## The hardest sudokus (new thread)

Everything about Sudoku that doesn't fit in one of the other sections

### Re: The hardest sudokus (new thread)

At the start, Cigarette has a variant of the sk-loop that I don't recall seeing before.

____

In particular, note that the clues in r8c9 and r5c5 differ. Ditto for the clues in r9c6 and r6c9.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: The hardest sudokus (new thread)

For my understanding of the SK loop this is just a basic one, the pairs loop
r4c56=13 -> r4c89=89 -> r56c7=24 -> r89c7=67 -> r7c89=15 -> r7c56=58 -> r89c4=15 -> r56c4=79 -> r4c56=13
is all you need for the eliminations.

Different to your last one, which needed more than a pure pairs loop.

For the record:
In the other thread Coloin has posted extremely high suexrat ratings for many puzzles. A part of these puzzles (including the hardest) had already been published by me in this or that thread without suexrat ratings, so i claim them for me. To honour Coloins findings i want to give the hardest his name:

Code: Select all
` +-------+-------+-------+ | 1 2 . | 3 . . | 4 . . | | 5 . . | 1 . . | 3 . . | | . . . | . 6 . | . 2 . | +-------+-------+-------+ | 3 . . | 4 . . | 5 . . | | . 7 . | . . . | . . . | | . . 8 | . . . | . 3 . | +-------+-------+-------+ | 9 . . | . . . | . . . | | . . . | 9 . . | . 5 3 | | . . . | . 4 1 | 9 . . | +-------+-------+-------+          Coloin`

It seems to be very asymmetric with its 6 minrow/colums with 2 clues, maybe a reason, why it has not been found before.
btw what are the options for gsf's program for finding a "best" symmetry ?

So these are the puzzles with suexrat9 > 6800 and/or suexratt > 4000 (both limits higher than the current top puzzles) with ED,q1,q2:

eleven
Code: Select all
`10378  5710  ..3......4...8..36..8...1...4..6..73...9..........2..5..4.7..686........7..6..5..  11.0 11.0 2.6   95078 98434 Coloin 9547  5174  ..3......4...8..36..8...1...4..6..73...9..........2..5..4.7..686....4...7.....5..   11.0 11.0 2.6   95226 98414  9220  5804  ..3......4...8..36..83..1...4..6..73...9..........2..5..4.7..686........7.....5..   10.9 10.9 2.6   95183 98587  8917  5333  ...4......5..8.2.6.....7...2...4....3......1...5.3.8.25...6.3.8..6....95..8......  10.4 10.4 2.6   95273 67100  8568  4143  1....6.8...71....66.....15..3.9.....7....184.....2........9.41.5....4..8...8..5..   10.3 10.3 10.0    95209 97527  8508  4880  .2....7..4....9.3.6..2.3.4.....1......89.....9....4.6..94....5.5.....6.3.....5...   10.9 10.9 2.6     95178 96787  8507  4354  ..3......4...8..36..8...1...4..6..73...9...1......2.....4.7..686........7..6..5..   11.0 11.0 2.6   98810 98383  8491  4603  1...5.7.9..7.......6.......2...........5.1..2....2.39.3.4.9...15...1...3...8...4.   10.3 10.3 2.6     95219 72396  8446  4487  ..3......4...8..36..83..1...4..6..73...9...1......2.....4.7..686........7.....5..   10.9 10.9 2.6   96128 98323  8042  4534  ..34.....4...8..36..8...1...4..6..73...9..........2..5..4.7..686........7.....5..   11.0 11.0 2.6     95316 98797  7927  3770  ...4......5...9...6...2..1.2...7.9.1..5....7......8.3...6....9.7...3.1......9.327   10.3 10.3 2.6     59168 25378  7799  4027  ...4......5..8.2.6.....71..2...4....3......1...5.3.8.25...6.3.8..6....9...8......   10.4 10.4 2.6     95223 74804  7515  5454  1...5.7.9..71......6.......2...........5.1..2....2.39.3...9...15...1...3...8...4.   10.4 10.4 2.6     95099 49425  7270  3085  1...56....5718...66...7.....9.3............9.8....5..35...17..8..2....1.......4..   10.2 10.2 2.6     58616 22275  7140  4410  1....6.8...7.....66.....15..3.9.........2....7....854.....9.81.8...41..5.1....4..   10.3 10.3 10.0  95140 21349  7052  3603  ..3......4...8..36..8...1...4..6..73...9..........2..5....7..686....4...7.....54.   11.0 1.2 1.2    95498 98798  6993  4979  ...4......5..8.2.6.....7...2...4....3......1...5.3.8.25...6.3.8..6..8.9...8......   10.4 10.4 2.6     95111 58050  6952  4241  ...4......5..8.2.6.....7...2........3.....51...5.3.8.25...6.3.8..6....9...8.7....   10.4 10.4 2.6     95327 95086  6903  3436  12..5...9.57...2...9..2..1....8..9.47...6.1.......4............57..9.6....6..3...   10.3 10.3 2.6     45827 77805  6753  4018  .2.4...8...7.....3.8.237.1.2.1....9..9....8.4...9......1.8...4.5............6...8   10.9 1.2 1.2      46997 97421  6752  4026  .2.4...8...7.....3...237.1.2.1....9..9....8.48..9......1.8...4.5.8..........6....   10.9 1.2 1.2      46997 97421  6747  4052  .2.4...8...7.....3.8.237.1.2.1....9..9....8.4...9......1.8...4.5.8..........6....   10.9 1.2 1.2      46997 97421  6678  4348  ..3..67.........2.79.2......3....6..5....4..76.7..3.453.5..74...............1...8   10.6 10.6 9.5     70048 91994  6645  4192  ..3.5.....5.1..2.66...2..4....8...9..8..1.6.5...6.....7.......4..........6...18.2   10.9 1.2 1.2      69047 97688  6628  4182  ..3.56....5.1..2.6....2..4...68...9..8..1.6.5...6.....7.......4..........6...18.2   10.9 1.2 1.2      69047 97688  6602  4877  ..3.....945...92....9..3.54....6....6..9..8....5..8.2..1.7................4..5.92   10.2 10.2 9.5     38405  1758  6374  4140  .....6..9..67...3.79...3....1...7.5...752......5.....2..167..2......14..8........   10.2 10.2 2.6     63468  4946  6344  4397  ..34.........8..36..8...1.4.4..6..73...9..........2..5..4.7..686........7.....5..   11.0 1.2 1.2      95358 98816  6338  4433  ...4......5..8.2.6.....71..2........3.....51...5.3.8.25...6.3.8..6..8.9...8......   10.7 10.7 2.6     97677 98790  6069  4284  .2.4...8......9..2..9.3............5..8..7....4.5..82...46..21.6.21..4...1......8   10.4 10.4 9.4     95596 97645  6067  4552  ........9.5.7...2.7.9..2....1.67..5.......4..8....5....7.31....6....7.3..3..6...1   10.2 1.2 1.2       9037 26212  5995  4032  ....5.7..4.7..9.3..8....1..2.8..7.....4..8....7..9...3......6...4...2.97..2.....1   10.4 1.2 1.2      77612 42046  5973  4360  .2.4.6..9..7......6...2..5......15...1.64...28......1..3.26.....6..1...39....3...   10.2 1.2 1.2      95257 41099  5812  4278  1....67.9.5.........9.....4....9..3.....1....9..6..8.1..27.....7..8...4.8...6.1.7   10.4 10.4 2.6     21741 95184  5778  4081  .2..5...9...7.....7.....5..2..........4..8....6..2..91.3.2..9..6...9..13..1.6..2.   10.4 1.2 1.2      51889 95234  5708  4095  .......8...67......8...36.5.4..3..5......4..66....83.4..1.9..2..3...25..9........   10.2 1.2 1.2      64720 23051 `
Coloin
Code: Select all
` 9456  4909  ..3.9....4...8..36..8...1...4..6..73...9..........2.....4.7..686........7.....5.4  10.4 10.4 2.6   95298 50600  8900  4556  ..3.9....4...8..36..8...1...4..6..73...9..........2.....4.7..686........7.....54.   10.4 10.4 2.6   95274 69328  8649  3845  ..39.....4...8..36..8...1...4..6..738......1......2.....4.7..686........7.....5..  11.0 11.0 2.6   46938 95442     8538  4092  ..3......4...8..36..8...1...4..6..73...9..........2.....4.7..686........7..6..59.   10.8 10.8 2.6   36455 95608  8399  4167  ..39.....4...8..36..8...1...4..6..73...3...1......2.....4.7..686........7.....5..  10.9 10.9 2.6   55568 97517     8342  3752  ..3.9....4...8..36..8...1...4..6..73...9....1.....2.....4.7..686........7.....5..   10.3 10.3 2.6   95217 74239  8168  4488  ..3......4...8..36..83..1...4..6..73...9..........2.....4.7..686........7.....59.   10.8 10.8 2.6   49382 95472  8065  3924  ..3......4...8..36..8...1...4..6..73...9..........7..5..4.7..686....2...7.....5..   10.9 10.9 2.6   95174 96815  7849  3471  ..3.2....4...8..36..8...1...4..6..73...9....1.....2.....4.7..686........7.....5..   10.4 10.4 2.6   95224 74804  7607  3356  ..3......4...8..36..8...1...4..6..73...9..........2.....4.7..686...2....7..6..5..   10.4 10.4 2.6   95122 37130  7522  3782  ..3......4...8..36..8...1...4..6..73...9..........4..5..4.7..686....2...7.....5..   11.1 11.1 2.6   96569 98832  7506  2900  ..3..2...4...8..36..8...1...4..6..73...9.......6........4.7..686........7.....59.  10.9 1.2 1.2    95184 78304     7443  4799  ..3.9....4...8..36..8...1...4..6..73...9..........2.....4.7..686........7..6..5..   10.4 10.4 2.6   95098 50898  7392  3990  ..3......4...8..36..8...1...4..6..73...9...1......2.....4.7..686....4...7.....5..   10.9 10.9 2.6   97628 98508  7273  3943  ..34.....4...8..36..8...1...4..6..73...9..........2.....4.7..686........7.....59.   10.8 10.8 2.6   56053 96586  7256  4302  ..3..2...4...8..36..8...1...4..6..73...9..........4.....4.7..686........7.....59.  10.9 10.9 2.6   54251 85324     7227  3243  ..3.9....1...4..36..8..21...4..8..73...9................4.7..686........7.....5.4  9.7 9.7 2.6     13330   706  7069  2829  ..3......4...8..36..8...1...4..6..73...9.........42..5..4.7..686........7.....5..   10.9 10.9 2.6   46041 97341  7034  3623  ..3.9....4...8..36..8...1...4..6..73...9..........2.....4.7..686..4.....7.....5..   10.4 10.4 2.6   95264 94486  6997  2761  ..3......4...8..36..8...1...4..6..73...9........7.2..5..4.7..686........7.....5..   10.8 10.8 2.6   14550 42333  6957  4279  ..3.9....4...8..36..8...1...4..6..73...9..........2.....4.7..686........7....65..   10.4 10.4 2.6   95112 60280  6853  4096  ..3..61..4...8..36..89......4..6..73..............2..1..4.7..686........7.....5..  10.9 1.2 1.2    69049 97687 `
eleven

Posts: 1799
Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

eleven wrote:So these are the puzzles with suexrat9 > 6800 and/or suexratt > 4000 (both limits higher than the current top puzzles) with ED,q1,q2:
eleven
Code: Select all
`10378  5710  ..3......4...8..36..8...1...4..6..73...9..........2..5..4.7..686........7..6..5..  11.0 11.0 2.6   95078 98434 Coloin`

Code: Select all
` *-----------------------------------------------------------------------------* | 1259    125679  3       | 12457   12459   145679  | 24789   24589   2479    | | 4       12579   12579   | 1257    8       1579    | 279     3       6       | | 259     25679   8       | 23457   23459   345679  | 1       2459    2479    | |-------------------------+-------------------------+-------------------------| | 12589   4       1259    | 158     6       158     | 289     7       3       | | 12358   12357   12567   | 9       1345    134578  | 2468    1248    124     | | 1389    1379    1679    | 13478   134     2       | 4689    1489    5       | |-------------------------+-------------------------+-------------------------| | 12359   12359   4       | 1235    7       1359    | 239     6       8       | | 6       123589  1259    | 123458  123459  134589  | 23479   1249    12479   | | 7       12389   129     | 6       12349   13489   | 5       1249    1249    | *-----------------------------------------------------------------------------*`

Just checked for the first one: double BB parttern (1259)r13c1/r89c3 => r2c3=7 & r7c1=3

ttt
ttt

Posts: 185
Joined: 20 October 2006
Location: vietnam

### Re: The hardest sudokus (new thread)

eleven

Posts: 1799
Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

Code: Select all
` *-----------------------------------------------------------------------------* | 1259    125679  3       | 12457   12459   145679  | 24789   24589   2479    | | 4       12579   12579   | 1257    8       1579    | 279     3       6       | | 259     25679   8       | 23457   23459   345679  | 1       2459    2479    | |-------------------------+-------------------------+-------------------------| | 12589   4       1259    | 158     6       158     | 289     7       3       | | 12358   12357   12567   | 9       1345    134578  | 2468    1248    124     | | 1389    1379    1679    | 13478   134     2       | 4689    1489    5       | |-------------------------+-------------------------+-------------------------| | 12359   12359   4       | 1235    7       1359    | 239     6       8       | | 6       123589  1259    | 123458  123459  134589  | 23479   1249    12479   | | 7       12389   129     | 6       12349   13489   | 5       1249    1249    | *-----------------------------------------------------------------------------*`

Code: Select all
`1  1  .   1  1  1   .  .  .  .  1B 1   1  .  1   .  .  .  .  .  .   .  .  .   X  .  .  1A .  1   1  .  1   .  .  .  1  1  1   .  1  1   .  1  1  1  1  1   1  1  .   .  1  .  1  1  .   1  .  1   .  .  .  .  1  1T  1  1  1   .  1  1  .  1  1T  .  1  1   .  1  1  `

A short explanation about BB pattern (1259)r89c3 for above puzzle:
- Look at candidates 1â€™s as above: if T=1 AND A&B<>1 => no 1â€™s on R7 or B9 => if T=1 then A or B must contain candidate 1â€™s. The same for candidates 2â€™s, 5â€™s, 9â€™s => Any extra candidates at A and B can be eliminated => r2c2<>7, r4c1<>8
Now, back to the puzzle then see that T must be one of (1,2), (1,5), (1,9), (2,5), (2,9), (5,9):
- If T=(1,2) => (A=1 AND B=2) OR (A=2 AND B=1) => r13c1=59 => r2c3 & r7c1<>1259, r2c3=7, r7c1=3
The same result for other cases T=(1,5), (1,9)â€¦

Conclusion: r2c3=7, r7c1=3
Iâ€™m sorry by my poor English...,
Hope you can understand what I explained (that took me very long time than solving the puzzle ).

ttt
ttt

Posts: 185
Joined: 20 October 2006
Location: vietnam

### Re: The hardest sudokus (new thread)

Thanks for the explanation. I start to understand this pattern without ever having read the article

This is my alternative illustration:

For each of the 4 numbers we have a potential impossible pattern, XY for 15, XZ for 2, YZ for 9. So one of the starred cells (guardians) must hold each number to prevent that. But this implies, that none of the 4 numbers can be both in r13c1 and in r89c3, i.e. the #-cells must have all of them - and you can eliminate them in r123c3 and r789c1.
Code: Select all
`     *-----------------------------------------------------------------------------*     |#1259    1259            | 125     1259    159     | 29      259     29      |     |        *1259   *1259    |X125            Y159     |Z29                      |     |#259     259             | 25      259     59      | 1       259     29      |     |-------------------------+-------------------------+-------------------------|     |*1259           *1259    |X15             Y15      |Z29                      |     | 125     125     125     | 9       15      15      | 2       12      12      |     | 19      19      19      | 1       1       2       | 9       19      5       |     |-------------------------+-------------------------+-------------------------|     |*1259   *1259            |X125            Y159     |Z29                      |     |         1259   #1259    | 125     1259    159     | 29      129     129     |     |         129    #129     |         129     19      | 5       129     129     |     *-----------------------------------------------------------------------------*`

[Added:]The first 3 puzzles in my "eleven" list and many in the "coloin" list can be solved this way.
eleven

Posts: 1799
Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

Thanks eleven - there is no problem with the attribution of all your and subsequently trivially produced puzzles.
but thanks for he name ! I think I found a higher suexrat9 value - will update it !

Indeed the clue distribution may well be the key to suexrats apparent over rating. The 3 clues of the same value in a shute is a prominent feature.

I just wonder if we can tweak suexrat9 furthur.

dukuso helped by giving us the xxx 2 function in suexratt - this gave us the "node" count for the easiest 2 % of tries. The higher the relative ratio suexratt/suexrat9 - tends to indicate harder puzzles.

The way that suexrat9 locates the paired loci is unclear to me but if we can understand the apparent over- rating - we might be able to improve on suexratt. The discrepancy between isomorphic puzzles was never addressed - and perhaps didnt need to be.

What might be interesting is the lowest node count out of 1000 tries say.
I hope i'm not being over simplistic !
Does this indicate the easiest way for the program to guess/solve the puzzle ?

C
coloin

Posts: 1709
Joined: 05 May 2005

### Re: The hardest sudokus (new thread)

For me the basic problem is, that suexrat is a pure machine rating, having not implemented any sudoku solution techniques but singles. So there seems to be a quite good correlation to singles chain ratings, but the more other techniques can crack a puzzle, the higher is the chance, that suexrat overrates.

Now many of these puzzles in the lists above can "easily" be solved over BB patterns. I just checked the next one. Same solution:
Code: Select all
`+----------------------------+----------------------------+----------------------------+| 16789    1236789  12379    | 4        1259     123569   | 1579     3578     1379     || 1479     5        13479    | 139      8        139      | 2        347      6        || 14689    1234689  12349    | 123569   1259     7        | 1459     3458     1349     |+----------------------------+----------------------------+----------------------------+| 2        16789   #179      | 156789   4        15689    | 5679     3567     379      || 3        46789   #479      | 256789   2579     25689    | 45679    1        479      || 14679    14679    5        | 1679     3        169      | 8        467      2        |+----------------------------+----------------------------+----------------------------+| 5        12479    12479    | 1279     6        1249     | 3        247      8        ||#147      12347    6        | 12378    127      12348    | 147      9        5        ||#1479     123479   8        | 123579   12579    123459   | 1467     2467     147      |+----------------------------+----------------------------+----------------------------+`

You can use the impossible patterns in r267c46 for 1, r26c8 for 4, r267c48 for 7, r267c46 for 9. [corrected typos, but nobody noticed it anyway]

So nr 5 in my list is the first one, where a solution cannot be found quickly this way (the BB pattern 2379 in r12c7/r79c9 is useless for me -  ok it places 7 in r1c7, but thats harder to see and does not solve it).
eleven

Posts: 1799
Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

q1 99495, q2 99587, ED 10.8/10.8/3.4
Code: Select all
` +-------+-------+-------+ | 1 2 . | 3 . . | . . . | | 3 4 . | . . . | 1 . . | | . . 5 | . . . | . . . | +-------+-------+-------+ | 6 . 2 | 4 . . | 5 . . | | . . . | . 6 . | . 7 . | | . . . | . . 8 | . . 6 | +-------+-------+-------+ | . . 4 | 2 . . | 3 . . | | . . . | . 7 . | . . 9 | | . . . | . . 9 | . 8 . | +-------+-------+-------+          Catboat`

A grid with only 1 strong link (ER 10.1)
Code: Select all
` +-------+-------+-------+ | 1 2 . | 3 . . | 4 . . | | 5 . . | . 1 . | . . 3 | | . . 3 | . . 6 | . . . | +-------+-------+-------+ | 7 . . | . . 8 | 9 . . | | . . 2 | 5 . . | . . 4 | | . . . | . . . | . . . | +-------+-------+-------+ | . . 1 | 6 . . | . 4 . | | . . . | . 9 . | 8 . . | | . 9 . | . . 4 | . 7 . | +-------+-------+-------+ *------------------------------------------------------------------------* | 1      2       6789   | 3      578    579    | 4       5689    5678    | | 5      4678    46789  | 24789  1      279    | 267     2689    3       | | 489    478     3      | 24789  24578  6      | 1257    12589   12578   | |-----------------------+----------------------+-------------------------| | 7      13456   456    | 124    2346   8      | 9       12356   1256    | | 3689   1368    2      | 5      367    1379   | 1367    1368    4       | | 34689  134568  45689  | 12479  23467  12379  | 123567  123568  125678  | |-----------------------+----------------------+-------------------------| | 238    3578    1      | 6      23578  2357   | 235     4       9       | | 2346   34567   4567   | 127    9      12357  | 8       12356   1256    | | 2368   9       568    | 128    2358   4      | 12356   7       1256    | *------------------------------------------------------------------------*`
eleven

Posts: 1799
Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

q1 99529, q2 99578, ED 10.4/10.4/10.0
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` +-------+-------+-------+ | 1 2 . | 4 . . | 3 . . | | 3 . . | . 1 . | . 5 . | | . . 6 | . . . | 1 . . | +-------+-------+-------+ | 7 . . | . 9 . | . . . | | . 4 . | 6 . 3 | . . . | | . . 3 | . . 2 | . . . | +-------+-------+-------+ | 5 . . | . 8 . | 7 . . | | . . 7 | . . . | . . 5 | | . . . | . . . | . 9 8 | +-------+-------+-------+        Discrepancy`

[Added:] Compare: ER 10.4, q1 17445, q2 147 (!)
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` +-------+-------+-------+ | 1 2 . | . . . | . . . | | 3 . . | 4 . . | . . . | | . . 5 | . 3 6 | 7 . . | +-------+-------+-------+ | . . 2 | . . . | . 6 . | | . . 8 | . 6 5 | . . 7 | | . . . | 7 . . | . 8 . | +-------+-------+-------+ | . . 3 | . 5 8 | . 7 . | | . . . | 9 . . | . . 3 | | . . . | . . . | . . 5 | +-------+-------+-------+`
eleven

Posts: 1799
Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

My list of currently 4151 puzzles with ER 11+
(including a few new 11.8's).

[Edit:]
I deleted the list, because it contained duplicates.
Last edited by eleven on Sat Mar 26, 2011 4:11 pm, edited 1 time in total.
eleven

Posts: 1799
Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

eleven wrote:My list of currently 4151puzzles with ER 11+ can be downloaded here (including a few new 11.8's).

According to my program, there are only 4093 unique sudokus in that list, for instance, puzzles #3853, #3854 and #3855 are the same.
Mauricio

Posts: 1174
Joined: 22 March 2006

### Re: The hardest sudokus (new thread)

Yes, sorry for that. I was sloppy, when i put the list together.
On the other hand some of my early puzzles (also with high rating) are missing.
I will post a corrected list in the next weeks, at the latest when champagne comes back.

Thanks for being so careful to check the list for duplicates.
I did not know, if there was any interest for it.
eleven

Posts: 1799
Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

Now i made a new list with 4506 ER 11+ puzzles, hopefully all minimal and without duplicates. It can be downloaded here.
To my knowledge together with the puzzles in champagne's list here these are all ER 11.x puzzles, which have been published.

A few new puzzles for the suexrat rating, which i had not posted yet:
Code: Select all
`1...5......7..9.3...9..754...4..3.7..6........9.8........79..2......24.3..2......  9924 6480 .23.....94.....1...9..3..4.2..81...4.....78..9...4...23...9...1.6..........5.....  8433 5517 1..4.6..........2..8..3.5.6.6...48.5............5..2.......3.9...7..8....4.6..3.8  8096 4859 ..3.5.....567....27..2...4......18..3...2...66...7...453..4...7.......9.......4..  7712 4114 ...4.67....7.....6....7..512......9...5.6.1...91.426..3...........8.......4.1.5..  7442 4377 1..4....9.56..9.......1..6..6....8..5....4.9.9....5.1..7....2..6....1.5....3.....  7141 5356 1.....7....6.8.1...89.....6.....4.5.6..59...19...1...8..2.........3.....8...6...7  7067 5315 1.....78...6.8.1....9.....6.....4.5.6..59...19...1...8..2.........3.....8...6...7  7046 5297 `

In sum i have checked more than 10 mio "step 1" puzzles (puzzles, which are not solvable with cell forcing chains using basics+jellyfish) now, all of them could be solved with T&E(NS+HS,2) (level 2 nested singles contradiction chains).
eleven

Posts: 1799
Joined: 10 February 2008

### Re: The hardest sudokus (new thread)

A couple of 11.3's
post63875.html#p63875
post64025.html#p64025

From patterns game 126, 3 puzzles
post204859.html#p204859

From patterns game 124, 3 puzzles
post204214.html#p204214
Mauricio

Posts: 1174
Joined: 22 March 2006

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