The New Sudoku Players' Forum

by **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

by **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.

by **gsf** » Mon May 15, 2006 5:20 pm

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

what technique(s) crack #9 #18 #43 ?

by **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

by **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

by **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

by **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

by **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

by **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

by **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

by **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!!!

by **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

by 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

by **ravel** » Mon May 22, 2006 8:22 am

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

by 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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