## The hardest sudokus

Everything about Sudoku that doesn't fit in one of the other sections
Very impressing to see how the "toughest" have progressed during the past 6 months. If you want a date for the Escargot, it was first published in "Aamulehti" on October 25th 2006. Thanks again ravel for the hard work!

RW
RW
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### Duplicates

Hey Ravel, you have at least 6 pairs of isomorphic puzzles in your recent list and I suspect there are more.
The culprits are (I had 8 pairs of suspects, but 2 were non isomorphic, I checked them by hand)

dml155 - dml11
dml13 - dml14
dml35 - dml36
dml22- dml160
dml159- dml20
dml26 - dml29

I suggest that someone with a program that can check for duplicates scans your list and then he or she posts the duplicates.

Here are the details (I only post the permutations, the other steps I did not write it down, sorry):

dml155-dml11, in dml155 permute:
1-6
2-8
3-4
4-1
5-2
6-7
7-9
8-3
9-5, and the rest is easy, only swap columns, rows, etc.

dml13-dml14, in dml13 permute:
1-2
2-5
3-3
4-4
5-7
6-6
7-1
8-8
9-9 then swap rows, etc

dml36-dml35, in dml36 permute
1-4
2-2
3-6
4-7
5-9
6-3
7-5
8-1
9-8 and then swap rows, etc

dml22-dml160, in dml22 permute
1-5
2-6
3-8
4-4
5-2
6-9
7-7
8-3
9-1 and then swap rows, etc

In this last two I am not sure what sudoku I began with to see that they are isomorphic.
dml159-dml20, permute
1-8
2-3
3-1
4-4
5-5
6-6
7-7
8-2
9-9 and the rest is easy

dml26-dml29, permute
1-7
2-9
3-2
4-4
5-8
6-3
7-5
8-6
9-1 and the rest is easy.

I noted that there are non minimal sudokus in your list too, I though that you only added minimal sudokus to your list.

Mauricio.
Mauricio

Posts: 1174
Joined: 22 March 2006

### Re: Duplicates

Mauricio wrote:Hey Ravel, you have at least 6 pairs of isomorphic puzzles in your recent list and I suspect there are more.
The culprits are (I had 8 pairs of suspects, but 2 were non isomorphic, I checked them by hand)

dml155 - dml11
dml13 - dml14
dml35 - dml36
dml22- dml160
dml159- dml20
dml26 - dml29

I suggest that someone with a program that can check for duplicates scans your list and then he or she posts the duplicates.

I checked the List with all puzzles here and found only two equivalents, naye duplicates. Puzzle #181 is a duplicate of #149 ... and #190 is a duplicate of #131.

I found only 196 unique solutions. Combining your 6 plus my 2 would be 204-6-2=196. Are you maybe permuting solutions rather than puzzles?
ronk
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Location: Southeastern USA

### Re: Duplicates

Mauricio wrote:Hey Ravel, you have at least 6 pairs of isomorphic puzzles in your recent list and I suspect there are more.

the dml puzzles have 13 dup pairs
here they are with the dml number in "..."
each pair followed by the (value row col) permutations that map the first to the second (-P option in my solver)

002600000030080000500009010004000002070010030900000500000005006100070090000200400 "40"
000050009000100070080006400200090000001700800030004000060800100007000002900000050 "43"
v894572631r465132879c465123879

002100000030080000500006400007000001090000020600005300000009008000020070400300600 "18"
003000600400009070080000001200070040000600800000003005060010000007500000900004020 "23"
v167294853r789312654c132546879

002900000030040010500006000008700002010000030400000500000002006000080040009300700 "37"
003050000400009000080100060010000070005000002900004300070060090000200001000003800 "39"
v419352687r465321897c312879564

003200000040090000600008010200000003010006040007000500000001002090040060000500700 "15"
100700000020030000004009005600000100070000020009040003000200600003080040000005009 "158"
v427963185r465231897c231798465

003500100040080000600009000800000002050700030001000400000006009000020080070100500 "22"
100900000020080050003004000900000100050007020006000003000300600000050040070002008 "160"
v568429731r231798465c465231897

100006000020070030005900000009005001070000020600000400300001006000040070000200800 "21"
003400000050009000700020010040300900000070020000005006002000008600000070090001500 "24"
v921645783r231456987c654312987

002600100030080000500009000006500002070000030100000400000003009000070080400100600 "38"
003400009000080200000006050200000100005000040070900003060002000800010000004300070 "42"
v352974186r312879654c645987123

002900000030080000400001050009070002010000030600000400000003001000060080007200900 "26"
020000600400080007009000010005001090000700002000060300300004000070020000001900500 "29"
v792483561r312987564c123879654

002900001030040000500006000008000002040000030900700500600001009000030040000200700 "35"
020050080006100000700003000000600001300008050000020400500040700090000020001000006 "36"
v826173495r123897546c132546798

003900000040070001600002000800000002070050030009000400200001008000040050000600900 "12"
100800000020090050004003000900000100080007020006000003000100600000050080003004007 "156"
v739856241r456321987c321789456

002100700030050000400006000001900002080000030700000400000008006000030050900400100 "13"
020400009006080000700003000000007300000060004010200050300000800005900020040000001 "14"
v253476189r645879231c978465213

100050000006009000080200004040030008007000060900000100030800002000004050000010700 "11"
100900000020050030004006000600000100030080020007000004000300700000020050080004009 "155"
v458391627r978213546c654897312

100050080000009003000200400004000900030000007800600050002800060500010000070004000 "20"
100500300020070000004008000500006100070000020009000004000300500000040090600001008 "159"
v382456719r789321645c123978645

for those interested here is the pipeline that generated the above from an
input file that labeled each puzzle with the original dml number in "..."
Code: Select all
`sudoku -qFN -f'%#0c %#0v "%i"' h-dml.dat |sort |uniq -Dseparate -w81 |cut -d' ' -f2-3 |sudoku -qFN -P -Fb'%#0v "%i"'`

the list of all puzzles at the end of the first post has two occurences of each of these
Code: Select all
`001002000030040050600700800008000007010000030900000500002001006040050020000600900500004300070020000008100006009000007010000080400000200900003700000040050006700001`

(both occurences exactly the same) and there are no other isomorphic dups
so it looks like not all of the dml puzzles are in that list
gsf
2014 Supporter

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

Many thanks, Mauricio, Ron and gsf.

I have not noticed that merallas had reposted a puzzle by Tarek, the second identical puzzle was due to a copy mistake, it is to replace by dml9.

I also thought that dml would check for isomorphic puzzles now.

As soon as i find the time, i will reorganize the list.

[Added:] gsf, i just noticed, that i got slightly different ratings for the isomorphic dml21 and dml24 (99954 and 99951).
ravel

Posts: 998
Joined: 21 February 2006

ravel wrote:
I also thought that dml would check for isomorphic puzzles now.

I am checking, probably some error or I am not using the good list of submitted sudokus
I will review the process, probably good to doublecheck this anyway : this is not an expensive task

Generally I post the highest ranked isomorphic version , because generally I have lot of them, for me it is expensive to find the highest ranked version
dml

Posts: 34
Joined: 12 November 2006

ravel wrote:[Added:] gsf, i just noticed, that i got slightly different ratings for the isomorphic dml21 and dml24 (99954 and 99951).

although batching helps, some of the lower level techniques are sensitive to
orientation, and this creeps into the proposition logic
gsf
2014 Supporter

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

gsf wrote:
ravel wrote:[Added:] gsf, i just noticed, that i got slightly different ratings for the isomorphic dml21 and dml24 (99954 and 99951).

although batching helps, some of the lower level techniques are sensitive to
orientation, and this creeps into the proposition logic

May be another option should be added to the program..........

-RGIx where x>1 : basically it goes through the same process again but with a random isomorhphic puzzle up to x times & returns the samllest rating (RGI:randomly generated isomorph )

Merry Christmas

Tarek

tarek

Posts: 2760
Joined: 05 January 2006

Here is a Christmas present for gsf:
Code: Select all
`## gsfr: "no-solution" (or more correct: no rating)# ER: 10.7# *-----------* |...|..1|.2.| |3..|.4.|5..| |...|6..|..7| |---+---+---| |..2|...|..6| |.5.|.3.|.8.| |4..|...|9..| |---+---+---| |9..|..2|...| |.8.|.5.|4..| |..1|7..|...| *-----------*`
Ocean

Posts: 442
Joined: 29 August 2005

tarek wrote:
gsf wrote:
ravel wrote:[Added:] gsf, i just noticed, that i got slightly different ratings for the isomorphic dml21 and dml24 (99954 and 99951).

although batching helps, some of the lower level techniques are sensitive to
orientation, and this creeps into the proposition logic

May be another option should be added to the program..........

-RGIx where x>1 : basically it goes through the same process again but with a random isomorhphic puzzle up to x times & returns the samllest rating (RGI:randomly generated isomorph )

Merry Christmas

yes, Merry Christmas to all
random re-run would be a last resort
better would be to understand why portions of the algorithm(s), despite
intentions, are still sensitive to isomorphic permutations
gsf
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Posts: 7306
Joined: 21 September 2005
Location: NJ USA

Ocean wrote:Here is a Christmas present for gsf:
Code: Select all
`# gsfr: "no-solution" (or more correct: no rating)# ER: 10.7 *-----------* |...|..1|.2.| |3..|.4.|5..| |...|6..|..7| |---+---+---| |..2|...|..6| |.5.|.3.|.8.| |4..|...|9..| |---+---+---| |9..|..2|...| |.8.|.5.|4..| |..1|7..|...| *-----------*`

so you don't want me to rest easy this Christmas
at least it doesn't break the singles backdoor conjecture (its singles 2-constrained)

here's the point where the propositions including multicoloring stall
Code: Select all
` 5678   4679  456789 |  35     789     1   |  368     2    3489     3    1267    678  |  289     4     789  |   5     169    189   1258   1249   4589  |   6     289    35   |  138    349     7   ---------------------+---------------------+---------------------  178   1379     2   | 14589  1789   45789 |  137   3457     6     167     5     679  | 1249     3    4679  |  127     8     124     4    1367   3678  |  128   12678  5678  |   9    1357   1235  ---------------------+---------------------+---------------------   9    3467   34567 | 1348    168     2   | 13678  13567  1358    267     8     367  |  139     5     369  |   4    1679   1239    256   2346     1   |   7     689   3489  | 2368   3569   23589 `

my solver doesn't do als/fins/kracken
do any of those solvers make progress at this point?
the backdoors point to [69]=2 as a possible key
gsf
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Posts: 7306
Joined: 21 September 2005
Location: NJ USA

What a discovery before Christmas! Congrats Ocean!

Who will take the honour to name this monster diamond? Could it be named the "Heart of the Ocean", or should we save it for even bigger diamonds?

BTW gsf, could you list out the backdoor twin cells to solve it with singles please? Thanks!
udosuk

Posts: 2698
Joined: 17 July 2005

udosuk wrote:BTW gsf, could you list out the backdoor twin cells to solve it with singles please? Thanks!

here's the command
Code: Select all
`sudoku -qFN -f%#Am ocean.dat`

and the output
Code: Select all
`[11]6{[69]2}[15]7{[69]2}[17]3{[69]2}[23]7{[69]2}[26]8{[69]2}[54]2{[83]6}[66]7{[69]2}[69]2{[83]6}`
gsf
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Joined: 21 September 2005
Location: NJ USA

gsf wrote:here's the point where the propositions including multicoloring stall

Thanks for the analysis!

Have been busy with other things lately, but enjoyed to watch the many new contributions and continuous interest in this thread. Tried to check some of the pattern types that were so successful for dml, and suddenly the one with this unusual feature emerged. (Glad you liked it, udosuk). A bit curious about how common these kinds of puzzles are.
Ocean

Posts: 442
Joined: 29 August 2005

Very nice puzzle Ocean!! My prophecy from Nov 14th turned out to be true! I knew this day would come, what would be the next milestone? A puzzle that cannot be solved by nested propositions... sounds very unlikely, but who knows... Maybe we should first aim for something easier: the ER 11! Does it exist? I think so. Can anyone find it? I hope so.

RW
RW
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Joined: 16 March 2006

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