347 | 12457 9 6 | 14578 24578 1258 |
| 12678 124678 5 | 1247 3 1247 | 146789 246789 12689 |
| 1267 9 47 | 12457 12457 8 | 14567 3 1256 |
+-------------------------+-------------------------+-------------------------+
%r: 11.9
%s: Contradiction Forcing Chain: r7c2.4 on ==> r8c6.4 both on & off
--- end of after section ---

Tarek
User avatar
tarek
 
Posts: 3745
Joined: 05 January 2006

ED=12.0/12.0/8.1

Postby m_b_metcalf » Wed Jan 08, 2020 7:44 pm

m_b_metcalf wrote:Overnight I've found a yet higher rating,

To wrap this up, barring any surprise from a batch still running, my highest achieved rating was:
Code: Select all
 . . 1 . . . 2 . .
 . . 2 3 . . . . 4
 4 . . . . . . . .
 5 . 3 . . . . 6 .
 . 1 . . . . . . 5
 . . 6 . . . . . .
 . . . . 7 8 . . .
 . . . . 9 . . . .
 . 7 . . . 1 . 9 .   ED=12.0/12.0/8.1 : Xtreme_gold


A list of the highest achieved ED for each ER is hidden here:
Hidden Text: Show
Code: Select all
..1...2....34....55..........5....1..6......7..2..........34.....7.8.....3...2.8.   ED=4.3/4.3/2.9   
.............1...2.345.67....2......4..8.72.9......8....86.234.3...8.............   ED=6.4/4.1/4.0   
......1....23....44........5.3....4..6......5..1..........73.....5.8.....7...1.8.   ED=7.6/4.3/2.9   
.............1...2..34.56....2......7.89.62.3......9....95.387.8...6.............   ED=7.8/4.3/4.3   
.............1...2..32.45....4......3.67.54.8......3....79.268.6...5.............   ED=8.0/8.0/4.3   
.............1...2.3.2.45....3......6.78.53.9......8....84.297.7...5.............   ED=8.3/4.3/4.3   
.............1...2.3.2.45....6......7.38.56.9......8....84.296.9...5.............   ED=8.4/7.9/4.3 
..1...2....34....56........7.4....6..2......7..5..........84.....7.9.....8...5.9.   ED=8.8/4.3/2.9   
.............1...2.342.5.....6......4.71.86.3......1....15.274.6...8.............   ED=9.0/9.0/4.3   
.............1...2..34.56....4......7.89.63.4......9....95.287.8...6.............   ED=9.1/9.1/7.7   
.............1...2.342.56....7......4..8.69.7......8....89.235.3...6.............   ED=9.2/9.2/7.8   
.............1...2.34..56....6......4.37.68.5......7....75.234.3...8.............   ED=9.3/9.3/7.7   
.............1...2.34..56....3......7.18.63.4......8....85.297.9...6.............   ED=9.4/9.4/7.8   
.............1...2..34.56....4......3.78.64.5......8....59.273.7...6.............   ED=9.5/9.5/7.8   
.............1...2..32.45....6......3.78.96.5......8....85.273.7...6.............   ED=9.6/9.6/7.8   
.............1...2.345.67....8......4..9.58.7......9....56.234.3...5.............   ED=9.7/9.7/7.8   
.............1...2.3.2.45....3......6.78.53.9......8....84.296.4...5.............   ED=9.8/9.8/7.9   
.............1...2.342.56....7......4.38.67.9......8....85.234.3...6.............   ED=9.9/9.9/7.8   
..1...2....34....55........1.4....6..2......7..6..........84.....7.9.....8...6.9.   ED=10.0/10.0/7.7
..1...2....34....55........6.4....7..1......6..7..........82.......9.....8...1.9.   ED=10.1/10.1/8.0
..1...2....23....45........4.6....1..1......3..7..........86.....5.9.....8...7.9.   ED=10.2/10.2/7.6
..1...2....34....52........6.4....3..7......6..8..........94.....6.5.....9...8.5.   ED=10.3/10.3/7.7
..1...2....23....44........2.3....5..5......6..7..........83.....6.9.....8...7.9.   ED=10.4/10.4/7.7
.............1...2.342.56....6......4..7.68.9......7....75.238.3...8.............   ED=10.5/10.5/7.8
..1...2....31....44........3.5....6..6......7..8..........95.....7.2.....9...8.2.   ED=10.6/10.6/7.8
..1...2....23....44........2.5....1..6......7..8..........95.....7.3.....9...8.3.   ED=10.7/10.7/7.7
..1...2....23....45........6.3....1..7......6..5..........87.......9.....8...5.9.   ED=10.8/10.8/7.8 
..1...2.....3....45........6.3....7..1......6..7..........25.....6.8.....9...7.8.   ED=10.9/10.9/7.7
..1...2....34....55........2.4....1..6......7..8..........34.....7.9.....3...8.9.   ED=11.0/11.0/4.3
..1...2....23....44........5.6....1..7......5..8..........97.....5.3.....9...8.3.   ED=11.1/11.1/2.9
..1...2....23....44........5.6....3..1......5..7..........81.....5.9.....8...7.9.   ED=11.2/11.2/7.7
..1...2....23....44........5.3....6..1......7..8..........67.....5.9.....6...8.9.   ED=11.3/11.3/7.8
..1...2....21....33........4.5....6..6......4..7..........85.....4.9.....8...7.9.   ED=11.4/11.4/7.7
..1...2....23....45........6.3....1..5......6..7..........83.....5.9.....8...7.9.   ED=11.5/11.5/7.7
......1....12....34........5.2....6..3......5..7..........68.....5.9.....6...7.9.   ED=11.6/11.6/7.7
..1...2....23....45........6.3....7..5......6..4..........83.......9.....8...1.9.   ED=11.8/11.8/7.7
..1...2....23....44........5.3....6..1......5..6..........78.....5.9.....7...6.9.   ED=11.9/11.9/7.7
..1...2.....3....45........6.3....1..5......6..7..........82.....6.9.....8...7.9.   ED=12.0/12.0/7.7 : Xtreme_bronze
..1...2....23....45........4.6....1..5......7..8..........96.....5.3.....9...8.3.   ED=12.0/12.0/7.8 : Xtreme_silver
..1...2....23....44........5.3....6..1......5..6..........78.......9.....7...1.9.   ED=12.0/12.0/8.1 : Xtreme_gold

I hope this is of some interest. For tarek, or anyone else, I can supply a file of 700-odd hard puzzles (unrated) if supplied with an e-mail address by PM.

I wiil now try to find some X-diamonds!

Regards,

Mike
Last edited by m_b_metcalf on Mon May 11, 2020 8:22 am, edited 1 time in total.
User avatar
m_b_metcalf
2017 Supporter
 
Posts: 11128
Joined: 15 May 2006
Location: Berlin

Re: X Sudoku (extreme)

Postby tarek » Sun May 10, 2020 8:32 pm

Apologies for the late reply. This is great Mike.
Unfortunately due to time constraints, I have no time to dedicate to Sukaku explainer similar to what I had in the last portion of last year. I will , however, try to squeeze a basic version of w-wing and tidy a few things up before releasing an updated version which should have what most people would use to rate puzzles

tarek
User avatar
tarek
 
Posts: 3745
Joined: 05 January 2006

Re: X Sudoku (extreme)

Postby m_b_metcalf » Mon May 11, 2020 7:16 am

tarek wrote:Apologies for the late reply. This is great Mike.
Unfortunately due to time constraints, I have no time to dedicate to Sukaku explainer similar to what I had in the last portion of last year. I will , however, try to squeeze a basic version of w-wing and tidy a few things up before releasing an updated version which should have what most people would use to rate puzzles

tarek, thanks for your comments. There's certainly no rush. Interest in these extreme puzzles seems to be completely lacking. None of our champion solvers seems attracted to attempt Xtreme_gold, for example.

Regards,

Mike
User avatar
m_b_metcalf
2017 Supporter
 
Posts: 11128
Joined: 15 May 2006
Location: Berlin

Previous

Return to Sudoku variants