## The hardest sudokus

Everything about Sudoku that doesn't fit in one of the other sections
Thanks gsf for the listing...

So, there are only 8 pairs of backdoor twins (for singles), and the cell r6c9=2 is featured predominantly...

So, we can group them out like this:
[69]2 + {[11]6,[15]7,[17]3,[23]7,[26]8,[66]7,[83]6}
[54]2 + [83]6
[83]6 + {[54]2,[69]2} (repeated above)

It'd be interesting to see the SE rating when [69]2 or [54]2 or [83]6 is set... However, since the original puzzle is solved by SE with a 10.7 rating, I presume there is a way to solve it without prepositions? Possibily some 38-step intersecting forcing chains which no human (except Carcul) can understand...
udosuk

Posts: 2698
Joined: 17 July 2005

udosuk wrote:However, since the original puzzle is solved by SE with a 10.7 rating, I presume there is a way to solve it without prepositions?

Hmm... I'd say it isn't. IMO SE's forcing chains are in the end no different from the propositions made by gsf's program. Only difference is that SE has a nice way of showing the step by step path from the proposition to the contradiction. In fact, SE uses double propositions (nested forcing chains) to solve this puzzle, single propositions are not enough to solve it (unless there is some eliminations using UR, XY-wing or similar within the propositions).

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

Ocean wrote:Tried to check some of the pattern types that were so successful for dml, and suddenly the one with this unusual feature emerged. . A bit curious about how common these kinds of puzzles are.

Yes this pattern is extremelly rich , there are probably millions of candidates >99900
If you find a sudoku with similar properties you have 97% probability to be >99000 !!!
1 every 70 is greater than 99500
1 every 2000 is greater than 99900

Then everybody can enter in the 99900 list
dml

Posts: 34
Joined: 12 November 2006

dml wrote:If you find a sudoku with similar properties you have 97% probability to be >99000 !!!
1 every 70 is greater than 99500
1 every 2000 is greater than 99900

Is that after filtering out isomophic equivalents?
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

ronk wrote:
dml wrote:If you find a sudoku with similar properties you have 97% probability to be >99000 !!!
1 every 70 is greater than 99500
1 every 2000 is greater than 99900

Is that after filtering out isomophic equivalents?

No filtering, this give your probability to find 1 for a specific form

The way my programs are constructed I have lot of isomorphic forms
I am trying to find a way to have less isomorphic forms and explore more systematically this patterns and some variants

I am sure there are many others much harder sudokus around there
But it's harder and harder to find them like climbing The Himalaya, the last meters are those that count.
I think we are in the base camp.
dml

Posts: 34
Joined: 12 November 2006

RW wrote:IMO SE's forcing chains are in the end no different from the propositions made by gsf's program. Only difference is that SE has a nice way of showing the step by step path from the proposition to the contradiction. In fact, SE uses double propositions (nested forcing chains) to solve this puzzle, single propositions are not enough to solve it (unless there is some eliminations using UR, XY-wing or similar within the propositions).

you can use these options to see the results of propositions using all constraints
Code: Select all
`-v2 -q+P-G`

-v2 will show the basic constraints applied plus the proposition results
-v3 will show details of each proposition (P) with results
Code: Select all
`D (deadend) contradictionS solutionotherwise inconclusive`

-q+P-G adds propositions to the constraints (+P) but disables guessing (-G) aka backtrack tree search
you can allow guessing to see how multi-tier propositions fare with -q+P (nested forcing chains)

the -v output models the constraints applied, not english, but the info is all there
this models the software architecture where new constraint methods are
easily added by assigning a constraint function to a letter -- all of the other

use --man output to map constraint letters like FNBTHWXYPG to english names

Code: Select all
`-Fpr%rc%c -Fe= -Fn'<>'`

or gurth's modified chess notation
Code: Select all
`-Fp%kc%r`
gsf
2014 Supporter

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

Ocean,

congratulations to this puzzle. Indeed a new milestone.
I added it as number 0 to my list, which i have reorganized (hopefully) for the last time.
ravel

Posts: 998
Joined: 21 February 2006

Finally a puzzle which is extreme and needs all power of my program. My program is not so fast, so more than 30 minutes were needed (not exactly known, because went threw midnight). But that is because r1c3=8 instead of e.g. 1.

To Ravel
" 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."

Sorry for the confusion. It was not my intension to add a new difficult sudoku. I only was wondering why my program had so much problem to solve them, while they are not known as very difficult.

merallas.
merallas

Posts: 39
Joined: 26 September 2006

To compare Ocean's Christmas present and dml11 i used a greedy method to find solutions with subnets (not yet automised), where following techniques were used (for solving and contradiction chains and subchains): Singles, Locked Candidates, Locked Sets (tuples) and x-wing.

Ocean's Christmas present for gsf:
1. r3c8<>4(r1c4<>5,r3c2<>4,r3c1<>2,r4c2<>9,r8c2<>1,r5c6<>4,r7c4<>1)
2. r4c6<>4(r3c5<>1,r1c4<>5,r3c3<>9,r5c7<>2)
3. r1c4<>3
4. r2c2<>1
5. r2c8<>9
6. r8c8<>9
7. r3c1<>5
8. r6c5<>6
9. r1c7<>6
10. r2c2<>7

dml11:
1. r5c7<>4 (r4c3<>1, r2c9<>1, r4c4<>9, r3c7<>6, r1c7<>6, r5c1<>8, r6c8<>3, r8c3<>2)
2. r3c6<>1 (r2c9<>5, r4c6<>7, r2c8<>1, r1c6<>8, r6c3<>9, r1c3<>4)
3. r6c2<>2
4. r1c3<>4

A possible rating then could be: 1 point for each contradiction chain and 3 extra points for a chain that needs sub contradiction chains. Then the result would be 27 to 24.
ravel

Posts: 998
Joined: 21 February 2006

### Ocean's Christmas present

First Thanks for this puzzle.
No technics for begin So I imagine a new way to approch the problem
It's NOT a Technic. Perhaps I'm lucky but I win

The idea is :

When a grid is solve the digits can be ineverted so the first rtow began 123456789
in our present
So if we just invert row 1 and 2 we have the maximum of clues by row(3)
on the row 1

the block is now

3...4.5..
.....1.2.
...6....7

Now we can permute the digits of all the clues to have
1...5.7..
.....3.2.
...6....4

Now if we try the value
123456789 in row 1 it's impossible because of digit 4 of row 3
it a 6 but a six could not be here conflict with digit 6 of row 1
If we study all the given clued of the digit
and memorize all permutations we will gat

At end the puzzle is

1____5_7__
______9_2_
___8_____3
__2______8
_7__1__6_
5_____4__
4____2___
_6__7_5__
__93_____

Now you CAN TRY to set the first row to 123456789
With 6 news clues the solution is neer!

Remplace the number at- inverse en you got the god problem with the good solution

The method is perhaps strange but Ocean your present is hard!
I have programmed the fuunction (if you are interexted gsf)
and I don't found at yet problem that resist bu I, just write it today
no many test!!!

For the creator of puzzle I write a code to detect if the grids is multi solution or no WITHOUT solve it (it's very fast)
You give positions of the clues, a valid grid and the soft detect if this disposition (clues+grids) have multi solution
but don't say if the disposition is good but it's not very hard to add
If some creators want to TEST my work I will be happy

Have a lot of .....

Papy
Papy

Posts: 131
Joined: 15 August 2006

Thanks to RW, dml, ravel, merallas, Papy, gurth, StrmCkr and ronk (in addition to gsf and udosuk) for comments, compliments, analysis, solutions, statistics, new ideas, etc!

RW wrote: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

Code: Select all
`## New Year's present for RW:# gsfr: "no-solution" (or: no rating)# ER: 11.2# 1 x Dynamic Contradiction Forcing Chains (+ Multiple Forcing Chains) - with 55 'views'.# *-----------* |...|..1|.2.| |3..|.4.|5..| |...|6..|..7| |---+---+---| |..2|...|..1| |.8.|.9.|.3.| |4..|...|8..| |---+---+---| |5..|..2|...| |.9.|.3.|4..| |..6|7..|...| *-----------*`

ravel wrote:To compare Ocean's Christmas present and dml11 i used a greedy method to find solutions with subnets (not yet automised), where following techniques were used (for solving and contradiction chains and subchains): Singles, Locked Candidates, Locked Sets (tuples) and x-wing.

Again, thanks ravel for the time and effort you put into rating the hardest, and into development of the methodology!
So, here is my New Year's present for you: A test package with some diversity. All four sudokus are currently beyond gsfr-rating, and they are easy starters, since the first digit is found by basic methods. Explainer ratings from 10.7 to 10.5, and with varying number of hardest steps.

#
# New Year's present for ravel:
#
000001020300040500000600001001000007050030040800000900400002000090050800006700000 # ER=10.7
000001020300040500000600007001000006040080090500000300800002000050090400006700000 # ER=10.6
000001020300040500000600007001000006050080030900000400800007000040050900006200000 # ER=10.5
000001020300040500000600007001000006080050040900000800500007000040080900006200000 # ER=10.5
Last edited by Ocean on Wed Jan 03, 2007 6:21 am, edited 1 time in total.
Ocean

Posts: 442
Joined: 29 August 2005

sweet !!! you broke 11.0 rateing congradulations ocean! another milestone.

i'll see what i can get for a solution.

this is going to take a bit as (the last thing i was testing proved invalid by myown work...)
Some do, some teach, the rest look it up.

StrmCkr

Posts: 862
Joined: 05 September 2006

Ocean,

thanks for the presents, they come in time for me to test my new program - and in time to keep you on top of the current ranking
Since my program now is about as slow as Sudoku Explainer, i have to improve some things and it will take some time, until i can start a new thread. At least it was good to see, that so far it does not get stuck.

I have scanned now the list down to the puzzles with RMS 20. Not very surprising the ranking often is rather different to gsfr and ER. Some of the puzzles that i could not rate before were downrated very much.

This is a temporary top ten list with the solutions i found, followed by a list with all puzzles i scanned (new rating, where a subnet counts 3 extra points, ER, gsfr, gsfrX or new rating, RMS, ER resp.)
Code: Select all
`1. Ocean's New Year's present for RW28 11.2 00000 000000 000001020300040500000600007002000001080090030400000800500002000090030400006700000r2c2<>6(r1c4<>9,r2c6<>7,r1c1<>8),r2c9<>9,r3c7<>1(r1c4<>9,r6c5<>1,r2c2<>2,r3c8<>4,r4c2<>5),r9c5<>1,r4c8<>9,r9c9<>3(r7c4<>9,r1c4<>9,r1c2<>5),r4c5<>8,r2c2<>12. dml16124 10.6 99953 099993 100300000020090400005007000800000100040000020007060003000400800000020090006005007r2c3<>3(r7c9<>2,r6c4<>8,r2c9<>1,r8c9<>4,r2c8<>1,r5c1<>6,r1c2<>8),r3c4<>6,r1c3<>9,r5c3<>1,r6c7<>5(r7c6<>6,r1c5<>5),r3c4<>2,r2c4<>6,r1c2<>7,r1c2<>63. dml4824 10.5 99918 099921 100007000020080000004300500005400001080000020900000300000005007000020060003100900r1c2<>3(r4c6<>8,r1c5<>4,r2c7<>1,r1c7<>2,r8c4<>7,r1c7<>4),r1c8<>9,r8c9<>5,r1c4<>2(r3c1<>7,r6c8<>7,r6c5<>5,r4c8<>9),r1c8<>4,r8c6<>4,r1c4<>94. dml1123 10.7 99993 100013 100050000006009000080200004040030008007000060900000100030800002000004050000010700r4c4<>9(r2c9<>5,r3c1<>3,r5c7<>4),r4c3<>1,r9c8<>4,r5c1<>8(r2c9<>1,r1c9<>6,r5c4<>9,r4c1<>6),r6c8<>3,r1c6<>8,r8c5<>2,r1c3<>4,r2c2<>2,r1c2<>95. dml1223 10.7 99984 099994 003900000040070001600002000800000002070050030009000400200001008000040050000600900r2c1<>5(r1c2<>2,r5c1<>1),r3c9<>3,r6c5<>2(r4c5<>6,r7c7<>6),r5c6<>4,r3c8<>9(r6c5<>8,r2c6<>6,r3c4<>4,r1c2<>2),r1c2<>16. dml2023 10.7 99954 099994 100050080000009003000200400004000900030000007800600050002800060500010000070004000r3c1<>3(r2c1<>4,r7c2<>9,r6c5<>9,r7c7<>3,r2c7<>5,r1c4<>3),r3c1<>6,r3c1<>9(r2c1<>4,r7c2<>9,r1c7<>6),r1c2<>4,r6c2<>1,r5c1<>9,r1c3<>9,r5c4<>57. dml5023 10.6 99910 099920 020400000006080100700003000000060300000200005090007040300000800001000090040500002r3c7<>2,r4c3<>2(r2c2<>5,r1c8<>3,r5c3<>3,r7c8<>5,r1c1<>1),r9c1<>6,r2c2<>3(r8c4<>8,r8c1<>5,r4c4<>9,r2c1<>4),r1c6<>5,r3c7<>4,r2c8<>3,r1c5<>78. dml5223 10.6 99902 099993 002900000030070000500004100008000002090000030600500400000003008000060070100200500r6c3<>3(r6c2<>1,r4c1<>7,r2c6<>5,r1c2<>4,r1c1<>7),r4c2<>7,r4c8<>5(r5c1<>2,r2c3<>4,r1c2<>1,r6c8<>1,r1c9<>5),r6c9<>1,r1c7<>3,r5c7<>8,r2c6<>29. Ocean's Christmas present for gsf22 10.7 00000 000000 000001020300040500000600007002000006050030080400000900900002000080050400001700000r2c2<>1(r3c8<>1,r2c6<>7,r7c2<>7),r2c3<>9,r4c2<>9(r6c2<>3,r1c7<>6),r5c9<>1,r8c9<>2,r3c2<>1,r1c1<>7,r5c7<>2,r5c4<>1,r4c1<>7,r1c1<>510. dml822 10.4 99948 099958 900004000050080070001200000002600009030000040700000500000009002080050030000700600r8c3<>9(r1c2<>2,r3c1<>3,r1c3<>3,r5c1<>1,r2c4<>1,r1c3<>7),r8c9<>1,r8c1<>2(r1c5<>1,r1c4<>5,r1c4<>1),r4c8<>1,r6c4<>4,r7c2<>4,r1c2<>2`

28 11.2 00000 000000 000001020300040500000600007002000001080090030400000800500002000090030400006700000 Ocean's New Year's present for RW
24 10.6 99953 099993 100300000020090400005007000800000100040000020007060003000400800000020090006005007 dml161
24 10.5 99918 099921 100007000020080000004300500005400001080000020900000300000005007000020060003100900 dml48
23 10.7 99993 100013 100050000006009000080200004040030008007000060900000100030800002000004050000010700 dml11
23 10.7 99984 099994 003900000040070001600002000800000002070050030009000400200001008000040050000600900 dml12
23 10.7 99954 099994 100050080000009003000200400004000900030000007800600050002800060500010000070004000 dml20
23 10.6 99910 099920 020400000006080100700003000000060300000200005090007040300000800001000090040500002 dml50
23 10.6 99902 099993 002900000030070000500004100008000002090000030600500400000003008000060070100200500 dml52
22 10.7 00000 000000 000001020300040500000600007002000006050030080400000900900002000080050400001700000 Ocean's Christmas present for gsf
22 10.4 99948 099958 900004000050080070001200000002600009030000040700000500000009002080050030000700600 dml8
21 10.6 99963 100003 002600000030080000500009100006000002080000030700001400000004005010020080000700900 dml16
21 10.6 99934 099974 020000600400080007009000010005006000300040900010200000000700004000001050800090300 dml31
21 10.5 99983 099983 800003000070060090004500000005000004090002070100000800000009003020010060000700500 dml2
21 10.5 99945 099975 100006080050700000009030000007000050030000002600001400000040900800005060000200007 dml25
21 10.5 99839 099869 100007000040050020006800000005090003020000040700000100000003005090040060000100800 dml9
21 10.4 99922 099962 100007000020030500004900000008006001090000020700000300000001008030050060000400700 dml45
21 10.4 99900 099900 100009000020060000003500400005000001060080020700000300080001009000020060000400700 dml53
20 10.7 99964 099974 003200000040090000600008010200000003010006040007000500000001002090040060000500700 dml15
20 10.7 99955 099965 900004000080020030005700000001000004060080070300000500000005001070030090000600200 dml6
20 10.7 00000 000000 000001020300040500000600001001000007050030040800000900400002000090050800006700000 Ocean's New Year's present for ravel #1
20 10.6 99995 100015 400009000030010020006700000001000004050200070800000600000004008070030010000500900 dml1
20 10.6 99961 099971 800003000070060090004500000002000004030001070500000800000009001060070030000200500 dml4
20 10.6 99954 099995 002400006030010000500008000007000002010000030900600400000007001000090080400200500 dml19
20 10.6 99909 099919 001002000030040050600700800008000007010000040900000500004001008020030010000600900 Ocean #6/gold list
20 10.6 00000 000000 000001020300040500000600007001000006040080090500000300800002000050090400006700000 Ocean's New Year's present for ravel #2
19 10.6 99994 100004 003100000040060000700008002500007003010000040009000600000005007000090010200300800 dml10
19 10.6 99984 100004 002100700030050000400006000001900002080000030700000400000008006000030050900400100 dml13
19 10.6 99972 099982 800003000070060090004500000005000007020009030100000800000007001030020060000400500 dml3
19 10.6 99954 099964 003500100040080000600009000800000002050700030001000400000006009000020080070100500 dml22
19 10.6 99943 099963 002900000030080000400001050009070002010000030600000400000003001000060080007200900 dml26
19 10.6 99931 099982 003900100040070000600002000800000003020050040001000600000006002050080070000300900 dml34
19 10.6 99859 099859 001002000030040050500600700007000006010000020800000400006001009040030010000700800 Ocean #2/gold list
19 10.5 99928 100008 002900000030040010500006000008700002010000030400000500000002006000080040009300700 dml37
19 10.4 99911 099921 020050009006100000700003000030090050000600100000008002005000700090020004800000060 dml49
18 23 10.0 001002000030040050500600700007000006010000080900000200002001004080030010000900500 Ocean #7/gold list
18 10.6 99932 099995 003700000040080020600001000500000003020900040001000600000006005000020090070400800 dml33
18 10.6 99337 099981 400000300010500020006080009020000050007090008000004600300007000050100000008060000 Tarek Mitrale
18 10.5 99958 099958 002100000030080000500006400007000001090000020600005300000009008000020070400300600 dml18
18 10.5 00000 000000 000001020300040500000600007001000006080050040900000800500007000040080900006200000 Ocean's New Year's present for ravel #4
17 10.6 99527 099963 001002000030040050500600700007000006010000030800000900009003002020010040000700800 Ocean #3/gold list
17 10.5 99933 100003 100009000020070000004500030008000001030400020900000500000001007000060040005300800 dml32
17 10.5 00000 000000 000001020300040500000600007001000006050080030900000400800007000040050900006200000 Ocean's New Year's present for ravel #3
17 10.4 99900 099900 003700010040080000500009000600000003020100040007000500000400007000060020800005900 dml54
16 10.6 99931 099941 002900001030040000500006000008000002040000030900700500600001009000030040000200700 dml35
16 10.5 99957 099987 400009000050010030006700000007000008030000010900002400000008007010050060000400200 dml5
16 10.5 99942 099977 003400600050009000700020000200008070000030001000500900004000020800010003060000500 dml28
16 10.5 99920 099920 100009005020080000003400000009000001080070020600000300000005008000010070040600900 dml47
16 10.5 99920 099920 100007090030020008009600500005300900010080002600004000300000010040000007007000300 ArtoI's AI Etana (Escargot
16 10.4 99951 099951 800003000070060090004500000005000004060007080200000100000008002030090060000100500 dml7
15 23 10.0 001002000030040050500600700007000006040000080900000200002001003080030010000700500 Ocean #8/gold list
15 22 10.6 900001800060030000002500007009000006050000020400000300300008100000040080007900005 Tarek Fluid Drive #8
15 10.6 99921 099998 003200000040090010600007000800000003010006040002000500000001007090040060000500800 dml46
15 10.5 99971 099971 100900000020050000004006003600000100080000020003070004900100800000030050000004006 dml157
15 10.5 99954 099984 100006000020070030005900000009005001070000020600000400300001006000040070000200800 dml21
15 10.5 99940 100001 000400600000080003009002010001005040030000800600000007040900020800070000005001000 dml30
15 10.5 99924 099976 020400009006080000700003000004000700500060030010000002300005800000900004000010060 dml41
14 10.6 99325 099985 001002000030040050500600300007000006080000040200000100006009007040070080000500900 Ocean Anemone
14 10.5 99925 099955 002600000030080000500009010004000002070010030900000500000005006100070090000200400 dml40
14 10.5 99909 099909 002900000030040100500006000009000002060005030800000400000008006000030070001200900 dml51
14 10.5 99851 099984 001002000030040050600700800006000007010000020900000500003001006040050030000800900 Ocean #4/gold list
14 10.4 99961 099961 002900000030080000400005001001004002070000030600000500005002006000070080000300900 dml17
14 10.4 99687 099859 001002000030040010500600700007000006010000030800000900002007001040050020000900800 Ocean #1/gold list
14 10.1 99848 099858 700009200050080000006400007001000006040000030900000700800002500000060070003100004 Tarek Fluid Drive #43
13 20 09.8 600001900080030000001700002002000007050000010400000300300009600000040080008200005 Tarek Fluid Drive #1
13 10.5 99927 099977 002600100030080000500009000006500002070000030100000400000003009000070080400100600 dml38
13 10.4 99960 099980 060900003500004020000080400800000050003000700090000001001050000070300009900002040 Tarek Gyroscope #1
12 10.6 99960 099970 001002000030040050600700800006000007010000030900000600007001008040030020000500900 Ocean #5/gold list
11 10.6 99922 099975 003200000040050000700008010900000003060070040002000500000003009800040060000100200 dml44
11 10.5 99943 099953 003000009400000100080002060200008400005300000060070000010004800000090070000500003 dml27
11 10.3 99850 099871 100900050000080400030000006400002100050040000000300007500700090060030200008009001 Mauricio #12
11 10.1 99820 099840 000400020600090008007005100400001200050040030006700000004900050100080400030000002 Mauricio #13
10 20 09.4 001000200030000040400050006000102000060070030000809000300000005050040060008000900 Ocean 1#vert.symm
10 10.3 99839 099869 001002000030040050600700800008000007010000030900000500002001006040050020000600900 Ocean Extreme Jade puzzle
ravel

Posts: 998
Joined: 21 February 2006

Thank you Ocean for another fantastic puzzle!! Very suitable as New Year's present, as it would probably take most people the whole new year to solve it! I find it quite amazing how the puzzles just keep getting harder and harder all the time, is there no upper limit...?

ravel, nice to see that you are making progress on your new program! Looking forward to the new thread!

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

Happy new year everybody.......

I hope everybody is happy with their Christmas & new year presents ,

Congrats Ocean on the FRONTIER-crossing puzzles

My theory of 21-clue puzzles not having the hardest puzzles was rubbish...... however....... it seems that a search for a pattern that harbours extra hard puzzles is how dml & ocean did it.....

Some luck is involved but hard work & plenty of CPU time is a must

Did I forget ravel to mention how splendid your work with these hardest puzzles is

could you elaborate on how your new method works .... (what new techniques are implemented, and when subnets are used)........

I won't post any new puzzles unless they are ER11+ or gsfU (gsf Unrated)....... So this might be NEVER

tarek

tarek

Posts: 2737
Joined: 05 January 2006

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