The New Sudoku Players' Forum

[tarek]

thanx gsf, your program with dukosu's suexrat are probably the programs to use for screening (Thanx for reminding me Ocean), I tried ravel to screen through a collection of diagonal patterns I generated then tried SE they all scored 9.2-9.3.... I post here 13 of them (It then becomes repetitively boring from for the next 1000 puzzles)

Code: Select all

500800700000050000009002001700000600010000030002000009600700800000060000003009002
800900700040030010000001002700000600060000080005000009200100000030040060009007005
500800700000050000009002003700000600010000020002000009600700800000060000003001002
800100900040030080000005006600000800020000030009000001700300000060040020001009005
800500100040030080000009002300000800060000040009000005600900000030040060005001007
500800700000050000009002001700000600010000030002000009600700800000060000003001002
800600700040030060000005001700000200010000080005000009100800000060040030009007005
400800700000050000009002001700000600010000030002000009600700800000060000003001002
800100900040030050000007002900000600030000080006000001600800000050040030001002005
800600900040030020000005007900000200010000080005000001700800000060040030001009005
000600300040050020000009007900000600050080040001000002100700000080040050003001000
800700300000050000009002001700000600050080040006000009500900800000040000003001002
800100900040030080000005006600000800030000020009000001700200000060040030001009005

tarek

[Jon]

Here is a free online sudoku solver that will solve and verify all your hardests Sudokus. It is very fast and it also tells if the sudoku has more than one solution. You'll need the Java plugin installed in your browser. Envoy: Jon's Sudoku Solver

BTW, here is the hardest Sudoku I ever found:
{ 0, 0, 2, 0, 9, 0, 1, 0, 7 },
{ 0, 3, 8, 6, 0, 0, 0, 0, 0 },
{ 4, 0, 0, 0, 0, 0, 0, 0, 0 },
{ 0, 0, 0, 0, 0, 5, 0, 0, 0 },
{ 0, 0, 9, 0, 1, 0, 3, 0, 0 },
{ 0, 0, 0, 4, 0, 0, 0, 0, 0 },
{ 0, 0, 0, 0, 0, 0, 0, 0, 4 },
{ 0, 0, 0, 0, 0, 7, 9, 2, 0 },
{ 8, 0, 6, 0, 3, 0, 7, 0, 0 },

[ravel]

Tarek,
thanks for the heavy list, the brute force step counts are
6,7,3,6,6,4,7,6,6,6,7,5,5.

Jon,
your puzzle can be solved with 2 steps, e.g. r1c6<>4, r3c7<>8.

[Eioru]

I find this one with 31 Forcing Chains
..........4..8..5...3..1..8...9..5...9..6..2...1..8..4...3..7...6..2..9...5..7..1

[ravel]

Thanks Eioru,
please note, that i am off for 2 weeks, so i cannot run my program in this time.

[tarek]

I'm not sure how much effort you're putting into this ravel, but from experience it seems like A LOT, keep up the good work........

tarek

[maria45]

Hi Ravel,

yeah, seems to me you put quite some work into it. That realized, what about starting a book project: "The world's hardest sudokus"? I could of course contribute the "human style" - solutions.

Regards, Maria

[Ocean]

I'm not sure how much effort you're putting into this ravel, but from experience it seems like A LOT, keep up the good work........

tarek

Supported!

Hi Ravel,

yeah, seems to me you put quite some work into it. That realized, what about starting a book project: "The world's hardest sudokus"? I could of course contribute the "human style" - solutions.

Regards, Maria

Good idea, Maria. I could contribute with some puzzles, if they pass the test of time.


Looking back:

I seem to remember that there's one very hard with the pattern

Code: Select all

 
+---+---+---+
|X..|.X.|..X|
|.X.|...|.X.|
|..X|...|X..|
+---+---+---+
|...|X.X|...|
|X..|.X.|..X|
|...|X.X|...|
+---+---+---+
|..X|...|X..|
|.X.|...|.X.|
|X..|.X.|..X|
+---+---+---+

I'd like to see it again. Can anybody help?

Exploring this pattern revealed a lot of hard puzzles - about doubling the number of available puzzles with Explainer rating between 9.5 and 9.9. Maybe also high stepcounts could appear.

Code: Select all

 *-----------*
 |1..|...|..2|
 |.3.|.4.|.5.|
 |..6|...|7..|
 |---+---+---|
 |...|1.4|...|
 |.8.|.7.|.4.|
 |...|5.8|...|
 |---+---+---|
 |..7|...|6..|
 |.5.|.3.|.8.|
 |2..|...|..1|
 *-----------*

Code: Select all

#
# ER-9.9:
100000002030040050006000700000103000040060080000405000002000900050030040700000001
100000002030040050006000700000103000040080090000405000007000100080030040200000006
100000002030040050006000700000103000080070040000406000002000600050030080900000001
100000002030040050006000700000104000080070040000508000007000600050030080200000001
# ER-9.8:
100000002030040050006000700000103000040060080000904000007000100050090030200000006
100000002030040050006000700000103000080070030000508000007000600050030080200000001
100000002030040050006000700000103000080070030000904000007000100040050080200000009
100000002030040050006000700000104000040070080000905000007000600050090030200000001
100000002030040050006000700000104000080070040000503000002000600040050030700000001
100000002030040050006000700000104000080090040000508000002000100050030080700000006
# ER-9.7:
100000002020030040005000600000307000040010030000805000008000500030020090600000001
100000002030040050006000700000103000080050040000409000007000100040030080200000006
100000002030040050006000700000103000080060030000904000007000100040050080200000009
100000002030040050006000700000104000080060030000903000007000100040050080200000009
# ER-9.6:
100000002030040050006000700000103000040060080000405000002000900080050040700000001
100000002030040050006000700000104000050020040000503000002000600040080030700000001
100000002030040050006000700000104000050030080000506000007000100020050030900000006
100000002030040050006000700000105000080060040000904000007000100050030080200000009
# ER-9.5:
100000002030040050006000700000103000040020030000504000007000600050080040200000001
100000002030040050006000700000103000040070080000405000007000600080050030200000001
100000002030040050006000700000103000050070040000408000002000100040080030700000006
100000002030040050006000700000103000050070080000504000007000600040050030200000001
100000002030040050006000700000104000080020040000508000002000600040030080700000001
#

[daj95376]

Code: Select all

 *-----------* # Original puzzle from Ocean
 |1..|...|..2|
 |.3.|.4.|.5.|
 |..6|...|7..|
 |---+---+---|
 |...|1.4|...|
 |.8.|.7.|.4.|
 |...|5.8|...|
 |---+---+---|
 |..7|...|6..|
 |.5.|.3.|.8.|
 |2..|...|..1|
 *-----------* # sans 9s

    b5  -  3     Locked Candidate (1)
    b7  -  1469  Naked  Quad
r258    -  1     Swordfish


Is there some sort of super fish here??? Look at the next 16 eliminations from my solver. In fact, Group 1 would probably be perfectly symmetrical in <9> -- like Group 2 -- if it wasn't for the Naked Quad eliminations in [r7c1] & [r9c4]. (You may wish to re-insert the 9s in these two cells while looking for the fish!)

Code: Select all

# Group 1: r1c3,r1c7,r3c1,r3c9,r5c3,r5c7,r7c9,r9c7 <> 9
 *-----------------------------------------------------------------------------*
 | 1       479     4589#   | 36789   5689    35679   | 3489#   369     2       |
 | 789     3       289     | 26789   4       12679   | 189     5       689     |
 | 4589#   249     6       | 2389    12589   2359    | 7       139     3489#   |
 |-------------------------+-------------------------+-------------------------|
 | 35679   2679    2359    | 1       269     4       | 23589   23679   356789  |
 | 569     8       1259#   | 2369    7       2369    | 1259#   4       569     |
 | 34679   124679  2349    | 5       269     8       | 239     123679  3679    |
 |-------------------------+-------------------------+-------------------------|
 | 38      149     7       | 2489    12589   259     | 6       239     3459#   |
 | 469     5       149     | 24679   3       12679   | 249     8       479     |
 | 2       469     38      | 46789   5689    5679    | 3459#   379     1       |
 *-----------------------------------------------------------------------------*


Code: Select all

# Group 2: r2c4,r2c6,r4c2,r4c8,r6c2,r6c8,r8c4,r8c6 <> 9
 *-----------------------------------------------------------------------------*
 | 1       479     4589    | 36789   5689    35679   | 3489    369     2       |
 | 789     3       289     | 26789#  4       12679#  | 189     5       689     |
 | 4589    249     6       | 2389    12589   2359    | 7       139     3489    |
 |-------------------------+-------------------------+-------------------------|
 | 35679   2679#   2359    | 1       269     4       | 23589   23679#  356789  |
 | 569     8       1259    | 2369    7       2369    | 1259    4       569     |
 | 34679   124679# 2349    | 5       269     8       | 239     123679# 3679    |
 |-------------------------+-------------------------+-------------------------|
 | 38      149     7       | 2489    12589   259     | 6       239     3459    |
 | 469     5       149     | 24679#  3       12679#  | 249     8       479     |
 | 2       469     38      | 46789   5689    5679    | 3459    379     1       |
 *-----------------------------------------------------------------------------*


[fermat]

Hi Ravel,

yeah, seems to me you put quite some work into it. That realized, what about starting a book project: "The world's hardest sudokus"? I could of course contribute the "human style" - solutions.

Regards, Maria

I would admire the book, or collection.

I truly doubt that it could be published, so very few people could solve any of them.

Bookshelf. It should be a chapter, expand the idea!

Edited, by author, to generalize.

[ronk]

Group 1 would probably be perfectly symmetrical in <9> -- like Group 2 -- if it wasn't for the Naked Quad eliminations in [r7c1] & [r9c3]. (You may wish to re-insert the 9s in these two cells while looking for the fish!)

Group 1: r1c3,r1c7,r3c1,r3c9,r7c1,r7c9,r9c3,r9c7 <> 9
(...)
Group 2: r2c4,r2c6,r4c2,r4c8,r6c2,r6c8,r8c4,r8c6 <> 9

Very interesting observation. I edited your Group 1 to cancel the effects of the naked quad and delete presumably unrelated exclusions in row 5.

If one can obtain the exclusions of Group 1, the exclusions of Group 2 follow using the strong inferences in boxes 1, 3, 7 and 9.

Code: Select all

 . *9  .  | 9  9  9  | . *9  .
*9  . *9  |-9 -. -9  |*9  . *9   
 . *9  .  | 9  9  9  | . *9  .   
----------+----------+--------- 
 9 -9  9  | .  9  .  | 9 -9  9
 9 -.  9  | 9  .  9  | 9 -.  9   
 9 -9  9  | .  9  .  | 9 -9  9   
----------+----------+--------- 
 . *9  .  | 9  9  9  | . *9  .   
*9  . *9  |-9 -. -9  |*9  . *9   
 . *9  .  | 9  9  9  | . *9  .

-r13c2=9=r2c13-9-r2c79=9=r13c8-9-r79c8=9=r8c79-9-r8c13=9=r79c2-9-
... implies r28c456<>9 and r456c28<>9

From the perspective of constraint sets ...
Set A (base): b1, b3, b7 and b9
Set B (cover): r2, r8, c2 and c8
Exclusions: r28c456 and r456c28<>9 (set B outside of set A)

Similarly, if one can obtain the exclusions of Group 2, the exclusions of Group 1 follow using the strong inferences of rows 2 and 8 and cols 2 and 8.

Code: Select all

-. *9 -9  | 9  9  9  |-9 *9 -.
*9  . *9  | .  .  .  |*9  . *9   
-9 *9 -.  | 9  9  9  |-. *9 -9   
----------+----------+--------- 
 9  .  9  | .  9  .  | 9  .  9
 9  .  9  | 9  .  9  | 9  .  9   
 9  .  9  | .  9  .  | 9  .  9   
----------+----------+--------- 
-9 *9 -.  | 9  9  9  |-. *9 -9   
*9  . *9  | .  .  .  |*9  . *9   
-. *9 -9  | 9  9  9  |-9 *9 -.

-r2c13=9=r2c79-9-r13c8=9=r79c8-9-r8c79=9=r8c13-9-r79c2=9=r13c2-9-
... implies r1379c1379<>9

From the perspective of constraint sets ...
Set A (base): r2, r8, c2 and c8
Set B (cover): b1, b3, b7 and b9
Exclusions: r1379c1379<>9  (set B outside of set A)

But I don't know how to first obtain either Group 1 or Group 2 exclusions.

[daj95376]

[Replace Initial Comments:] Almost all of the Group 1 eliminations in <9> occur in cells with a strong link for a second value in the box ... and this forces a Locked Candidate to occur for a third value. A Naked Quad and additional Locked Candidates often follow. No wonder my solver had to perform complex elimination logic!!!

SL: Strong Link
LC: Locked Candidate

Code: Select all

r1c3,r3c1: SL on <5>. Setting a cell to <9> forces <5> and LC on <8>.
r1c7,r3c9: SL on <4>. Setting a cell to <9> forces <4> and LC on <3>.
r7c9,r9c7: SL on <5>. Setting a cell to <9> forces <5> and LC on <3>.


[Eioru]

Can I ask you
what time did you spend completing a pattern ( find all puzzles rated over 9.0 )
and what program to use finding these super hard puzzles?

[daj95376]

[Edited] Misunderstood who was to answer above question.

[Eioru]

Code: Select all

#
# ER-9.9:
100000002030040050006000700000103000040060080000405000002000900050030040700000001
100000002030040050006000700000103000040080090000405000007000100080030040200000006
100000002030040050006000700000103000080070040000406000002000600050030080900000001
100000002030040050006000700000104000080070040000508000007000600050030080200000001
# ER-9.8:
100000002030040050006000700000103000040060080000904000007000100050090030200000006
100000002030040050006000700000103000080070030000508000007000600050030080200000001
100000002030040050006000700000103000080070030000904000007000100040050080200000009
100000002030040050006000700000104000040070080000905000007000600050090030200000001
100000002030040050006000700000104000080070040000503000002000600040050030700000001
100000002030040050006000700000104000080090040000508000002000100050030080700000006
# ER-9.7:
100000002020030040005000600000307000040010030000805000008000500030020090600000001
100000002030040050006000700000103000080050040000409000007000100040030080200000006
100000002030040050006000700000103000080060030000904000007000100040050080200000009
100000002030040050006000700000104000080060030000903000007000100040050080200000009
# ER-9.6:
100000002030040050006000700000103000040060080000405000002000900080050040700000001
100000002030040050006000700000104000050020040000503000002000600040080030700000001
100000002030040050006000700000104000050030080000506000007000100020050030900000006
100000002030040050006000700000105000080060040000904000007000100050030080200000009
# ER-9.5:
100000002030040050006000700000103000040020030000504000007000600050080040200000001
100000002030040050006000700000103000040070080000405000007000600080050030200000001
100000002030040050006000700000103000050070040000408000002000100040080030700000006
100000002030040050006000700000103000050070080000504000007000600040050030200000001
100000002030040050006000700000104000080020040000508000002000600040030080700000001
#

some of them changed my record
1.......2.3..4..5...6...7.....1.4....8..7..4....5.8.....7...6...5..3..8.2.......1 ~ 19 Dynamic Contration Forcing Chains(+)
1.......2.3..4..5...6...7.....1.3....8..7..4....4.6.....2...6...5..3..8.9.......1 ~ 10 Dynamic Region Forcing Chains(+)
1.......2.3..4..5...6...7.....1.4....8..2..4....5.8.....2...6...4..3..8.7.......1 ~ 23 Region Forcing Chains
1.......2.3..4..5...6...7.....1.4....8..2..4....5.8.....2...6...4..3..8.7.......1 ~ 12 Dynamic Cell Forcing Chains
1.......2.3..4..5...6...7.....1.3....4..6..8....4.5.....2...9...8..5..4.7.......1 ~ 4 Dynamic Double Forcing Chains