The New Sudoku Players' Forum

[morl]

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...|63.|...
...|.5.|...
12.|4..|...
---+---+---
..3|...|8..
9..|...|..1
..5|...|4..
---+---+---
...|..7|.26
...|.9.|...
...|.84|...

Have fun!
morl

[Leren]

Too hard to solve in one move but I'll just illustrate a Sudoku X Move late in the solving process.

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*-----------------------------------------------------*
| 57    a5789   79    | 6   3  1   | 2     b789  4    |
| 347-8 f3789   479-8 | 89  5  2   | 6      1    79   |
| 1      2      6     | 4   7 d89  | 359   c3589 359  |
|---------------------+------------+------------------|
| 27     67     3     | 1   4  59  | 8      5679 2579 |
| 9      467-8  478   | 78  2  358 | 357    3567 1    |
| 278    1      5     | 789 6 e389 | 4      379  2379 |
|---------------------+------------+------------------|
| 3458   3459-8 89    | 35  1  7   | 359    2    6    |
| 357    357    12    | 235 9  6   | 157    4    8    |
| 6      3579   12    | 235 8  4   | 13579  3579 3579 |
*-----------------------------------------------------*

X Chain : (8) r1c2 = r1c8 - r3c8 = r3c6 - r6c6 = (8) r2c2 => - 8 r2c13, r57c2

and the solution :

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*-----------------------*
| 7 5 9 | 6 3 1 | 2 8 4 |
| 3 8 4 | 9 5 2 | 6 1 7 |
| 1 2 6 | 4 7 8 | 9 5 3 |
|-------+-------+-------|
| 2 6 3 | 1 4 5 | 8 7 9 |
| 9 4 7 | 8 2 3 | 5 6 1 |
| 8 1 5 | 7 6 9 | 4 3 2 |
|-------+-------+-------|
| 4 9 8 | 5 1 7 | 3 2 6 |
| 5 3 1 | 2 9 6 | 7 4 8 |
| 6 7 2 | 3 8 4 | 1 9 5 |
*-----------------------*

Leren

[m_b_metcalf]

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 . . . . . . . 1 .
 1 2 . . . 9 7 . 6
 . . . . 7 . . . 8
 . . . . . . . . .
 9 . 7 . 8 . 1 . 4
 . . . . . . . . .
 4 . . . 2 . . . .
 8 . 9 5 . . . 3 7
 . 7 . . . . . . .

Even harder (and still symmetric). Have even more fun.

[Leren]

.......1.12...97.6....7...8.........9.7.8.1.4.........4...2....8.95...37.7.......

Pretty brutal. I had to add diagonal weak links to my solver's forcing chain routines to solve. Anyway here is one X Sudoku move I did see.

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*-----------------------------------------------------------------------*
| 7    345689 34568   |f23468   3456    f234568   | 3459   1      g2359 |
| 1    2      3458    | 348     345      9        | 7      45      6    |
| 356  34569  456     |e12346   7       e123456   | 3459  d2459    8    |
|---------------------+---------------------------+---------------------|
| 2356 134568 1234568 | 1469    134569 ha134567-2 | 35689  256789  2359 |
| 9    356    7       |b236     8       b2356     | 1     c256     4    |
| 2356 134568 1234568 | 1234679 134569   1456     | 35689  256789  2359 |
|---------------------+---------------------------+---------------------|
| 4    1356   1356    | 136789  2        13678    | 569    5689    159  |
| 8    16     9       | 5       146      146      | 2      3       7    |
| 2356 7      12356   | 13689   1369     1368     | 45689  45689   159  |
*-----------------------------------------------------------------------*

X Chain DisContinuous Loop: (2) r4c6 - r5c46 = r5c8 - r3c8 = r3c46 - r1c46 = r1c9 - r4c6 => - 2 r4c6 And the solution, after all those forcing chains

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*-----------------------*
| 7 9 8 | 4 3 6 | 5 1 2 |
| 1 2 3 | 8 5 9 | 7 4 6 |
| 6 5 4 | 1 7 2 | 3 9 8 |
|-------+-------+-------|
| 3 4 5 | 6 1 7 | 8 2 9 |
| 9 6 7 | 2 8 3 | 1 5 4 |
| 2 8 1 | 9 4 5 | 6 7 3 |
|-------+-------+-------|
| 4 3 6 | 7 2 1 | 9 8 5 |
| 8 1 9 | 5 6 4 | 2 3 7 |
| 5 7 2 | 3 9 8 | 4 6 1 |
*-----------------------*

Leren

[tarek]

the 1st puzzle should yield to a complex fish as SE v1.14.7 rates it at 6.7 (Forcing X-chain)
The 2nd unfortunately is unfair with a difficulty rating: 9.5 (Dynamic Contradiction Forcing Chains)

tarek

[m_b_metcalf]

On some thread it was stated that the new version of SE had been used to rate 400,000+ X-sudokus, but I don't remember if it was stated whether there were any high ratings among them. Anyway, I've generated a few dozen hard X-sudokus and the one I selected to test the new version with came out as

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 . . . 2 . . 3 . 8
 . . . . . . . . .
 5 . . . . 7 . . .
 2 . 1 . . . . . .
 4 . 9 . . . . 3 .
 . . 6 . 8 . . . 4
 . 6 . . . . 1 . .
 . . . . . . 5 4 .
 . . . . . . . 7 .  ED=10.6/2.9/2.9

SE passes through an astounding range of individual steps.

I'll try to rate them all later and post them here.

Thanks for making this available.

Mike

[m_b_metcalf]

I'll try to rate them all later and post them here.

Now done. It took 83 minutes to rate 41 puzzles. The one already posted was not the hardest. A selection of 17 of them is below.

Regards,

Mike

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001000000000020000030000004510600000007000000000410070000100000000034086200000090   ED=9.3/1.2/1.2   
100000000000002300000140000000000005216000700800000000000051280000000600000070003   ED=9.4/1.5/1.5   
000001200020300004000000000005600000040700000030000806000000000070006009001004508   ED=9.6/9.6/2.9   
000102300000004000002030500600000700200700080094000000006900030005000200000000000   ED=9.7/1.2/1.2   
001000000000020030000040056720000000010000060000060001080900000009000003000036008   ED=9.8/1.2/1.2   
001000020003004000002005000600000000400000030000050078000000000000040012080700900   ED=9.8/2.3/2.3   
001002000003400000050000000100000200004000060006000700000080000900006010800030000   ED=9.8/9.8/2.9   
000010000200003040000000000020000560074005800000000007058071300090000000000040000   ED=9.9/1.5/1.5   
001000020000013000040500000000000000067100082050000009500000000014070000209000060   ED=10.0/ 1.2/ 1.2
000102300000000000003040005206007000890000000005000409700006000008000000000080000   ED=10.0/ 7.7/ 2.9
000000010000000203041000000000050000065007080900300700000001006800204000000030000   ED=10.1/10.1/ 2.9
010002000000030000400005001600000070000000002000000400002000030000500080007090006   ED=10.4/ 9.4/ 2.9
100023000000400005607000030000000003004000780003000200000000000000901000090080000   ED=10.5/ 7.7/ 2.9
000001000000000203004500000000000006000700000130000800000050040900470600400002080   ED=10.6/ 1.2/ 1.2
000100203000000000400005000106000000708000020009030007090000600000000470000000050   ED=10.6/ 2.9/ 2.9
010000020002000000000300000040500006300007008000009740690050000008000000000001000   ED=10.6/10.6/ 2.9
010000020203400000000000050006007800000000700000000062000030090359000070000500000   ED=10.7/10.6/ 2.9


[1to9only]

tarek posted a few rated 12.x: here.

[m_b_metcalf]

tarek posted a few rated 12.x: here.

Thanks for the link, but those ratings were wrong. If you scroll down there, you will see his highest was 10.6.

M

[m_b_metcalf]

I generated too a batch of 59 symmetrical puzzles that took 67 minutes to process. A selection is

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001230405000000000000000000002000060060103070010000800000000000000000000605021900   ED=9.1/1.2/1.2   
001200000000000000000300000043506708076109450502804360000003000000000000000002900   ED=9.2/1.2/1.2   
000000000123450000000060000005000000780040012000000600000080000000017459000000000   ED=9.2/9.0/2.9   
001023040035060000000000000000000000703208901000000000000000000000080420090570600   ED=9.3/2.3/2.3   
000001000000000200300405000603000000007852300000000904000209001005000000000500000   ED=9.4/1.2/1.2   
000010000000000000230400510560000700080070050007000062056003071000000000000090000   ED=9.4/9.2/2.9   
000102030400506007000000000000000000385000679000000000000000000500807002010904000   ED=9.5/2.0/2.0   
000012340000000000000005060007000000608103902000000600010800000000000000084230000   ED=9.5/9.5/2.9   
100020000000300400000000000500006007010708020900100005000000000006003000000070006   ED=9.6/1.2/1.2   
000000010203001400000003000000000050060725030070000000000300000008500106090000000   ED=9.6/1.5/1.5   
012003000000402500000000000600000000027185930000000008000000000001708000000500890   ED=9.7/1.2/1.2   
000100000000000200300204005006000000045708690000000100200503008007000000000001000   ED=9.7/2.0/2.0   
000000000000012034000500000030000006160357082800000090000004000570120000000000000   ED=9.8/1.2/1.2   
010200000003004256000000000000000000570806093000000000000000000128600500000001060   ED=9.8/1.5/1.5   
010000000002304500000000000003000050600107004020000800000000000005903200000000040   ED=9.9/7.8/2.9   
000000000000010002034205600007000000403806709000000800008502340300060000000000000   ED=9.9/9.9/7.8   
000000000000001000002030040560007200008040700007600084090050300000300000000000000   ED=10.0/ 1.2/ 1.2
000000000001002300400010050000000600027463580005000000070080005004500900000000000   ED=10.0/10.0/ 2.9
000100000200003045000005000030000500620000073005000080000400000910500008000006000   ED=10.1/ 1.2/ 1.2
000000000000012304000400020000000050032060780050000000090008000107950000000000000   ED=10.1/10.1/ 4.3
000000000102030004000400000500000060078040250010000009000002000800090507000000000   ED=10.4/ 9.9/ 2.9
000000000001234005000500060200000000007802400000000002010007000800159600000000000   ED=10.4/10.4/ 2.9
000000000000010000230400051000000500610708093004000000860005047000080000000000000   ED=10.5/10.5/ 2.9
000010000203000000000000000304000010056203780080000503000000000000000906000050000   ED=10.6/ 1.5/ 1.5
000100200000000000003045006000000600401603708009000000200810500000000000004002000   ED=10.6/ 4.0/ 2.9


[m_b_metcalf]

No diamond yet, but here's my best pearl so far.

Mike

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 . 1 . . 2 3 . . .
 4 . . 5 6 . . . .
 3 . . . . . . . .
 . 4 . . 1 . . . .
 . 6 . . . . . 7 .
 . . . . . . 8 . .
 . 7 . . 3 . . . .
 . . . . . . . . 2
 . 3 . . 9 2 . 4 .   ED=10.7/10.7/2.9

[m_b_metcalf]

Here are a few more, even higher. The first is a real test for any solver.
Regards,

Mike

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 . . . . . 1 2 . .
 . . 3 . 4 . . . 5
 . . . . 6 . . . .
 4 1 . . . . . . 7
 7 . . . . . 5 . .
 . . . . . . . 6 .
 3 . . . . 8 . . .
 . . . . . . . . 9
 . . 7 6 . . . 2 .   ED=11.3/7.6/2.9


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...1..2......3...425..6...............4..61.78......62.2...1......95.............   ED=11.3/1.2/1.2 
.....1.......2....13.45...661....4.7...............8.24...3..7.5...........8..9..   ED=10.8/10.8/4.3
.........1..234......5...4...3.2...5..6...7..2...7.8...2...9......142..8.........   ED=10.8/4.3/2.9   symmetric
..1..234.5.......6.........45........7.2.5.1........58.........3.......4.856..9..   ED=10.8/1.5/1.5   symmetric

[tarek]

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 . . . . . 1 2 . .
 . . 3 . 4 . . . 5
 . . . . 6 . . . .
 4 1 . . . . . . 7
 7 . . . . . 5 . .
 . . . . . . . 6 .
 3 . . . . 8 . . .
 . . . . . . . . 9
 . . 7 6 . . . 2 .   ED=11.3/7.6/2.9


Looks terrifying! Approach at your own risk!

Well done on catching this. With SE now handling several variants, there are many "Hardest Puzzles" frontiers that are yet to be explored.

[m_b_metcalf]

With SE now handling several variants, there are many "Hardest Puzzles" frontiers that are yet to be explored.

Before leaving for a week, I thought I'd give the X-factory another spin, and this pearl was the second off the production line:

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 . . 1 . . . 2 . .
 . . 2 3 . . . . 4
 4 . . . . . . . .
 5 . 3 . . . . 1 .
 . 6 . . . . . . 5
 . . 7 . . . . . .
 . . . . 8 3 . . .
 . . 5 . 9 . . . .
 . 8 . . . 7 . 9 .   ED=11.3/11.3/7.7

Bonus:

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.1.........2.34...5......6..7.....32.....1.8...6...5.....8...4.8...1.......9.....   ED=11.3/11.3/2.9

[tarek]

. . 1 . . . 2 . . . . 2 3 . . . . 4 4 . . . . . . . . 5 . 3 . . . . 1 . . 6 . . . . . . 5 . . 7 . . . . . . . . . . 8 3 . . . . . 5 . 9 . . . . . 8 . . . 7 . 9 . ED=11.3/11.3/7.7

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!!!