Looking for some very very very hard sudoku

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

Postby Karlson » Mon May 15, 2006 4:15 pm

Here my #2 from this thread:
Code: Select all
..8....5.7.562.83.1.....2.....1..6.....4.7......398.....3....7.6.7.3.12.8.....5..

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


Have fun and good luck solving it:)
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Postby Ruud » Mon May 15, 2006 4:31 pm

claudiarabia wrote:
Code: Select all
+---+---+---+
|X..|...|..X|
|.X.|.x.|.X.|
|..X|...|X..|
+---+---+---+
|x..|X.X|..x|
|.x.|.X.|.x.|
|x..|X.X|..x|
+---+---+---+
|..X|...|X..|
|.X.|.x.|.X.|
|X..|...|..X|
+---+---+---+


once I tried to make such a sudoku. I produced the pattern to be seen above with even more clues than kjell had, but apparently the structure of the whole 9x9-matrix isn't for having a one-solutional Sudoku with this pattern.

This is not a difficult pattern to produce unique puzzles from.

Here are 50:
Code: Select all
700000004060070050001000900900302005030050080200704003009000300010060020500000008
600000003070020090003000100800601004050080070900407005004000800080070030300000002
100000003040080020007000800200408006070030010500102004006000100020040070900000005
400000008030060040008000600300907001010030070500608004001000500040050030700000009
100000004090060050006000800500309008010050090200706001007000300030090010800000006
200000006030080010005000900400702009020060050600304001002000300080010070900000008
800000001050070020003000400300509002020030040700204006009000100040060030500000008
700000008020060050009000600100809004060070010400106003001000900050010030800000005
800000001070010030002000600500901003080050090100408007006000400020080070300000009
700000006010080070009000400100203007090010080300608004004000200070040090200000005
600000005020050090008000600400907008010080040300501002003000900060020080200000007
300000006010050070009000800700408003040060020600705004004000200050070040100000007
200000005060090080008000900600209004080060020400501007009000500040020070700000001
500000008010090030009000600100308007020060010300507002006000500080070040900000001
300000005090010030002000100100206007070090080900405003005000800030060040700000002
500000009070060040006000100800407005040080010600901002009000500050030020100000004
800000003050040020001000600300905007060070010700302006006000100070050090500000008
100000005040060070002000400700105006060070040300602008001000300080020050900000007
900000003050020070004000600100508009040030050800709004008000900010090040300000006
800000003020080050003000900600507008030010090700402006009000400050020030100000009
800000006090040050006000300100809004040010090300204007007000600010090040200000008
200000004040010070003000800400906002070020030500804006005000100020090040900000008
400000006090080010003000500600903008030010040800502003002000300040070090100000007
500000009060030080004000200900307008080040060200506001002000900070010050100000003
900000002010030070004000300100702009030050010800603005008000100050070040600000007
100000002020040070003000400400802009090030080300605001002000100070080050600000004
100000009060050030009000200700204006090060040800309005004000800010020060900000004
100000005090020070004000900400209001020010060900508002003000400070090080600000007
300000002080070050005000900800703009020060070600201003001000700090010040200000001
100000006070080090006000300400506007030070060700902005008000400050040020900000001
200000009090010070005000400700605004050040030800702006006000700010050080900000002
300000009070060040006000100800103006030080090900605001002000300040030060700000008
600000005090030080004000700800103009010050020500708004009000300020060010100000007
200000006050060080003000400700205003010090040500603009008000300030050090100000002
600000007040090060009000100400807009010050020200601005005000800070030040800000001
900000002050090080002000500800704005060050040100206007001000700070080030400000008
700000004050080070001000900300801009060090050100703006008000200040010090600000007
100000009040090050008000100900103005080050010300407002004000300060070080200000006
300000009010070040004000800200601003070020060100507008003000600040050070900000005
300000009060050010007000400600908001070020080400703005004000300010090050500000006
300000002050090060008000900500706008060020070900401006001000700020040050600000003
600000009010070060002000500200605003040010090700408006005000200030080040900000007
100000004090010060005000200800605003060070090300104002002000400010050080900000007
500000004020080030003000100100507002090060040800102006006000500070020010900000007
100000005030080010007000900500309006040050020200708009002000600050010030400000008
500000001060080030003000700900502008040030070300907005009000200020060010700000003
600000001080010050007000900300806004090020080400301007006000300010030040500000008
600000009010030070003000100700602008050040010900508006008000400070050080300000002
300000007060030040009000300800109006050080010900507008001000500070050080600000001
600000003030010070002000800100307004090040030300809006004000200070090040800000001

#7 and #25 are pretty hard.

With a slight alteration, I also found this one:

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

This pattern does not easily give unique puzzles.

Ruud.
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Postby gsf » Mon May 15, 2006 5:20 pm

Ruud wrote:#7 and #25 are pretty hard.

what technique(s) crack #9 #18 #43 ?
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Postby ravel » Mon May 15, 2006 5:32 pm

Ruud wrote:#7 and #25 are pretty hard.

Toughies, but with 2 brute force steps far away from the hardest in my list there
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Postby gfroyle » Tue May 16, 2006 1:28 pm

Ruud wrote:With a slight alteration, I also found this one:

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

This pattern does not easily give unique puzzles.

Ruud.


Doesn't it?

I found plenty... not guaranteed to be difficult though, but at least uniquely solvable and different..

http://www.csse.uwa.edu.au/~gordon/sudokupat.php?cn=9

Gordon
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Postby Carcul » Tue May 16, 2006 6:11 pm

Gsf wrote:what technique(s) crack #9 #18 #43 ?


Regarding puzzle #9:

Code: Select all
 *--------------------------------------------------------------------*
 | 8      349    3459   | 256    469    24569  | 7      245    1      |
 | 6      7      45     | 258    1      245    | 9      3      2458   |
 | 49     1      2      | 3578   3479   34579  | 6      458    458    |
 |----------------------+----------------------+----------------------|
 | 5      46     47     | 9      267    1      | 8      246    3      |
 | 2      8      347    | 367    5      367    | 1      9      46     |
 | 1      369    39     | 4      236    8      | 25     256    7      |
 |----------------------+----------------------+----------------------|
 | 7      59     6      | 1235   39     2359   | 4      1258   258    |
 | 49     2      1      | 56     8      49     | 3      7      56     |
 | 3      45     8      | 12567  467    24567  | 25     1256   9      |
 *--------------------------------------------------------------------*

[r3c1](-4-[r1c23])-4-[r2c3]-5-[r1c3]=4,5|6=[r6c2]-6-[r4c2]-4-[r9c2]=4=[r8c1]-4-[r3c1],

(Type-3 AUR in cells r1c23/r2c3/r6c23) which implies r3c1<>4 and the puzzle is solved.

Carcul
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Postby Carcul » Tue May 16, 2006 11:20 pm

Regarding puzzle #43:

Code: Select all
 *---------------------------------------------------------*
 | 1    378   3678 | 35789  2    36789  | 35789  357  4    |
 | 2    9     3478 | 34578  1    378    | 3578   6    58   |
 | 67   3478  5    | 3789   346  36789  | 2      137  189  |
 |-----------------+--------------------+------------------|
 | 8    2     17   | 6      9    5      | 17     4    3    |
 | 45   6     14   | 23     7    23     | 158    9    158  |
 | 3    57    9    | 1      8    4      | 6      57   2    |
 |-----------------+--------------------+------------------|
 | 567  3578  2    | 3789   36   136789 | 4      135  1569 |
 | 467  1     3467 | 23479  5    23679  | 39     8    69   |
 | 9    3458  368  | 38     346  1368   | 135    2    7    |
 *---------------------------------------------------------*

1. [r7c8]-5-[r7c1]=5=[r5c1]-5-[r6c2]=5=[r6c8]-5-[r7c8], => r7c8<>5.

2. [r9c6]=1=[r7c6]-1-[r7c8]-3-[r7c5]-6-[r9c6], => r9c6<>6.

3. [r9c3]=6=[r9c5]-6-[r7c5]-3-[r9c4]-8-[r9c3], => r9c3<>8.

4. [r8c1]-6-[r9c3]=6=[r9c5]=4=[r3c5]-4-[r3c2]=4|6=[r3c1]-6-[r8c1], => r8c1<>6.

5. [r7c1]-6-[r3c1]=6|4=[r3c2]-4-[r3c5]=4=[r9c5]=6=[r9c3]-6-[r7c1], => r7c1<>6.

6. [r2c4]=5=[r1c4](-5-[r1c8])=9=[r1c7]-9-[r8c7]-3-[r7c8]-1-[r3c8]=(AUR: r13c28)=1|4=[r3c2]-4-[r2c3]=4=[r2c4], => r2c4<>3,7,8.

7. [r1c3]=8=[r2c3]=4=[r2c4](-4-[r3c5]-3-[r3c8])=5=[r1c4]=9=[r1c7]-9-[r8c7]-3-[r7c8]-1-[r3c8]-7-[r6c8]=7=[r6c2]-7-[r1c2]-3-[r1c3|r2c3], => r1c3/r2c3<>3.

8. [r2c4]=5=[r1c4]=9=[r1c7]-9-[r8c7]=9=[r8c9]=6=[r7c9]-6-[r7c5]-3-[r3c5]-4-[r2c4], => r2c4<>4 and the puzzle is solved.

Carcul
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Postby daj95376 » Wed May 17, 2006 4:12 am

Any technique(s) that generate the following assignments will crack these deals open.

Code: Select all
#7:   r1c2 = 9
#9:   r2c6 = 4
#18:  r1c3 = 6
#25:  r2c1 = 2
#43:  r3c5 = 4
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Postby Karlson » Wed May 17, 2006 10:40 am

Carcul - have you tried my #2 (..8....5.7.562.83.1.....2.....1..6.....4.7......398.....3....7.6.7.3.12.8.....5..)?

Regards:)
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Postby gsf » Wed May 17, 2006 2:38 pm

daj95376 wrote:Any technique(s) that generate the following assignments will crack these deals open.

these puzzles have a lot of singles backdoors
(place any of these and the puzzle solves with singles)
Code: Select all
 7 [12]9[13]7[16]2[18]6[31]2[34]9[72]7[74]8[81]1[87]2[93]2[97]6
 9 [12]4[39]4[48]4[53]4[59]6[65]6[74]5[84]6[89]5[98]6
18 [13]6[14]4[16]9[18]2[21]5[24]2[26]8[29]3[31]8[32]3[34]5[38]6[39]9
   [71]4[72]5[79]2[81]6[87]9[89]4[94]8[95]5[96]4
25 [12]7[16]4[24]5[36]7[74]4[84]2[95]8
43 [14]9[17]7[18]5[23]4[24]5[27]3[32]7[35]4[43]7[47]1[51]4[53]1
   [59]5[62]5[68]7[71]5[78]3[84]4[92]4[95]3
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Postby daj95376 » Wed May 17, 2006 6:49 pm

gsf,

Thanks for the info!

Until now, I didn't understand references to singles backdoors ... let alone realize that my invalid() routine was trapping them. I've corrected this in my solver. Thanks Again!!!
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Postby daj95376 » Wed May 17, 2006 10:09 pm

If you resolve naked and hidden singles along a forced chain, then you get the following for Ruud's puzzles.

Code: Select all
< #7 >

r4c3    =  4     Hidden Single
r4c2    =  6     Hidden Single
r6c7    =  3     Hidden Single
r2c1    =  4     Hidden Single
r2c9    =  3     Hidden Single
r7c9    =  4     Hidden Single
  c5    =  18    Naked  Pair
    b5  =  18    Naked  Pair
r5      =  67    Naked  Pair
r5      =  1     Locked Candidate (2)
r2c3    =  6     [r2c3]=1 ... =>[r1c2]=EMPTY
r7c1    =  6     Hidden Single
    b1  =  1     Locked Candidate (1)
r7      =  2     Locked Candidate (2)
r2c7    =  9     [r2c7]=8 ... =>[r1c8]=EMPTY
r3c8    =  8     Hidden Single
    b3  =  6     Locked Candidate (1)
r1c2    =  9     [r1c2]=7 ... =>[r8c4]=EMPTY
trivial from here

< #9 >

r3c2    =  1     Hidden Single
r5c7    =  1     Hidden Single
r5c1    =  2     Hidden Single
r2c1    =  6     Hidden Single
r7c1    =  7     Hidden Single
r9c3    =  8     Hidden Single
r8c3    =  1     Hidden Single
r8c7    =  3     Hidden Single
r1c7    =  7     Hidden Single
r2c7    =  9     Hidden Single
r4c7    =  8     Hidden Single
r8      =  56    Naked  Pair
    b1  =  3     Locked Candidate (1)
    b5  =  2     Locked Candidate (1)
    b7  =  5     Locked Candidate (1)
r2c3    =  5     [r2c3]=4 ... =>[r3c4]=EMPTY
r2c4    =  8     [r2c4]=2 ... =>[r4c5]=EMPTY
r2c6    =  4     [r2c6]=2 ... =>[r1c8]=EMPTY
trivial from here

< #18 >

r6c7    =  7     Hidden Single
r6c2    =  1     Hidden Single
r6c8    =  9     Naked  Single
r4c7    =  2     Naked  Single
r4c8    =  3     Naked  Single
r5c9    =  1     Naked  Single
r6c5    =  4     Naked  Single
r4c2    =  9     Naked  Single
r4c5    =  8     Naked  Single
r5c7    =  5     Naked  Single
r6c3    =  5     Naked  Single
r4c3    =  4     Naked  Single
r5c3    =  8     Naked  Single
r5c1    =  2     Naked  Single
r9      =  4     Locked Candidate (2)
r28     =  1     X-Wing
r1c2    =  7     [r1c2]=3 ... =>[r2c7]=EMPTY
r8c3    =  7     Hidden Single
  c4    =  39    Naked  Pair
    b7  =  3     Locked Candidate (1)
  c5    =  3     Locked Candidate (2)
r1c5    =  3     [r1c5]=9 ... =>[r2c7]=EMPTY
r1c3    =  6     [r1c3]=9 ... =>[r2c9]=EMPTY
trivial from here

< #25 >

r6c8    =  2     Naked  Single
r1c3    =  3     Hidden Single
r4c8    =  3     Hidden Single
r4c3    =  5     Hidden Single
r6c5    =  1     Hidden Single
r9c4    =  3     Hidden Single
r3c9    =  1     Hidden Single
    b5  =  9     Locked Candidate (1)
  c3    =  7     Locked Candidate (2)
r2c3    =  6     [r2c3]=2 ... =>[r1c7]=EMPTY
r4c2    =  6     Hidden Single
r2c9    =  4     [r2c9]=8 ... =>[r7c5]=EMPTY
r1c2    =  7     [r1c2]=8 ... =>[r3c5]=EMPTY
trivial from here

< #43 >

r6c7    =  6     Hidden Single
r6c5    =  8     Hidden Single
r6c3    =  9     Hidden Single
r4c5    =  9     Hidden Single
r4c2    =  2     Hidden Single
r2c1    =  2     Hidden Single
r9c8    =  2     Hidden Single
r1c5    =  2     Hidden Single
r4c8    =  4     Hidden Single
  c25   =  4     X-Wing
r9c4    =  8     [r9c4]=3 ... =>[r2c9]=EMPTY
r7c2    =  8     Hidden Single
r1c2    =  3     [r1c2]=7 ... =>[r1c4]=EMPTY
  c8    =  57    Naked  Pair
r1c8    =  5     [r1c8]=7 ... =>[r1c7]=EMPTY
trivial from here
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Postby RW » Sat May 20, 2006 12:16 pm

Here's a nice symmetric&minimal 24:

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


Seems quite tough to me, how would your solvers rate the difficulty?

RW
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Postby ravel » Mon May 22, 2006 8:22 am

Needs 4 brute force steps in my program, i added it to my toughiest list.
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Postby RW » Mon May 22, 2006 8:43 am

Thanks ravel, I'm honored! I didn't think it would make that list, I somehow imagined 24 clues was too much to make it hard enough, but I was terribly wrong. I just noticed that gfroyle's beauty is the only puzzle on the list with <20 clues (19). The other 6 puzzles have 23-25 clues each. It seems to be a lot harder to make superfiendish puzzles with few clues. Can anybody explain this? Also, have you ran the known 17s through your program to find out if there are any really tough there?

RW
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