## Looking for some very very very hard sudoku

Everything about Sudoku that doesn't fit in one of the other sections
Here my #2 from this thread:
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`..8....5.7.562.83.1.....2.....1..6.....4.7......398.....3....7.6.7.3.12.8.....5..`

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`. . 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
Karlson

Posts: 26
Joined: 14 May 2006

claudiarabia wrote:
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`+---+---+---+ |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:
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`700000004060070050001000900900302005030050080200704003009000300010060020500000008600000003070020090003000100800601004050080070900407005004000800080070030300000002100000003040080020007000800200408006070030010500102004006000100020040070900000005400000008030060040008000600300907001010030070500608004001000500040050030700000009100000004090060050006000800500309008010050090200706001007000300030090010800000006200000006030080010005000900400702009020060050600304001002000300080010070900000008800000001050070020003000400300509002020030040700204006009000100040060030500000008700000008020060050009000600100809004060070010400106003001000900050010030800000005800000001070010030002000600500901003080050090100408007006000400020080070300000009700000006010080070009000400100203007090010080300608004004000200070040090200000005600000005020050090008000600400907008010080040300501002003000900060020080200000007300000006010050070009000800700408003040060020600705004004000200050070040100000007200000005060090080008000900600209004080060020400501007009000500040020070700000001500000008010090030009000600100308007020060010300507002006000500080070040900000001300000005090010030002000100100206007070090080900405003005000800030060040700000002500000009070060040006000100800407005040080010600901002009000500050030020100000004800000003050040020001000600300905007060070010700302006006000100070050090500000008100000005040060070002000400700105006060070040300602008001000300080020050900000007900000003050020070004000600100508009040030050800709004008000900010090040300000006800000003020080050003000900600507008030010090700402006009000400050020030100000009800000006090040050006000300100809004040010090300204007007000600010090040200000008200000004040010070003000800400906002070020030500804006005000100020090040900000008400000006090080010003000500600903008030010040800502003002000300040070090100000007500000009060030080004000200900307008080040060200506001002000900070010050100000003900000002010030070004000300100702009030050010800603005008000100050070040600000007100000002020040070003000400400802009090030080300605001002000100070080050600000004100000009060050030009000200700204006090060040800309005004000800010020060900000004100000005090020070004000900400209001020010060900508002003000400070090080600000007300000002080070050005000900800703009020060070600201003001000700090010040200000001100000006070080090006000300400506007030070060700902005008000400050040020900000001200000009090010070005000400700605004050040030800702006006000700010050080900000002300000009070060040006000100800103006030080090900605001002000300040030060700000008600000005090030080004000700800103009010050020500708004009000300020060010100000007200000006050060080003000400700205003010090040500603009008000300030050090100000002600000007040090060009000100400807009010050020200601005005000800070030040800000001900000002050090080002000500800704005060050040100206007001000700070080030400000008700000004050080070001000900300801009060090050100703006008000200040010090600000007100000009040090050008000100900103005080050010300407002004000300060070080200000006300000009010070040004000800200601003070020060100507008003000600040050070900000005300000009060050010007000400600908001070020080400703005004000300010090050500000006300000002050090060008000900500706008060020070900401006001000700020040050600000003600000009010070060002000500200605003040010090700408006005000200030080040900000007100000004090010060005000200800605003060070090300104002002000400010050080900000007500000004020080030003000100100507002090060040800102006006000500070020010900000007100000005030080010007000900500309006040050020200708009002000600050010030400000008500000001060080030003000700900502008040030070300907005009000200020060010700000003600000001080010050007000900300806004090020080400301007006000300010030040500000008600000009010030070003000100700602008050040010900508006008000400070050080300000002300000007060030040009000300800109006050080010900507008001000500070050080600000001600000003030010070002000800100307004090040030300809006004000200070090040800000001`

#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.
Ruud

Posts: 664
Joined: 28 October 2005

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

what technique(s) crack #9 #18 #43 ?
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

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

Toughies, but with 2 brute force steps far away from the hardest in my list there
ravel

Posts: 998
Joined: 21 February 2006

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
gfroyle

Posts: 214
Joined: 21 June 2005

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

Regarding puzzle #9:

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` *--------------------------------------------------------------------* | 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
Carcul

Posts: 724
Joined: 04 November 2005

Regarding puzzle #43:

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` *---------------------------------------------------------* | 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
Carcul

Posts: 724
Joined: 04 November 2005

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

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`#7:   r1c2 = 9#9:   r2c6 = 4#18:  r1c3 = 6#25:  r2c1 = 2#43:  r3c5 = 4`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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
Karlson

Posts: 26
Joined: 14 May 2006

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]618 [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]425 [12]7[16]4[24]5[36]7[74]4[84]2[95]843 [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`
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

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!!!
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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

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`< #7 >r4c3    =  4     Hidden Singler4c2    =  6     Hidden Singler6c7    =  3     Hidden Singler2c1    =  4     Hidden Singler2c9    =  3     Hidden Singler7c9    =  4     Hidden Single  c5    =  18    Naked  Pair    b5  =  18    Naked  Pairr5      =  67    Naked  Pairr5      =  1     Locked Candidate (2)r2c3    =  6     [r2c3]=1 ... =>[r1c2]=EMPTYr7c1    =  6     Hidden Single    b1  =  1     Locked Candidate (1)r7      =  2     Locked Candidate (2)r2c7    =  9     [r2c7]=8 ... =>[r1c8]=EMPTYr3c8    =  8     Hidden Single    b3  =  6     Locked Candidate (1)r1c2    =  9     [r1c2]=7 ... =>[r8c4]=EMPTYtrivial from here< #9 >r3c2    =  1     Hidden Singler5c7    =  1     Hidden Singler5c1    =  2     Hidden Singler2c1    =  6     Hidden Singler7c1    =  7     Hidden Singler9c3    =  8     Hidden Singler8c3    =  1     Hidden Singler8c7    =  3     Hidden Singler1c7    =  7     Hidden Singler2c7    =  9     Hidden Singler4c7    =  8     Hidden Singler8      =  56    Naked  Pair    b1  =  3     Locked Candidate (1)    b5  =  2     Locked Candidate (1)    b7  =  5     Locked Candidate (1)r2c3    =  5     [r2c3]=4 ... =>[r3c4]=EMPTYr2c4    =  8     [r2c4]=2 ... =>[r4c5]=EMPTYr2c6    =  4     [r2c6]=2 ... =>[r1c8]=EMPTYtrivial from here< #18 >r6c7    =  7     Hidden Singler6c2    =  1     Hidden Singler6c8    =  9     Naked  Singler4c7    =  2     Naked  Singler4c8    =  3     Naked  Singler5c9    =  1     Naked  Singler6c5    =  4     Naked  Singler4c2    =  9     Naked  Singler4c5    =  8     Naked  Singler5c7    =  5     Naked  Singler6c3    =  5     Naked  Singler4c3    =  4     Naked  Singler5c3    =  8     Naked  Singler5c1    =  2     Naked  Singler9      =  4     Locked Candidate (2)r28     =  1     X-Wingr1c2    =  7     [r1c2]=3 ... =>[r2c7]=EMPTYr8c3    =  7     Hidden Single  c4    =  39    Naked  Pair    b7  =  3     Locked Candidate (1)  c5    =  3     Locked Candidate (2)r1c5    =  3     [r1c5]=9 ... =>[r2c7]=EMPTYr1c3    =  6     [r1c3]=9 ... =>[r2c9]=EMPTYtrivial from here< #25 >r6c8    =  2     Naked  Singler1c3    =  3     Hidden Singler4c8    =  3     Hidden Singler4c3    =  5     Hidden Singler6c5    =  1     Hidden Singler9c4    =  3     Hidden Singler3c9    =  1     Hidden Single    b5  =  9     Locked Candidate (1)  c3    =  7     Locked Candidate (2)r2c3    =  6     [r2c3]=2 ... =>[r1c7]=EMPTYr4c2    =  6     Hidden Singler2c9    =  4     [r2c9]=8 ... =>[r7c5]=EMPTYr1c2    =  7     [r1c2]=8 ... =>[r3c5]=EMPTYtrivial from here< #43 >r6c7    =  6     Hidden Singler6c5    =  8     Hidden Singler6c3    =  9     Hidden Singler4c5    =  9     Hidden Singler4c2    =  2     Hidden Singler2c1    =  2     Hidden Singler9c8    =  2     Hidden Singler1c5    =  2     Hidden Singler4c8    =  4     Hidden Single  c25   =  4     X-Wingr9c4    =  8     [r9c4]=3 ... =>[r2c9]=EMPTYr7c2    =  8     Hidden Singler1c2    =  3     [r1c2]=7 ... =>[r1c4]=EMPTY  c8    =  57    Naked  Pairr1c8    =  5     [r1c8]=7 ... =>[r1c7]=EMPTYtrivial from here`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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 .|. . 74 1 .|. . 5|. 9 .`

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

RW
RW
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Posts: 1010
Joined: 16 March 2006

Needs 4 brute force steps in my program, i added it to my toughiest list.
ravel

Posts: 998
Joined: 21 February 2006

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
RW
2010 Supporter

Posts: 1010
Joined: 16 March 2006

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