The hardest sudokus

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

Postby RW » Sat Dec 02, 2006 10:24 am

dml wrote:But are they the same sudoku? ... Here we have same steps but remove different values in different order.

The only difference in the solutions is the finned Swordfish required to solve r2c4 in dml1. Compared to the overall difficulty of the puzzles, you could say that dml2 is like running a marathon and dml1 is like first clapping your hands, then running a marathon. That difference is not significant enough to make them different efforts.

dml wrote:logically there should be only 1 path to single sudoku after we remove the clones obtained by exchanging the rows,columns,rotations,symmetries,...

There is never only one path to solve a single sudoku. All false candidates can be proven false at any point, depending on what techniques you wish to use. Rating programs like SE that always look for the easiest available move does usually always find the same path for scrambled puzzles. But, occassionaly there could be two moves of the exact same difficulty at some point, depending on which you choose, the remaining solving path can vary a bit. This doesn't affect the rating of the puzzle as SE only rates by the toughest move.

RW
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Postby Carcul » Mon Dec 04, 2006 10:33 am

In Sat Sep 23, 2006 6:05 am, Eioru Wrote:

Code: Select all
 . 2 . | 1 . 6 | . . .
 8 . 6 | . 2 . | . . .
 . 7 . | 3 . . | . . .
-------+-------+-------
 1 . 9 | . . . | . . 4
 . 5 . | . . . | . 7 .
 2 . . | . . . | 9 . 3
-------+-------+-------
 . . . | . . 1 | . 4 .
 . . . | . 5 . | 2 . 8
 . . . | 7 . 9 | . 6 .        ...9.0

 . 2 . | 1 . 3 | . . .
 9 . 8 | . 5 . | . . .
 . 1 . | 4 . . | . . .
-------+-------+-------
 7 . 9 | . . . | . . 5
 . 3 . | . . . | . 4 .
 8 . . | . . . | 6 . 1
-------+-------+-------
 . . . | . . 7 | . 6 .
 . . . | . 6 . | 2 . 3
 . . . | 3 . 2 | . 5 .         ...8.9

For the first puzzle:

Code: Select all
 *------------------------------------------------------------*
 | 3459   2      345 | 1      479    6    | 34578  3589   579 |
 | 8      1349   6   | 459    2      457  | 1347   139    179 |
 | 459    7      145 | 3      49     8    | 1456   1259   26  |
 |-------------------+--------------------+-------------------|
 | 1      368    9   | 568    367    2357 | 568    258    4   |
 | 346    5      348 | 4689   13469  234  | 168    7      26  |
 | 2      468    7   | 4568   146    45   | 9      158    3   |
 |-------------------+--------------------+-------------------|
 | 3569   3689   358 | 2      368    1    | 357    4      579 |
 | 7      13469  134 | 46     5      34   | 2      139    8   |
 | 345    1348   2   | 7      348    9    | 135    6      15  |
 *------------------------------------------------------------*

1. [r5c4]=9=[r2c4]=5=[r2c6]=7=[r4c6]=2=[r5c6]-2-[r5c9]-6-[r5c1]=6=
=[r7c1]-6-[r8c2]=6=[r8c4](-6-[r5c4])-6-[r46c4|r6c6]-4,8-[r5c4], => r5c4<>4,6,8.

2. [r8c8](-1-[r6c8]=1=[r5c7]-1-[r5c5])-1-[r8c36]-4-[r8c4]-6-[r46c4|r6c6]-
-4-[r5c5]: =6=[r5c5](-6-[r5c1])-6—[r5c9]-2-[r5c6]=5=[r9c1]-5-[r9c9]-1-
-[r8c8]; -6-[r5c5]-3-[r4c56]=3=[r8c6]=4=[r8c3]-4-[r9c179]-1-[r8c8], => r8c8<>1.

3. =5=[r9c9](-5-[r9c1])(=1=[r9c7]-1-[r5c7])=1=[r2c9]-1-[r2c2]=1=
=[r8c2]-1-[r8c3|r9c1]-3,4-[r9c2]-8-[r7c3]=8=[r5c3]-8-[r5c7](-6-[r5c1])-
-6-[r5c9]-2-[r5c6]-{TILA(3,4): r5c1|r5c6|r8c6|r8c3|r9c1}, => r9c9<>5.

4. [r8c8]=9=[r7c9]-9-[r2c9]-7-[r2c6]=7|3=[r8c6]-3-[r8c8], => r8c8<>3.

5. [r7c2]=9=[r2c2]-9-[r2c9]-7-[r2c6]=7=[r4c6]=2=[r5c6]-2-[r5c9]-6-
-[r5c1]=6=[r7c1]=9=[r7c2], => r7c2=9.

6. [r4c6]=2=[r4c8]-2-[r5c9]-6-[r5c1]=6=[r7c1]-6-[r8c2]=6=[r8c4]-6-
-[r46c4|r6c6]-5-[r4c6], => r4c6<>5.

7. [r6c6]=5=[r2c6](=7=[r4c6]=2=[r4c8])=7=[r2c7]-7-[r79c7]-5-[r4c7]=
=5=[r6c8]-5-[r6c6], => r6c4<>5, r2c6<>4.

8. [r5c6](=2=[r4c6]-2-[r4c8]=2|3=[r4c2])-4-[r5c13]=4=[r6c2]=8=[r5c3]-
-8-[r7c3]=8=[r7c5]=6=[r8c4]-6-[r46c4|r6c6]-4-[r5c6], r5c6<>4.

9. [r8c4]=6=[r7c5]=8=[r7c3]-8-[r5c3]=8=[r5c7]=1=[r6c8]=5=[r6c6]=4=
=[r8c6]-4-[r8c4], => r8c4<>4.

10. [r3c7]=6=[r3c9]=2=[r5c9]-2-[r5c136]-8-[r6c2]-6-[r6c5]-1-[r6c8]=1=
=[r5c7]-1-[r3c7], => r3c7<>1, r5c7<>6.

11. [r5c3]=8=[r5c7](=1=[r6c8]=5=[r6c6]=4=[r8c6]-4-[r8c23])=1=[r2c7]
=7=[r2c6]=5=[r2c4]=4=[r2c2]-4-[r9c2]=4=[r9c1]=5=[r7c3]=8=[r5c3], => r5c3=8 and the puzzle is solved.

For the second puzzle:

Code: Select all
 *----------------------------------------------------------------------*
 | 456     2       4567 | 1       789     3     | 45789   789     46789 |
 | 9       47      8    | 27      5       6     | 13      13      247   |
 | 356     1       3567 | 4       2789    89    | 5789    2789    26789 |
 |----------------------+-----------------------+-----------------------|
 | 7       46      9    | 268     12348   148   | 38      238     5     |
 | 1256    3       1256 | 256789  2789    589   | 789     4       2789  |
 | 8       45      245  | 2579    23479   459   | 6       2379    1     |
 |----------------------+-----------------------+-----------------------|
 | 23      4589    23   | 589     1489    7     | 1489    6       489   |
 | 145     45789   1457 | 589     6       14589 | 2       1789    3     |
 | 146     46789   1467 | 3       1489    2     | 14789   5       4789  |
 *----------------------------------------------------------------------*

1. [r56c4]-5-[r7c4]=5=[r7c2]-5-[r6c2](-4-[r2c2]-7-[r2c4])-4-[r4c2]-6-
-[r4c4]=6=[r5c4]=7=[r6c4], => r5c4/r6c4<>5.

2. -2-[r6c3]{=2|9=[r6c6](-9-[r6c8])-9-[r26c4]-2-[r4c4]}=2=[r5c13]-2-
-[r5c4579]=2|6=[r5c4]-6-[r4c4](-8-[r4c5])(=6=[r4c2]-6-[r9c2])-8-
-[r4c78](-2,3-[r4c5]){-3-[r2c7]-1-[r79c7]=1=[r8c8](-1-[r8c13])-1-
-[r8c6]=1=[r4c6]-1-[r4c5]}-2,3-[r5c79|r6c8]-8,9-[r5c5]-7-[r13c5]
=7=[r2c4]-7-[r2c2]-4-[r789c2]=4=[r8c13]-4-[r8c6]=4=[r46c6]-4-
-[r4c5]
, => r6c3=2.

3. [r9c2]=6=[r4c2]-6-[r4c4](-8-[r4c5])-8-[r4c78](-2,3-[r4c5])-3-[r2c7]-1-
-[r79c7]=1=[r8c8](-1-[r8c13])-1-[r8c6]=1=[r4c6]-1-[r4c5]-4-[r79c5]=4=
=[r8c6]-4-[r8c13]=4,1=[r9c13]=6=[r9c2], => r9c2=6 solving the puzzle.

Carcul
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Postby ravel » Mon Dec 04, 2006 12:16 pm

Nice to see a Carcul solution in this thread, thanx.

Finally i have the ratings for Tarek's last lists. 75% of the puzzles qualified !

Code: Select all
Aries: 10 steps

Daemonicus (10 of 18 qualified)
18: 2
11: 16
10: 17,18
9: 8,13,14
8: 6,11,15

Fluid Drives 9-41 (28 of 33 qualified)
16: 12
15: 18
13: 23,30,43,41
12: 9,13,14,39
11: 16,38,40
10: 15,19,28,32
9:  10,17,21,22,26,27
8:  11,24,29,35,37

Pincer: 11

dml,

congratulations to your puzzle. It is leader now in the gsf and ER ratings (my program cant rate it, like the next 10 puzzles). And the only one in the top ten that does not have a diagonal pattern with an empty box. I added it to the top lists.
I will insert it into my list, when i have scanned Ocean's last puzzle list (the last of Meralla's puzzles also qualifies with 10 steps, but not RW's Mjolnir).

I dont accept non mimimal versions of the same puzzle in the list, also if they would qualify. The reason is, that with a solution for the minimal puzzle you always have a solution for the non minimal one (with possibly redundant steps), though there might be an "easier" solution for the latter. So i only take a hardest one of such a sudoku family.
ravel
 
Posts: 998
Joined: 21 February 2006

Postby tarek » Tue Dec 05, 2006 6:29 pm

Great work again ravel, I will kepp on repeating every now & then the amount of effort you are putting into this so that it wouldn't be taken for granted.....

That & to feel less guilty when I post my next collection of puzzles:D

tarek
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Posts: 2622
Joined: 05 January 2006

Postby dml » Tue Dec 05, 2006 7:21 pm

RW wrote:
dml wrote:But are they the same sudoku? ... Here we have same steps but remove different values in different order.

The only difference in the solutions is the finned Swordfish required to solve r2c4 in dml1. Compared to the overall difficulty of the puzzles, you could say that dml2 is like running a marathon and dml1 is like first clapping your hands, then running a marathon. That difference is not significant enough to make them different efforts.

RW


some others marathons to run:)

Some are very close to each others , some quite different
Take the most interesting in your suites

Most of them ranked between 10.4 and 10.5
Cannot we get finer resolution in difficulties ?

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800003000070060090004500000005200003090000070100000800000007002030010060000800500 99948
800003000070060090004500000005100008020000030900000700000008005060070020000900100 99948
800003000070060090004500000005100003090000070200000800000007001030020060000800500 99948
800003000070060020004500000005900008010000030200000700000008005060070010000200900 99948
800003000070060020004500000005900003020000070100000800000007009030010060000800500 99948
800003000070060020004500000005100008090000030200000700000008005060070090000200100 99948
800003000070060020004500000005100003020000070900000800000007001030090060000800500 99948
800003000070060010004500000005900008020000030100000700000008005060070020000100900 99948
800003000070060010004500000005900003010000070200000800000007009030020060000800500 99948
800003000070060010004500000005200008090000030100000700000008005060070090000100200 99948
800003000070060010004500000005200003010000070900000800000007002030090060000800500 99948
700003000090040050006800000008007006020000090400000300000006001030050040000200800 99948
700003000090040050006800000008007006010000090400000300000006002030050040000100800 99948
700003000090040050006800000005006007080000020300000400000007001020090080000500300 99948
700003000090040050006800000005006007080000010300000400000007002010090080000500300 99948
700003000090040020006800000008007006050000090400000300000006001030020040000500800 99948
700003000090040020006800000008007006010000090400000300000006005030020040000100800 99948
700003000090040020006800000002006007080000050300000400000007001050090080000200300 99948
700003000090040020006800000002006007080000010300000400000007005010090080000200300 99948
700003000090040010006800000008007006050000090400000300000006002030010040000500800 99948
700003000090040010006800000008007006020000090400000300000006005030010040000200800 99948
700003000090040010006800000001006007080000050300000400000007002050090080000100300 99948
700003000090040010006800000001006007080000020300000400000007005020090080000100300 99948
700002000080050030009100000003009007010000060200000500000007004060080010000300200 99948
700002000080050030009100000003009007010000040200000500000007006040080010000300200 99948
700002000080050030009100000001007009060000080500000200000009004020030050000600100 99948
700002000080050030009100000001007009040000080500000200000009006020030050000400100 99948
600001000020050030009400000004800006070000010300000200000006004050020070000300800 99948
600001000020050030009400000004800001030000020700000600000002008010070050000600400 99948
600001000020050030009400000004700006080000010300000200000006004050020080000300700 99948
600001000020050030009400000004700001030000020800000600000002007010080050000600400 99948
500001000040030020006700000002006005070000090100000300000005008090040070000200100 99948
500001000040030020006700000002006005070000080100000300000005009080040070000200100 99948
400009000050010030006700000008000006030000050900002700000006009070080010000500200 99948
400009000050010030006700000003000005080000070900002600000003002010050080000600900 99948
400009000050010030006700000003000005020000070900008600000003008010050020000600900 99948
400009000050010030006700000002000006030000050900008700000006009070020010000500800 99948
400009000050010020006700000008000006020000050900003700000
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Postby ronk » Tue Dec 05, 2006 10:10 pm

dml wrote:Some are very close to each others , some quite different
Take the most interesting in your suites

Most of them ranked between 10.4 and 10.5
Cannot we get finer resolution in difficulties ?

800003000070060010004500000009000008020001030600000400000002005030070060000400900 #99995

(725 puzzles deleted here)

400009000050010030006700000002000006030000050900008700000006009070020010000500800 #99948

There are only 8 non-isomorphic puzzles in your list of 727.Therefore, in an ideal ratings world, I would expect only 8 different difficulty ratings.
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Postby RW » Tue Dec 05, 2006 10:21 pm

ronk wrote:There are only 8 non-isomorphic puzzles in your list of 727.Therefore, in an ideal ratings world, I would expect only 8 different difficulty ratings.

And in an ideal posting world, the poster would only post the 8 non-isomorphic puzzles.

RW
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Postby ravel » Wed Dec 06, 2006 5:57 pm

Ocean's Mjolnir list (plus 2 M21) was rated following:
14,11,13,<8,12,15,<8,<8,<8,8,11,17,17

I added the puzzles to the list and also Meralla's puzzle.

dml,
4 of your 8 puzzles are leaders now both in ER and gsf's rating (but not the same 4) ! The patterns you use, 18 fixed cells and 3 boxes with 1 clue, seem to be extremely fruitful for ultrahard puzzles.

Please note, that you can also canonicalize puzzles with gsf's program using the options
-qFN -f%#0c
For equivalent puzzles the canonicalized versions are identical.
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Postby dml » Wed Dec 06, 2006 6:57 pm

ravel wrote:Ocean's Mjolnir list (plus 2 M21) was rated following:
14,11,13,<8,12,15,<8,<8,<8,8,11,17,17

I added the puzzles to the list and also Meralla's puzzle.

dml,
4 of your 8 puzzles are leaders now both in ER and gsf's rating (but not the same 4) ! The patterns you use, 18 fixed cells and 3 boxes with 1 clue, seem to be extremely fruitful for ultrahard puzzles.

Please note, that you can also canonicalize puzzles with gsf's program using the options
-qFN -f%#0c
For equivalent puzzles the canonicalized versions are identical.


Thanks for giving me a way to isolate canonical forms
I was writing a program to do that , but you already made it : cool

I should recognize that I have not red all the posts and I am quite new with sudoku , working on that since only 3 weeks when a friend referenced to me an article on the hardest sudoku found by a finnish mathematician
It was puzzling for me that we could rate the sudoku

I wrote various programs and after 1 week somebody pointed me on that forum

In fact I dont know how to solve the sodoku, I build some sudokus and ask my wife and children to resolve them and wait explanations on technics they use to progress
After I find ways to put them in difficulties
I am happy to have succeeded beyond expectations

Are there some forms or properties you would like to find even in less high ranked forms?
I say that because I have a very large list of sudokus >99000 , with probably dominant canonical forms , but maybe many others forms could be interesting. Or is it just >99900 that make the interest?
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Postby Ocean » Wed Dec 06, 2006 7:30 pm

ravel wrote:Ocean's Mjolnir list (plus 2 M21) was rated following:
14,11,13,<8,12,15,<8,<8,<8,8,11,17,17

I added the puzzles to the list and also Meralla's puzzle.

Thank you, Ravel, for doing this work! (I feel a bit guilty because I have posted so many puzzles here).

dml: Very nice findings!!
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Postby tarek » Wed Dec 06, 2006 8:06 pm

dml wrote:I am quite new with sudoku , working on that since only 3 weeks when a friend referenced to me an article on the hardest sudoku found by a finnish mathematician

A 3 weeker sudoku novice ......... Well done dml ........ some mathematicians needed 3+ months to achieve a result.

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Postby ravel » Wed Dec 06, 2006 8:37 pm

dml wrote:Thanks for giving me a way to isolate canonical forms
I was writing a program to do that , but you already made it : cool
Yes, thanks to gsf, his program is most useful.
I should recognize that I have not red all the posts and I am quite new with sudoku , working on that since only 3 weeks ...
very impressing
Are there some forms or properties you would like to find even in less high ranked forms?
I say that because I have a very large list of sudokus >99000 , with probably dominant canonical forms , but maybe many others forms could be interesting. Or is it just >99900 that make the interest?
For a longer time now it seemed, that only puzzles with a "diagonal pattern"
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 | . . x | . . x |
 +-------+-------+-------+
have chances for the top hardest, but your patterns cannot be transformed to that (by equivalence operations like described here). So we are interested in other patterns, that allow such hard sudokus.
Of course you can send a list with the puzzles highest rated by gsf's program (but please not more than 50 at a time:) )
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Postby RW » Thu Dec 07, 2006 11:01 am

ravel wrote:For a longer time now it seemed, that only puzzles with a "diagonal pattern" ... have chances for the top hardest

Wasn't this originally defined as:
tso wrote:"Puzzles generated with no more than 3 givens per box in which no two givens are in the same row or column have a greater chance of being more difficult than others."

In puzzles like this, no two clues are in the same two groups. Maybe *that's* the rule of thumb:

"Puzzles in which no two clues are in two groups are more likely to be very difficult others."

dml's puzzles do fulfill these criteria. I always wondered why so few diagonal puzzles were made that cannot be transformed to have all diagonals in the same direction.

RW
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Ravel's Work

Postby gurth » Thu Dec 07, 2006 11:11 am

tarek wrote:Great work again ravel, I will kepp on repeating every now & then the amount of effort you are putting into this so that it wouldn't be taken for granted.....

That & to feel less guilty when I post my next collection of puzzles:D

tarek


Ravel, I would also like to voice my thanks and appreciation for all the work you do to organise the puzzles and their solutions.

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Postby ravel » Thu Dec 07, 2006 12:35 pm

Oh yes, RW, i had forgotten this fine observation by tso - and the puzzle creators also, it seems.

Thanks to Tarek and gurth for the compliment.
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