Shooting for a Very Difficult Puzzle

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

Shooting for a Very Difficult Puzzle

Postby daj95376 » Wed Jun 21, 2006 6:29 pm

I keep altering my puzzle generator in hopes of generating a really difficult puzzle. Here's my latest results ... and your chance to show that it isn't. Have fun!!!

Code: Select all
 *-----------*
 |...|1..|4..|
 |18.|..2|.5.|
 |.42|..7|..8|
 |---+---+---|
 |..5|...|..1|
 |.24|.3.|58.|
 |7..|...|6..|
 |---+---+---|
 |2..|8..|37.|
 |.7.|6..|.15|
 |..1|..5|...|
 *-----------*
daj95376
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difficult puzzle

Postby holliday71366 » Thu Jun 22, 2006 7:10 pm

does this work?

569 183 427
187 462 953
342 597 168

895 624 731
624 731 589
713 958 642

256 819 374
978 346 215
431 275 896
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Postby udosuk » Thu Jun 22, 2006 8:00 pm

Wrong. The given clue in r8c4 should be 6 not 3.
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Postby daj95376 » Tue Jun 27, 2006 11:42 pm

Here are 25 consecutive puzzles from my generator. SS solved puzzles #13/15/18. I suspect that puzzle #14 may be a handful, but don't know for sure. If you get a moment, would you scan these puzzles and let me know if any qualify as complex for your solver to handle. TIA!!!

Code: Select all
.....6.78.2.4..1.93...1.....9.3.....1...5...3.....4.2.....8...52.7..5.1.56.2.....
.251...4..9...2...3.7........1.85..42..7.4..67..61.8........9.1...9...6..3...125.
.672...9.12..5...4.3...6..2...58.9.............3.14...8..3...7.3...2..19.5...934.
7...516...4.....8...64..1.....6..23.8..5.3..6.63..2.....2..73...7.....9...412...7
7.9.5...4.4.......8..6.4.7..3.5.......2.7.4.......3.8..7.3.1..8.......5.6...4.9.1
.8....2..6...15...15.3.....4..5....7.7..6..3.5....9..2.....3.84...47...6..9....7.
2..51.3...8..4.7.1..9....5......72..5...3...4..16......3....9..9.4.6..2...6.91..3
3....8....9.7...2...8..2..98.1...9...34...27...9...3.45..2..7...8...4.5....5....2
2...5..13...........5.927...63..9...85..3..27...5..38...841.5...........91..7...4
.31.982...2......7..6..4...5....6..4.9.1.3.8.1..4....3...8..4..6......3...963.57.
15.9.3....4..5.39....7....2.2.4..7...8..2..1...1..5.2.8....4....16.7..4....1.8.65
56341.....2.7.....8.7.....5..5.6.1...8.....4...9.4.3..1.....2.3.....2.8.....81764
...1..4...58.....11..7.38......3...7.97...65.2...9......69.2..44.....28...3..8...
7.......5.4.7..9...6..92.....32...5.8.2.4.3.7.5...82.....85..3...4..3.1.3.......4
21...48....98..72...8....3.....9...8...1.8...3...7.....2....6...45..32....12...57
..5..68...1.3.......9....2.4...38..5..3.9.6..5..76...8.3....5.......1.4...82..9..
3......75.7.86.....41.........39...713.....528...51.........58.....26.9.96......3
8.......1.1.2..9....7..6..3..846..1..3.....7..6..754..7..9..6....6..4.5.3.......4
.5....7.84.78.5.....2..7.5.7.....2....97148....8.....7.1.5..3.....4.19.63.6....1.
8.2.......4.2....75.69..1.....768...2...1...3...432.....3..46.51....5.3.......7.2
8.1..7....94.6.....2.8.......769...124..1..951...524.......6.5.....8.14....4..3.8
2.......394.3.......5.1.8.....2...7...1.6.3...9...8.....9.8.5.......9.367.......4
3...6.9..15.....4...2..9....4..1.5..2..4.7..8..6.8..2....7..1...3.....79..8.9...5
4.....56..5...8.....65.7.3......43....9.1.4....52......6.7.21.....8...5..83.....9
9...1.6...3...8..44.89..........67.1..4...8..3.68..........32.81..2...7...7.9...5
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Postby Mike Barker » Wed Jun 28, 2006 2:21 am

My solver can solve 21 of the 25 (all except 2, 14, 21, and 22) with 13, 15, and 18 being trivial and 17 and 24 only moderately tough, but this doesn't mean that they are not very hard. Watching the techniques summary it was obvious that a significant number of advanced techniques are required (at least without finding the minimum number of steps - I'll leave that the Carcul). This is really clear when comparing techniques to the Top1465. For the comparison I'm using the number of times a technique is used in successful puzzles over the total number of puzzles.
Code: Select all
Technique   Daj25 Top1465
Fish         204%     74%
X-cycles       8%     11%
Wings/Rings  212%     82%
UR/Bugs      136%     91%
ALS          104%     91%
Nice Loops   364%    181%
Grouped NL     0%     22%
Total Solved  84%     71%

So these puzzles require 2-3 times as many Fish, Wings/Rings (XY-wings, mYZ-wings, XY-rings, XY-chains), and nice loops as the Top1465. I'd say that qualifies this set as tough puzzles!
Mike Barker
 
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Postby daj95376 » Wed Jun 28, 2006 4:12 am

Thank You very much for the infomation Mike !!!!!!!

I just finished a major overhaul of my program. I had enough techniques written to make the overhaul time consuming, but not near enough to do a proper analysis on my own puzzles. I plan to add new techniques soon and then won't have to bother others. Again, Thanks!!!
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Postby tso » Wed Jun 28, 2006 5:48 am

Here are your puzzles rated by suexrat9.exe:

Code: Select all
rating:    173 ,  .....6.78.2.4..1.93...1.....9.3.....1...5...3.....4.2.....8...52.7..5.1.56.2.....
rating:    192 ,  .251...4..9...2...3.7........1.85..42..7.4..67..61.8........9.1...9...6..3...125.
rating:     84 ,  .672...9.12..5...4.3...6..2...58.9.............3.14...8..3...7.3...2..19.5...934.
rating:    150 ,  7...516...4.....8...64..1.....6..23.8..5.3..6.63..2.....2..73...7.....9...412...7
rating:    105 ,  7.9.5...4.4.......8..6.4.7..3.5.......2.7.4.......3.8..7.3.1..8.......5.6...4.9.1
rating:    114 ,  .8....2..6...15...15.3.....4..5....7.7..6..3.5....9..2.....3.84...47...6..9....7.
rating:    142 ,  2..51.3...8..4.7.1..9....5......72..5...3...4..16......3....9..9.4.6..2...6.91..3
rating:    127 ,  3....8....9.7...2...8..2..98.1...9...34...27...9...3.45..2..7...8...4.5....5....2
rating:    137 ,  2...5..13...........5.927...63..9...85..3..27...5..38...841.5...........91..7...4
rating:    119 ,  .31.982...2......7..6..4...5....6..4.9.1.3.8.1..4....3...8..4..6......3...963.57.
rating:    114 ,  15.9.3....4..5.39....7....2.2.4..7...8..2..1...1..5.2.8....4....16.7..4....1.8.65
rating:     93 ,  56341.....2.7.....8.7.....5..5.6.1...8.....4...9.4.3..1.....2.3.....2.8.....81764
rating:    126 ,  ...1..4...58.....11..7.38......3...7.97...65.2...9......69.2..44.....28...3..8...
rating:    224 ,  7.......5.4.7..9...6..92.....32...5.8.2.4.3.7.5...82.....85..3...4..3.1.3.......4
rating:    106 ,  21...48....98..72...8....3.....9...8...1.8...3...7.....2....6...45..32....12...57
rating:    126 ,  ..5..68...1.3.......9....2.4...38..5..3.9.6..5..76...8.3....5.......1.4...82..9..
rating:    139 ,  3......75.7.86.....41.........39...713.....528...51.........58.....26.9.96......3
rating:    103 ,  8.......1.1.2..9....7..6..3..846..1..3.....7..6..754..7..9..6....6..4.5.3.......4
rating:    127 ,  .5....7.84.78.5.....2..7.5.7.....2....97148....8.....7.1.5..3.....4.19.63.6....1.
rating:    142 ,  8.2.......4.2....75.69..1.....768...2...1...3...432.....3..46.51....5.3.......7.2
rating:    224 ,  8.1..7....94.6.....2.8.......769...124..1..951...524.......6.5.....8.14....4..3.8
rating:    225 ,  2.......394.3.......5.1.8.....2...7...1.6.3...9...8.....9.8.5.......9.367.......4
rating:    156 ,  3...6.9..15.....4...2..9....4..1.5..2..4.7..8..6.8..2....7..1...3.....79..8.9...5
rating:    135 ,  4.....56..5...8.....65.7.3......43....9.1.4....52......6.7.21.....8...5..83.....9
rating:    164 ,  9...1.6...3...8..44.89..........67.1..4...8..3.68..........32.81..2...7...7.9...5


By comparision, here are twenty at random created by SOLO.exe (at the "unreasonable" setting):

Code: Select all
rating:     91 ,  921.7..........92...4..6..5..........8...13.2..9.6.7.8..6.2.5.3....1.....57..92..
rating:    136 ,  ..8....356.....2.....7.2...8.1....53..2..648.9...3.......3..564.6...8.....9.2....
rating:     96 ,  ..9.....4....38.9..8....26....793.5.....24..8...1.....56...14..9.12......4.3..51.
rating:    135 ,  12.9...4.673...8..........7.1..6.......4.2.7.4...3..8.8...1.....6..74.....9...2..
rating:     89 ,  ......9...953...4147.8....2..3..7...7.....4..8.261....23...1..4.......9......95..
rating:     90 ,  .7..1...9..14..3..8...9...25.2.6...7...5...........4.3.9....6..73...4.....5..1.3.
rating:    169 ,  .7.....2.8..7.26.......54........9.21..2.......781.5..6.1.......45...1.8.2.5...9.
rating:    129 ,  .7....92..4...6..5...7.5...9...1.......6...1..51.43..7..42.........648...8...1..3
rating:    143 ,  .....3.8.2.4.5...9.6.........317.6...96.....8.....4.5..8.........5.82.1.1.7.....4
rating:    113 ,  .9...3.7....1.6...4...2.....2....3...59...2.8..3.1..97...3.1....37.5.9...6..79.2.
rating:    194 ,  53.9.4...7.18...9..8..6.....1..9...7..9...4..3...8..1.....4..7..9...85.3...6.2.48
rating:    100 ,  ...3..546.1....23.....86.......6..79.9.2.4.8.17..3.......62.....61....5.827..3...
rating:     85 ,  ...2....7...78..4......16.8.3..72..55.8...7.27..54..6.4.29......5..16...3....4...
rating:    162 ,  4.759....9....2....3.........1.5..3.56.843.17.8..7.6.........7....1....9....853.4
rating:    126 ,  4..17.....6.2...7..1...32...3...65....6...1....54...3...83...6..2...1.9.....98..2
rating:     87 ,  65.4......29......1....6.25.6..7.9....4...1....2.9..8.87.3....1......86......2.74
rating:    117 ,  .4.9.8.....5.4...92..7...6.......79..19...28..58.......6...1..34...5.9.....4.9.7.
rating:     89 ,  8.4..1....624.7..9.9..2......7...69....3.6....53...7......1..8.1..2.394....8..2.1
rating:     67 ,  ..281.3.......2.9.8.49....7.71..4...5..1.9..4...3..57.6....57.2.4.2.......3.814..
rating:    111 ,  ....83..2.......6.3142...8.1...9..24..3...9..62..5...8.3...7215.6.......5..81....


... and the first and last 20 from the top1465:

Code: Select all
rating:   1586 ,  4...3.......6..8..........1....5..9..8....6...7.2........1.27..5.3....4.9........
rating:   1546 ,  7.8...3.....2.1...5.........4.....263...8.......1...9..9.6....4....7.5...........
rating:   1487 ,  7.8...3.....6.1...5.........4.....263...8.......1...9..9.2....4....7.5...........
rating:   1518 ,  3.7.4...........918........4.....7.....16.......25..........38..9....5...2.6.....
rating:   1115 ,  5..7..6....38...........2..62.4............917............35.8.4.....1......9....
rating:   1215 ,  4..7..6....38...........2..62.5............917............43.8.5.....1......9....
rating:   1246 ,  .4..1.2.......9.7..1..........43.6..8......5....2.....7.5..8......6..3..9........
rating:   1233 ,  7.5.....2...4.1...3.........1.6..4..2...5...........9....37.....8....6...9.....8.
rating:   1088 ,  ......41.9..3.....3...5.....48..7..........62.1.......6..2....5.7....8......9....
rating:   1103 ,  7.5.....2...4.1...3.........1.6..4..2...5...........9....37.....9....8...8.....6.
rating:   1142 ,  .8..1......5....3.......4.....6.5.7.89....2.....3.....2.....1.9..67........4.....
rating:   1047 ,  8.9...3.....7.1...5.........7.....263...9.......1...4..6.2....4....8.5...........
rating:   1122 ,  6.9.....8...7.1...4............6...4.2.....3..3....5...1.5...7.8...9..........2..
rating:    976 ,  ......41.9..3.....3...2.....48..7..........52.1.......5..2....6.7....8......9....
rating:    978 ,  1...48....5....9....6...3.....57.2..8.3.........9............4167..........2.....
rating:    986 ,  7.8...3.....6.1...4.........6.....253...8.......1...9..9.5....2....7.4...........
rating:    949 ,  4.3.....2...6.1...8...........5..79.2...3.....1..........84.....9....6...7.....5.
rating:    871 ,  .1.62....5......43....9....7......8...5.....4...1..........36...9....2..8....7...
rating:    934 ,  4.3.....2...6.1...8...........5..97.2...3.....1..........84.....9....6...7.....5.
rating:    881 ,  8.5.....2...9.1...3.........6.7..4..2...5...........6....38.....1....9...4.....7.

rating:    257 ,  .5..812.....5.......9...5.......3..8.1......9..8.9.41.4...3876.8.7.6.....3.......
rating:    239 ,  .9.....7..6.....9...1..8.......92..6...8..4...34.5..19....1....4.....1..5..38.9..
rating:    240 ,  ....2...59..3.1...........9....7...26.4.........4.816..9.2.5...4.6.......1...78..
rating:    235 ,  7.1....4....8.56..3.........8.6..5..1......3...........2....8.....47........1....
rating:    250 ,  ..4.81.7...3.749....2........5.2.1.....8.6.........4..4...6.51.......6....1..5.29
rating:    267 ,  ....714.2.........2.7....3..4.19.25..8.......7....3.4...3..7...5.4....9.....2....
rating:    225 ,  9..4..3......89....3....5...81.7.........57...........5...371...9.2...8...6......
rating:    243 ,  27....1..1...........5.......53.8....3.4...........9....4....836...1........2....
rating:    215 ,  ......52....3.1..4.4..57.8.286................3.8..91...1....5..9.7..16..5.....7.
rating:    202 ,  ....4...1...2.9..3.731.........8.62..6....83.8.......4.5..1..9.7.16....23.2......
rating:    218 ,  ....1...78....562...5..7....58.7..1...26...........7.6........14....38....3.9..5.
rating:    211 ,  ..8....47.1.3..8....5.......5.6........2.9...83...4.9...6.8.1..7....2.......5...3
rating:    195 ,  6..3..2....7....49.........32.6............871............47....5....3......9....
rating:    188 ,  1.7..259.4...8.7....2......54.1......8.7..6........94.....7.....65..94..3........
rating:    201 ,  ...6...34.....96.....4.89....395....4......2.6.7.....5..1.........5.1.9.....2.7..
rating:    197 ,  ...5...........9.1.5...4...6..4......73...8.4..2..6..3...7..6..9.....7.2..48.2.3.
rating:    226 ,  .68..7......3...1....9.2.8...6.5.247.147..5..5........7.......4..5.9.........8.2.
rating:    191 ,  ....5...9.6.....3....3.941.3..6.....6..8.1..3.....5..7.315.7..4.5.....2.4...8....
rating:    196 ,  412.3.....7.5.............43.4.98....59....2....2..9...6.78...384......1..7......
rating:    203 ,  ....7...1..6.....5......4...9....5..6.81.5..........8731..9....76..2....2..31...9


I don't know the criteria used. I do know I've seen a few puzzles that rated over 170 that had no advanced tactics but needed *lots* of locked candidates, and others that rated under 100 that needed one very hard tactic and very little else.
tso
 
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Joined: 22 June 2005

Postby ravel » Wed Jun 28, 2006 9:54 am

From the list the hardest "brute force ratings" were 3 steps for numbers 14, 21 and 22.
This about corresponds to what Mike said and to the suexrat9 ratings.

But the first one Daj posted (didn't you try it Mike?) needed 5 steps and i am happy to add a new one to my hardest list:)
ravel
 
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Joined: 21 February 2006

Postby gsf » Wed Jun 28, 2006 10:22 am

#21 #22 both have only 1 backdoor up to x-wing
a solver falling back to chaining (look for chains, hope they work) or guessing
would have a higher probability of missing on these
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Postby Mike Barker » Wed Jun 28, 2006 12:32 pm

I wasn't able to solve the first puzzle. In fact my solver gave up pretty quickly which indicates a tough puzzle.

Code: Select all
+------------------+--------------------+------------------+
|   359   36  3679 |      1   5689  389 |    4  2369  2379 |
|     1    8  3679 |     34    469    2 |   79     5  3679 |
|   359    4     2 |    359    569    7 |    1   369     8 |
+------------------+--------------------+------------------+
|    38   39     5 |   2479  24789    6 |  279  2349     1 |
|     6    2     4 |     79      3    1 |    5     8    79 |
|     7    1   389 |   2459  24589  489 |    6  2349  2349 |
+------------------+--------------------+------------------+
|     2    5    69 |      8      1   49 |    3     7   469 |
|  3489    7    89 |      6    249   34 |  289     1     5 |
|  3489  369     1 |  23479   2479    5 |  289  2469  2469 |
+------------------+--------------------+------------------+

    Hidden Single: r6c2 => r6c2=1,r6c56<>1
    Hidden Single: r7c2 => r7c2=5,r1c2<>5
    Hidden Single: r7c5 => r7c5=1,r7c6<>1
    Hidden Single: r5c6 => r5c6=1
    Hidden Single: r5c1 => r5c1=6,r1349c1<>6,r4c2<>6
    Hidden Single: r3c7 => r3c7=1
    Column X-Wing Fillet-o-Fish: r19c2|r139c8 => r1c9<>6
    UR+4C/3SL (68): r14c56 => r4c6<>8
    Nice Loop: r8c6=3=r1c6=8=r6c6-8-r6c3=8=r8c3~8~r8c6 => r8c3<>3
    ALS xz-rule with A=1 cells: r7c6-4-r8c357 => r8c6<>9
    Nice Loop: r5c4-7-r5c9=7=r4c7-7-r2c7~9~ => r2c4<>9
    Nice Loop: r7c6=4=r7c9=6=r7c3-6-r9c2=6=r1c2-6-r1c6=6=r4c6~6~r7c6 => r4c6<>4
    ALS xy-rule with B=3 cells: r4c2-3-r678c3-6-r13c1|r12c3 => r1c2<>9,r4c1<>9
    XY-wing: r14c2|r4c6 => r1c6<>6
    Hidden Single: r4c6 => r4c6=6,r4c5<>6
    Incomplete solution
Mike Barker
 
Posts: 458
Joined: 22 January 2006

Postby JPF » Wed Jun 28, 2006 1:08 pm

ravel wrote:But the first one Daj posted (didn't you try it Mike?) needed 5 steps and i am happy to add a new one to my hardest list:)

What about one of its minimal, but without symmetry ?

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


JPF
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Postby daj95376 » Wed Jun 28, 2006 2:22 pm

Thanks tso for running a rating on my puzzles and then providing a comparison to other puzzles!!! Very informative and useful!

ravel, thanks for testing my puzzles! I'm honored that my very first puzzle made it to your hardest list!!!

gsf, thanks for the backdoor observation on puzzles #21/22. Yes, this would help explain their relative difficulty because no lucky elimination is going to lead to a cascade of basic techniques for them.

Mike, thanks for the break-down on the very first puzzle I posted.

JPF, I'll be interested as well in how your version of the puzzle turns out.

Everyone, this is a fantastic response and I'm very appreciative. Now, I know that I'm on the right track. Thanks Again!!!

===== ===== ===== ===== ===== =====

FYI: The very first puzzle posted in this thread was from an experiment I tried. My puzzle generator creates a filled grid (solution) and then clears symmetric pairs of cells while attempting to locate a difficult puzzle within. I recently added the ability to force clearing of all symmetric pairs with a specific value at the beginning of this process. As is obvious, there are no 9s among the the clues.
Last edited by daj95376 on Wed Jun 28, 2006 11:11 am, edited 2 times in total.
daj95376
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Postby ravel » Wed Jun 28, 2006 2:47 pm

JPF wrote:What about one of its minimal, but without symmetry ?

This one also needs 5 steps, but one of the 4 ways for 5 step solutions i found for the symmetrical one did not work.
I dont have a program to get the minimal puzzles, maybe someone wants to post a list with them.
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Postby JPF » Wed Jun 28, 2006 3:12 pm

ravel wrote:I dont have a program to get the minimal puzzles, maybe someone wants to post a list with them.

Code: Select all
000100400180002050040007008005000001024030000700000600200800370070600015001005000
000100400180002050042000008005000001024030000700000600200800370070600015001005000
000100400080002050042007008005000001024030000700000600200800370070600015001005000

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Postby ravel » Wed Jun 28, 2006 4:09 pm

Thanks JPF,

both new ones also were solved with 5 steps, so i will keep the symmetrical one in my list.
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