The hardest sudokus

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

Postby ronk » Thu Feb 21, 2008 2:40 am

A couple of puzzles ... to see if one is tough enough.
Code: Select all
-q1 M2
1.......2.3.4...5...6...7...8.39.........5......874.9...7...6...9...8.3.2.......1 # 95622 ronk-02-20-08 #2

[edit 1: added 02-21]
Code: Select all
-q1 M3
1.......2.3.4...5...6...7...5.94........63......8.5.9...7...6...9...8.4.2.......1 # 99018 ronk-02-21-08 #3

[edit 3: #1 deleted, since it's isomorphic to q1-taxonomy]
Last edited by ronk on Fri Feb 22, 2008 5:26 pm, edited 3 times in total.
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Postby champagne » Thu Feb 21, 2008 10:30 am

Here the results for ronk's puzzles and the hardest of the lot from coloin I tested

ronk-02-20-08 #1 78 10s375
ronk-02-20-08 #2 32 8s203
col-02-08-072 141 34s750

col-02-08-072 is for sure in the family of hardest, but not in the top list. I'll run now the full lot of coloin

Note:
I am not organized to share my solver, but if anybody would be willing to use it, we can find a way to do it.
It's run on a PC in Windows mode and written in 'Cplus', so it must be an execute file, unless somebody wants to work on source files.
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Postby tarek » Thu Feb 21, 2008 8:15 pm

very interesting ronk,

these are symmetrical ultra difficult puzzles. I'm surprised that they were not unearthed before, good work:D

I think we reached the point of uncertainty when trying to label a puzzle as "THE HARDEST"

here is the suexrat9 & suxratt output using the "10000 2" option:
Code: Select all
rating:   1489 ,718 , 1.......2.3.4...5...6...7...9.58........64......3.9.8...7...6...4...5.9.2.......1
rating:   1173 ,645 , 1.......2.3.4...5...6...7...8.39.........5......874.9...7...6...9...8.3.2.......1
rating:   1401 ,676 , 1.......2.3.4...5...6...7...5.94........63......8.5.9...7...6...9...8.4.2.......1
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Postby coloin » Fri Feb 22, 2008 11:42 am

Code: Select all
1.......2.3.4...5...6...7...9.58........6.......3.9.8...7...6...4...5.9.2.......1 # ronk-02-20-08  #1 1.......2.3.4...5...6...7...9.5.........64......3.9.8...7...6...4...5.9.2.......1 # ronk-02-22-08  #5


C
Last edited by coloin on Fri Feb 22, 2008 2:40 pm, edited 2 times in total.
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Postby ronk » Fri Feb 22, 2008 6:10 pm

coloin wrote:actually ronk 02-20-08 #1 is non-minimal, which improves the rating for 1b

Thanks coloin. Unfortunately these minimals are already in gsf's q1-taxonomy. Here are a few more ...
Code: Select all
# -q1 M2

1.......2.3.4...5...6...7...8..36......825......1...3...7...6...5...9.8.2.......1 # 95735 ronk-02-22-08 #9
1.......2.3.4...5...6...7...8.93.......2.4.......65.9...7...6...5...8.3.2.......1 # 95662 ronk-02-22-08 #10
1.......2.3.4...5...6...7...5.8.4......92........36.8...7...6...8...3.4.2.......1 # 95646 ronk-02-22-08 #11
1.......2.3.4...5...6...7...8.39.......6.5......8.4.9...7...6...9...8.3.2.......1 # 95613 ronk-02-22-08 #12

I'm somewhat arbitrarily using a q1 rating of 95600 as the cutoff.

[edit: Deleted five puzzles that were equivalent to q1-taxonomy entries.:( ]
Last edited by ronk on Fri Feb 22, 2008 5:20 pm, edited 2 times in total.
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Postby coloin » Fri Feb 22, 2008 6:15 pm

Ahhh you beat me to it !!!!

Over 7000 minimal puzzles adding 5 clues to box 5
Over 95000 minimal puzzles adding 6 clues to box 5

Perhaps lets see what champagne and Obi-whan make of these....from the 8 variations of ronks template !

heres the best according to suexrat9 with 21 clues

1.......2.3.4...5...6...7...5.9.4.......23......8...9...2...6...9...8.4.7.......1 # 1895 #
1.......2.3.4...5...6...7...5..39.......6.......8.5.9...2.....6.9...8.4.7.....1.. # 1777 #
1.......2.3.4...5...6...7...5.9.4.......1........53.9...7...6...9...8.4.2.......1 # 1693 #
1.......2.3.4...5...6...7...5.8.4.......29......3...9...7.....1.9...8.4.2.....6.. # 1762 #
1.......2.3.4...5...6...7...5...3......91.......8.4.9...2.....1.9...8.4.7.....6.. # 1653 #
1.......2.3.4...5...6...7...5.9.3.......1........54.9...7...6...9...8.4.2.......1 # 1741 # ronk-02-22-08 #5
1.......2.3.4...5...6...7...5.9.........13......8.4.9...2...6...9...8.4.7.......1 # 1622 #
1.......2.3.4...5...6...7...5.9.3......81.........4.9...7...6...9...8.4.2.......1 # 1619 # ronk-02-20-08 #1
1.......2.3.4...5...6...7...5.8.3......57.........4.9...2.....6.9...8.4.7.....1.. # 1513 #
1.......2.3.4...5...6...7...5.9.4......81.........3.9...7...6...9...8.4.2.......1 # 1607 #
1.......2.3.4...5...6...7...5...3......91.......8.4.9...2...6...9...8.4.7.......1 # 1547 #
1.......2.3.4...5...6...7...5.8.3.......74......5...9...7...6...9...8.4.2.......1 # 1508 #
1.......2.3.4...5...6...7...5.8.3......91.........4.9...7...6...9...8.4.2.......1 # 1436 #
1.......2.3.4...5...6...7...5.8.3......91.........4.9...7...6...9...8.4.2.......1 # 1424 # ronk-02-22-08 #4
1.......2.3.4...5...6...7...5.2.9...............835.9...7.....6.9...8.4.2.....1.. # 1316 #
1.......2.3.4...5...6...7...5...4......96.......8.3.9...7...6...9...8.4.2.......1 # 1328 #
1.......2.3.4...5...6...7...5.9.........1.......854.9...2...6...9...8.4.7.......1 # 1180 #
1.......2.3.4...5...6...7...5.3........97.......8.4.9...7.....6.9...8.4.2.....1.. # 1192 #
1.......2.3.4...5...6...7...5.7.4......513..........9...7...1...9...8.4.2.......6 # 1117 #
1.......2.3.4...5...6...7...5.2.9...............853.9...7.....6.9...8.4.2.....1.. # 1078 #
1.......2.3.4...5...6...7...5...4......6........583.9...7...6...9...8.4.2.......1 # 1081 #
1.......2.3.4...5...6...7...5.734......56...........9...2...1...9...8.4.7.......6 # 1054 #
1.......2.3.4...5...6...7...5.893.......7.......5...9...7...6...9...8.4.2.......1 # 1095 #
1.......2.3.4...5...6...7...5.983.......7.......5...9...7...6...9...8.4.2.......1 # 1077 #
1.......2.3.4...5...6...7...5.983.......1.......5...9...7...6...9...8.4.2.......1 # 1061 #
1.......2.3.4...5...6...7...5.3.9......61........5..9...7.....6.9...8.4.2.....1.. # 1010 #
1.......2.3.4...5...6...7...5.2.3......564..........9...7...1...9...8.4.2.......6 # 1062 #
1.......2.3.4...5...6...7...5..9.......61.......5.4.9...2...6...9...8.4.7.......1 # 1033 #

q1
1.......2.3.4...5...6...7...5.8.3......91.........4.9...7...6...9...8.4.2.......1 # 99032 # ronk-02-22-08 #4
1.......2.3.4...5...6...7...5.9.3.......1........54.9...7...6...9...8.4.2.......1 # 98871 # ronk-02-22-08 #5
1.......2.3.4...5...6...7...5..39.......6.......8.5.9...2.....6.9...8.4.7.....1.. # 97161 #
1.......2.3.4...5...6...7...5.9.4.......23......8...9...2...6...9...8.4.7.......1 # 96496 #
1.......2.3.4...5...6...7...5.9.3......81.........4.9...7...6...9...8.4.2.......1 # 96133 # ronk-02-20-08 #1
1.......2.3.4...5...6...7...5.8.4.......29......3...9...7.....1.9...8.4.2.....6.. # 95767 #
1.......2.3.4...5...6...7...5.9.........13......8.4.9...2...6...9...8.4.7.......1 # 95676 #
1.......2.3.4...5...6...7...5.3........97.......8.4.9...7.....6.9...8.4.2.....1.. # 95495 #
1.......2.3.4...5...6...7...5.8.9.......2.......7.3.9...2.....1.9...8.4.7.....6.. # 95253 #
1.......2.3.4...5...6...7...5.9........6........213.9...2...1...9...8.4.7.......6 # 95185 #
1.......2.3.4...5...6...7...5.8.3......57.........4.9...2.....6.9...8.4.7.....1.. # 95166 #
1.......2.3.4...5...6...7...5.87.......315..........9...7...6...9...8.4.2.......1 # 95139 #
1.......2.3.4...5...6...7...5...3......91.......8.4.9...2...6...9...8.4.7.......1 # 95127 #
1.......2.3.4...5...6...7...5...3......91.......8.4.9...2.....1.9...8.4.7.....6.. # 95110 #
1.......2.3.4...5...6...7...5.94.......76.........1.9...7.....6.9...8.4.2.....1.. # 95090 #

heres the best according to suexrat9 with 22 clues [rather more puzzles]

1.......2.3.4...5...6...7...5..32......9........845.9...2...6...9...8.4.7.......1 # 1695 #
1.......2.3.4...5...6...7...5.879......3.........54.9...2...6...9...8.4.7.......1 # 1634 #
1.......2.3.4...5...6...7...5.9.3......8.2.......54.9...2.....1.9...8.4.7.....6.. # 1610 #
1.......2.3.4...5...6...7...5.9.4......7.3......85..9...2...6...9...8.4.7.......1 # 1589 #
1.......2.3.4...5...6...7...5.3.9......5.4......18..9...2.....1.9...8.4.7.....6.. # 1577 #
1.......2.3.4...5...6...7...5.9.3......2.4......85..9...7...6...9...8.4.2.......1 # 1555 #
1.......2.3.4...5...6...7...5.8........9.3......645.9...2.....6.9...8.4.7.....1.. # 1545 #
1.......2.3.4...5...6...7...5.964........3......85..9...2...6...9...8.4.7.......1 # 1540 #
1.......2.3.4...5...6...7...5.194......8........3.5.9...2.....1.9...8.4.7.....6.. # 1532 #
1.......2.3.4...5...6...7...5.936........4......8.5.9...2.....6.9...8.4.7.....1.. # 1522 #
1.......2.3.4...5...6...7...5.3.........91......854.9...2...6...9...8.4.7.......1 # 1516 #
1.......2.3.4...5...6...7...5.9.4........3......856.9...2...6...9...8.4.7.......1 # 1509 #
1.......2.3.4...5...6...7...5.8.4......9........753.9...2...1...9...8.4.7.......6 # 1502 #
1.......2.3.4...5...6...7...5..3.......9.6......845.9...2...6...9...8.4.7.......1 # 1495 #
1.......2.3.4...5...6...7...5.3.4......9.7.......85.9...2.....6.9...8.4.7.....1.. # 1487 #
1.......2.3.4...5...6...7...5.8.3......9.2.......54.9...2.....1.9...8.4.7.....6.. # 1485 #
1.......2.3.4...5...6...7...5.8.4......9.7.......35.9...7...6...9...8.4.2.......1 # 1459 #
1.......2.3.4...5...6...7...5.9.........36......845.9...2...6...9...8.4.7.......1 # 1450 #
1.......2.3.4...5...6...7...5.97........3.......845.9...2...6...9...8.4.7.......1 # 1441 #
1.......2.3.4...5...6...7...5.94........15......8.3.9...2.....1.9...8.4.7.....6.. # 1432 #
1.......2.3.4...5...6...7...5.314......9.........85.9...2.....6.9...8.4.7.....1.. # 1431 #
1.......2.3.4...5...6...7...5.9.4......5.7......83..9...2...1...9...8.4.7.......6 # 1424 #
1.......2.3.4...5...6...7...5.984.......65......3...9...2...1...9...8.4.7.......6 # 1423 #
1.......2.3.4...5...6...7...5.9.3......8........645.9...2...6...9...8.4.7.......1 # 1416 #
1.......2.3.4...5...6...7...5.9.4........3......582.9...2.....6.9...8.4.7.....1.. # 1405 #
1.......2.3.4...5...6...7...5.73.......9........845.9...2...6...9...8.4.7.......1 # 1388 #
1.......2.3.4...5...6...7...5..13......9........854.9...2.....1.9...8.4.7.....6.. # 1388 #
1.......2.3.4...5...6...7...5.9.4........3......857.9...7.....6.9...8.4.2.....1.. # 1385 #
1.......2.3.4...5...6...7...5.9.4......73........52.9...2...1...9...8.4.7.......6 # 1385 #
1.......2.3.4...5...6...7...5.9.4......8........135.9...2.....6.9...8.4.7.....1.. # 1374 #
1.......2.3.4...5...6...7...5.794......5........8.3.9...2.....6.9...8.4.7.....1.. # 1374 #
1.......2.3.4...5...6...7...5..73......9........584.9...2...6...9...8.4.7.......1 # 1374 #
1.......2.3.4...5...6...7...5.893.......4.......7.5.9...7.....6.9...8.4.2.....1.. # 1369 #
1.......2.3.4...5...6...7...5..79......3........854.9...2...6...9...8.4.7.......1 # 1367 #
1.......2.3.4...5...6...7...5.24........9.......583.9...7.....6.9...8.4.2.....1.. # 1365 #
1.......2.3.4...5...6...7...5.981........5......3.4.9...2...6...9...8.4.7.......1 # 1364 #
1.......2.3.4...5...6...7...5.679.......8.......35..9...2...1...9...8.4.7.......6 # 1356 #
1.......2.3.4...5...6...7...5.982........3......5.4.9...7.....6.9...8.4.2.....1.. # 1353 #
1.......2.3.4...5...6...7...5.8.9........4......351.9...7...6...9...8.4.2.......1 # 1345 #
1.......2.3.4...5...6...7...5.239........4......8.5.9...2.....6.9...8.4.7.....1.. # 1344 #
1.......2.3.4...5...6...7...5.93........25.......47.9...2.....1.9...8.4.7.....6.. # 1343 #
1.......2.3.4...5...6...7...5..41.......69......35..9...2.....6.9...8.4.7.....1.. # 1335 #
1.......2.3.4...5...6...7...5.149......8........3.5.9...7...6...9...8.4.2.......1 # 1332 #
1.......2.3.4...5...6...7...5.8.9......3........154.9...2.....6.9...8.4.7.....1.. # 1331 #
1.......2.3.4...5...6...7...5.8.4......9........635.9...7...6...9...8.4.2.......1 # 1320 #
1.......2.3.4...5...6...7...5..94......2.3.......85.9...2.....6.9...8.4.7.....1.. # 1319 #
1.......2.3.4...5...6...7...5.239........5......8.4.9...2.....6.9...8.4.7.....1.. # 1304 #
1.......2.3.4...5...6...7...5..94......36.......8.1.9...2.....1.9...8.4.7.....6.. # 1303 #
1.......2.3.4...5...6...7...5.9.3......8........145.9...2.....6.9...8.4.7.....1.. # 1287 #
1.......2.3.4...5...6...7...5.94........63......8.5.9...7...6...9...8.4.2.......1 # 1287 # ronk-02-21-08 #3
1.......2.3.4...5...6...7...5.893.......4.......7.5.9...7...6...9...8.4.2.......1 # 1287 #
1.......2.3.4...5...6...7...5..14.......9.......385.9...2.....6.9...8.4.7.....1.. # 1285 #
1.......2.3.4...5...6...7...5.92.........3......584.9...7...6...9...8.4.2.......1 # 1283 #
1.......2.3.4...5...6...7...5.984......3.5........1.9...7...1...9...8.4.2.......6 # 1280 #
1.......2.3.4...5...6...7...5.693........4.......85.9...2.....6.9...8.4.7.....1.. # 1279 #
1.......2.3.4...5...6...7...5.8.4......9........653.9...7.....6.9...8.4.2.....1.. # 1277 #
1.......2.3.4...5...6...7...5.98.......7........235.9...2...6...9...8.4.7.......1 # 1274 #
1.......2.3.4...5...6...7...5..13......7.4......85..9...7...1...9...8.4.2.......6 # 1268 #
1.......2.3.4...5...6...7...5.7.4........3......586.9...7...6...9...8.4.2.......1 # 1261 #
1.......2.3.4...5...6...7...5.91.........3......854.9...2...6...9...8.4.7.......1 # 1260 #
1.......2.3.4...5...6...7...5...4......79.......385.9...2.....6.9...8.4.7.....1.. # 1257 #
1.......2.3.4...5...6...7...5.289......3........5.4.9...7...1...9...8.4.2.......6 # 1256 #
1.......2.3.4...5...6...7...5.942.......7........85.9...2.....1.9...8.4.7.....6.. # 1256 #
1.......2.3.4...5...6...7...5.194........3.......85.9...2.....6.9...8.4.7.....1.. # 1252 #

C
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Postby champagne » Fri Feb 22, 2008 7:32 pm

After Golden Nugget, difficult to be in the target.
This is on my side an homogeneous file, but far form hardest.
I picked up the most representative on both sides:
Highest counting time 156 milliseconds,
Highest processing time 17s
Lowest counting time 15 milliseconds (but processing time 15s)



Code: Select all
1.......2.3.4...5...6...7...5.3.8.......7.......95..4.7.....6...8...3.9...2.....1 # 99408 ronk-02-22-08 #6  156  13s812
1.......2.3.4...5...6...7...5.8.4......92........36.8...7...6...8...3.4.2.......1 # 95646 ronk-02-22-08 #11 31  6s93
1.......2.3.4...5...6...7...5.734......56...........9...2...1...9...8.4.7.......6 # 1054 #  15  15s609
1.......2.3.4...5...6...7...5.2.3......564..........9...7...1...9...8.4.2.......6 # 1062 #  47  14s265
1.......2.3.4...5...6...7...5.964........3......85..9...2...6...9...8.4.7.......1 # 1540 #  62  15s516
1.......2.3.4...5...6...7...5.9.4........3......856.9...2...6...9...8.4.7.......1 # 1509 #  46  15s453
1.......2.3.4...5...6...7...5.9.4......5.7......83..9...2...1...9...8.4.7.......6 # 1424 #  46  16s421
1.......2.3.4...5...6...7...5.679.......8.......35..9...2...1...9...8.4.7.......6 # 1356 #  78  17s313
1.......2.3.4...5...6...7...5.92.........3......584.9...7...6...9...8.4.2.......1 # 1283 #  62  5s297



for the time being, the most surprising for me is still

Code: Select all
000001020300040500000600007001000006040080090500000300800002000050090400006700000 Ocean's New Year's present for ravel #2


with the set of indicators
counting:47 processing:94s985 Print size:528K
Very low structural figure and close to Golden Nugget!!!
I'll start to morrow analysis of the proposed solution for that puzzle
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Postby ronk » Fri Feb 22, 2008 9:36 pm

coloin, tarek, champagne etal, I had a flaw in my method to check non-equivalence to gsf's q1-taxonomy. As a result, six of my twelve posted puzzles were duplicates. Posts now corrected. Sorry.
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Postby tarek » Tue Feb 26, 2008 11:22 pm

has anyone checked this ?

On another website, Bob Hanson From St. Olaf College wrote:I would appreciate comments regarding www.stolaf.edu/people/hansonr/sudoku/easter_monster.htm
which I believe to be a quite easy solution to the Easter Monster based on Medusa chains and a few new ideas.
Bob Hanson
hansonr@stolaf.edu

tarek
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Postby gsf » Wed Feb 27, 2008 12:30 am

tarek wrote:has anyone checked this ?

On another website, Bob Hanson From St. Olaf College wrote:I would appreciate comments regarding www.stolaf.edu/people/hansonr/sudoku/easter_monster.htm
which I believe to be a quite easy solution to the Easter Monster based on Medusa chains and a few new ideas.
Bob Hanson
hansonr@stolaf.edu

tarek

at first glance it looks similar to a portion of a kurzhals loop
I also emailed Bob (currently bouncing due to an apparent st olaf spam firewall problem) to correct
the easter monster attribution to JPF
Last edited by gsf on Wed Feb 27, 2008 12:56 pm, edited 1 time in total.
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Postby daj95376 » Wed Feb 27, 2008 2:28 am

tarek wrote:has anyone checked this ?

On another website, Bob Hanson From St. Olaf College wrote:I would appreciate comments regarding www.stolaf.edu/people/hansonr/sudoku/easter_monster.htm
which I believe to be a quite easy solution to the Easter Monster based on Medusa chains and a few new ideas.
Bob Hanson
hansonr@stolaf.edu

tarek

Since it's not the original Easter Monster puzzle presented by JPF, I'm assuming that it's the canonicalized equivalent that was picked up (maybe) from a gsf listing.
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Postby champagne » Wed Feb 27, 2008 10:18 am

I checked quickly Bob proposal.

It seems to be a clone of EM. At least, I got similar results.

Down to that point

"This proves that the two Medusa chains in Blocks 5 and 7 are synced as shown."


This is equivalent to SK loop plus the first step of "couple tags" clearing in my solver proposal.

The way to get "We can set r2c7=1. " is very long compared to a Virus patten analysis or to SK triangular probe.


The so called "Final Analysis" is not developped. It was pretty long in my first shot, it is still a long task with the last version.
We have the same clearing #3r8c7 at that point

Bob can have shorter paths than me using "oriented forcing chains" which are not allowed in my process.

I notice that he started "Strong Chain Pairing Analysis" which seems the only way to crack such puzzles.
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Postby gsf » Wed Feb 27, 2008 5:01 pm

daj95376 wrote:Since it's not the original Easter Monster puzzle presented by JPF, I'm assuming that it's the canonicalized equivalent that was picked up (maybe) from a gsf listing.

[edit: correction due to ronk] it is easter monster in solution row order minlex form (%c in my solver)
Last edited by gsf on Wed Feb 27, 2008 2:08 pm, edited 1 time in total.
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Postby ronk » Wed Feb 27, 2008 5:59 pm

deleted; fully quoted by gsf below
Last edited by ronk on Wed Feb 27, 2008 2:14 pm, edited 1 time in total.
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Postby gsf » Wed Feb 27, 2008 6:10 pm

ronk wrote:Looks like simple row minlex c14n to me. JPF's Easter Monster:
Code: Select all
1.......2.9.4...5...6...7...5.9.3.......7.......85..4.7.....6...3...9.8...2.....1

-qFN -f%#.c of above:
Code: Select all
1......89.....9..2......45...76......3..4....9....2..5..4.7....5....8.1..6.3.....

At the Bob Hanson EM link:
Code: Select all
1......89.....9..2......45...76......3..4....9....2..5..4.7....5....8.1..6.3.....

thanks ronk, I don't know what I was looking at -- I corrected my post
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