## The hardest sudokus

Everything about Sudoku that doesn't fit in one of the other sections
I don't remember the highest posted SE rating for this pattern.
Here's an other one : Jolie Fleur 3
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` 1 . . | . 2 . | . . 3 . 4 . | . . . | . 5 . . . 6 | . . . | 7 . .-------+-------+------- . . . | 5 . 7 | . . . 8 . . | . 6 . | . . 1 . . . | 8 . 9 | . . .-------+-------+------- . . 7 | . . . | 6 . . . 5 . | . . . | . 4 . 3 . . | . 4 . | . . 8`

Difficulty rating: 9,9
This Sudoku can be solved using the following logical methods:
58 x Hidden Single
2 x Naked Single
11 x Pointing
5 x Claiming
5 x Naked Pair
5 x Hidden Pair
2 x Naked Triplet
2 x Swordfish
1 x XY-Wing
1 x BUG type 1
1 x Turbot Fish
5 x Bidirectional Y-Cycle
1 x Bidirectional Cycle
13 x Forcing Chain
4 x Region Forcing Chains
2 x Cell Forcing Chains
17 x Dynamic Contradiction Forcing Chains
11 x Dynamic Region Forcing Chains
2 x Dynamic Cell Forcing Chains
2 x Dynamic Contradiction Forcing Chains (+)

JPF
JPF
2017 Supporter

Posts: 3754
Joined: 06 December 2005
Location: Paris, France

This came out of the blue.
Similar to the previous puzzle's pattern, coincidently.
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`+---+---+---+|1..|...|..2||.2.|...|.6.||..3|4..|5..|+---+---+---+|...|8.5|...||..8|.3.|9..||...|9.4|...|+---+---+---+|..5|..3|4..||.7.|...|.1.||6..|...|..7|+---+---+---+  dukuso diamond `

Code: Select all
`suexratt  rating:   4157 ,    2067 , -q1 1.......2.2.....6...34..5.....8.5.....8.3.9.....9.4.....5..34...7.....1.6.......7 # 97134 FNP C21.m/S2.p/M3.535.993-q2 1.......2.2.....6...34..5.....8.5.....8.3.9.....9.4.....5..34...7.....1.6.......7 # 97726 FNBP C21.m/S2.p/M3.535.993`

For the pattern with 4 single clues in a box the sx* rating is rather high.

C
coloin

Posts: 1733
Joined: 05 May 2005

But not quite as high as this one
Breaking many records

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`Sx9:   5105 , Sxt   2105 , .......12........3..23..4....18....5.6..7.8.......9.....85.....9...4.5..47...6...-q1 .......12........3..23..4....18....5.6..7.8.......9.....85.....9...4.5..47...6... # 99485 FNBP C21.m/M3.389.1366-q2 .......12........3..23..4....18....5.6..7.8.......9.....85.....9...4.5..47...6... # 99551 FNBP C21.m/M3.389.1366`

Code: Select all
`+---+---+---+|...|...|.12||...|...|..3||..2|3..|4..|+---+---+---+|..1|8..|..5||.6.|.7.|8..||...|..9|...|+---+---+---+|..8|5..|...||9..|.4.|5..||47.|..6|...|+---+---+---+ Platinum Blonde`

Code: Select all
`.......12........3..23..4....18....5.6..7.8.......9.....85.....9...4.5..47...6...`

C
coloin

Posts: 1733
Joined: 05 May 2005

coloin wrote:Platinum Blonde
Code: Select all
`.......12........3..23..4....18....5.6..7.8.......9.....85.....9...4.5..47...6...`
Fantastic coloin, I'm sure dukuso would love to see Sx9's rating for this ..... maybe this is the spark for a new fresh search

tarek

tarek

Posts: 2699
Joined: 05 January 2006

tarek wrote:maybe this is the spark for a new fresh search

Thank-you, it might well be. There seems no end to the number of 21 clue puzzles. My search methods are definitly brutish ! It came from a repetitve {-2+2} on 100 or so [diamond] puzzles at a time.

It might be more productive to hand over to the pattern puzzlemakers - it seems the "final" pattern might be something along the lines of ?
Code: Select all
`+---+---+---+|...|...|.12||...|...|..3||...|...|4..|+---+---+---+|...|*..|...||...|.*.|...||...|..*|...|+---+---+---+|..8|...|...||5..|...|...||67.|...|...|+---+---+---+ plus 10 [or 11] clues !`

Unfortunatly, the initial single clue in PB perhaps means the champagne rating is only 48s.

Is there no word on SE being able to handle these and other puzzles ?

C
coloin

Posts: 1733
Joined: 05 May 2005

I think that if you've extensively went through the Neighbourhood search, there is little to do from that aspect without actually knowing the Frontier of your search. If somebody is going that route then it will take considerable time before hitting something.

Searching for pearls has been always my strategy & payed off several times in finding difficult puzzles.

Regarding puzzle configurations: I note that the puzzle you've posted has a specific pattern.

I laso noted that with the recent hardest the 4 single boxxes seem to be 2 single boxes & 2 boxes with 2 clues.

tarek

tarek

Posts: 2699
Joined: 05 January 2006

tarek wrote:knowing the Frontier of your search.

I think this is a "game sans frontiere"

21 puzzles - well there must be more than 10 ^13 different

I only know the puzzles I have searched - the PB puzzle came from a relatively lowly specimen. And I only searched the tip of the "iceberg".

I recently only searched diamond puzzles - but I easily could have lowered this limit

Code: Select all
`sudoku -f%v -e "(%#Dq)==99" diamondstosudoku -f%v -e "(%#Pq)>02"    [puzzles without an initial single]`

As to the pattern, indeed the patterns esp in GN are now more obvious.

I might put a s2 pattern similarish to PB on the "patterns game" !!!!!

champagne has kindly analysed with his solver/rater many of the apparently hard puzzles and I will post a shortened list.

C
coloin

Posts: 1733
Joined: 05 May 2005

coloin wrote:I might put a s2 pattern similarish to PB on the "patterns game" !!!!!
I've actually put some diagonal patterns with 24 & 25 clues that allow diamonds in the patterns game, this will hopefully produce a nidus of diamonds that will snowball into a bigger & more effective search for hardest puzzles.

I'll give it a shot with some strategies of mine (possibly futile) & will report anything extra-ordinary

tarek

tarek

Posts: 2699
Joined: 05 January 2006

coloin wrote:Is there no word on SE being able to handle these and other puzzles ?

PB is rated by gsf's instrumented version of SE as 10.6/1.2/1.2. I leave to someone else to fill r9c3 and get a revised rating.

Regards,

Mike Metcalf

P.S. This took about 45min @ 1.6GHZ.

P.P.S. Changing r7c4 to 1 gives a rating of 10.5/1.2/1.2.

m_b_metcalf
2017 Supporter

Posts: 9210
Joined: 15 May 2006
Location: Berlin

although I'm sure that q2 & q1 must reflect many aspects of a puzzle's difficulty, some of the most recent postings did not score highly in SE's book.

Is that due to the fact that uniqueness is not factored into what Sx9 Sxt q1 q2 do while it does with SE or am I missing something ?!

tarek
[Edit: corrected grammer]
Last edited by tarek on Fri Jun 06, 2008 10:23 am, edited 1 time in total.

tarek

Posts: 2699
Joined: 05 January 2006

tarek wrote:although I'm sure that q2 & q1 must reflect many aspects of a puzzle's difficulty, some of the most recent postings did not score highly in SE's book.

Is that due to the fact that uniqueness is not factored into what Sx9 Sxt q1 q2 do while it does with SE or I'm I missing something ?!

tarek

I feel nobody knows how to rate a potential "hardest puzzle" because nobody can figure out which path will solve it. What is for sure is that all puzzles having the SK loop are "relatively easy to solve" and have usually a very high rating using the tools you mention.

I worked hard recently with coloin on new puzzles. At the end, my short list of hardest has in the top the followings (coloin could comment on how they were generated and how they are rated with other tools).

As far as I could see, they were not the highest rated in the sublists he gave me. Some are diamonds, some are not ...

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`100000007020400060003000500090040000000062040000900800005000003060200080700001000 Silver Plate    000000039000001005003050800008090006070002000100400000009080050020000600400700000 Golden Nugget   003010005020400000100000700040806000000049060002000000007000100080900020500000003 col809# 92145     100000005020400060003000700040006000000049080002800000000050100060900020007000003 col803# 98781    000000039700000000003090060008050006070002500100400800000080050020700000400001000 col702# 97573     000001009000000065009050030008030006070200000100004800003080050020000000400700000 col402# 98183   000001030000000065003050900008090006070002000100400800009080050020000000400700000 col080501        000001009000000035009050060008030006070200000100004800003080050020000000400700000 col602# 98959    300001005020400000001000700040860000000009080000000402007000100060900020500000003 col805# 97901   100000005020400060003000700040809000000046080000000200007001000080900020500000300 col807# 95104     `
champagne
2017 Supporter

Posts: 6542
Joined: 02 August 2007
Location: France Brittany

[quote="JPF"]I don't remember the highest posted SE rating for this pattern.
Here's an other one : Jolie Fleur 3
Code: Select all
` 1 . . | . 2 . | . . 3 . 4 . | . . . | . 5 . . . 6 | . . . | 7 . .-------+-------+------- . . . | 5 . 7 | . . . 8 . . | . 6 . | . . 1 . . . | 8 . 9 | . . .-------+-------+------- . . 7 | . . . | 6 . . . 5 . | . . . | . 4 . 3 . . | . 4 . | . . 8`

[size=9]Difficulty rating: 9,9

This one is only rating 9,8 but the same morphologic pattern. It came just refining a 9.3 puzzle of 20clues:

Code: Select all
`1 . . . . . . . 5. 9 . . 3 . . 4 .. . 7 . . . 2 . .. . . 3 . 7 . . .. 4 . . 8 . . 6 .. . . 4 . 9 . . .. . 2 . . . 7 . . . 6 . . 9 . . 3 .5 . . . . . . . 1`
Rating 9,8

Hidden Triplet
Naked Triplet
2 X-Wing
Swordfish
Jellyfish (only after some eliminations of 8 by forcing chains)
XY-Wing
XYZ-Wing
4 Turbot-Fish
Forcing-X-Chain
3 Bi-directional-Y-Cycle
5 Cell forcing chains
7 Region forcing chains
4 Dynamic region forcing chains
8 Dynamic region forcing chains+
Dynamic cell forcing chain+
claudiarabia

Posts: 288
Joined: 14 May 2006

A brief recap on published puzzles prior to a furthur posting of puzzles.
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`Cloudy Bay      #1.........2.4...6...3...5.1.4..86.......49.8....2.....5.7...3...6.9...4.........7 Bronze Medalian #1.......7.2.4...6...3...5...9..82.......9..8....6..4....5...1...6.8...2.7....3... Silver Plate    #1.......7.2.4...6...3...5...9..4........62.4....9..8....5.....3.6.2...8.7....1... Platinum Blonde #.......12........3..23..4....18....5.6..7.8.......9.....85.....9...4.5..47...6... Tungston Rod    #........7.2.4...6.1.....5...9...2.4....8..6..6..9.......5..3....3..8..2.7....4..1 Golden Nugget   #.......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7..... dukdiamond1     #1.......2.2.....6...34..5.....8.5.....8.3.9.....9.4.....5..34...7.....1.6.......7 dukdiamond2     #1.......2.2.....6...34..5.....8.5.....8.3.9.....9.4.....53..4...6......77......1. weekender2      #..1.....7.2..4..6.3.....5...9.4.6.......92.4.......8....7..3....6..2..8.5.......1 weekender1      #........91......35..9.3.8....3.5...67....2......4.......6.8..9..2.7..6..4.....1.. `

Code: Select all
`Rating          -q2                                  sx9        sxt         SE121                 Cloudy Bay      # 45364 FNBP C21.m/M2.4.8200         #3924      #2363       #                      Bronze Medalian # 98041 FNBP C21.m/M2.8.5740         #3298      #2052       #                      Silver Plate    # 98036 FNBP C21.m/M2.1.314928       #3316      #2164       #                      Platinum Blonde # 99551 FNBP C21.m/M3.389.1366       #5059      #2095       #                      Tungston Rod    # 99307 FNBP C21.m/M3.310.1714       #2950      #1510       #                      Golden Nugget   # 99220 FNBP C21.m/M2.1.164025       #3639      #2175       #11.9                  dukdiamond1     # 97726 FNBP C21.m/S2.p/M3.535.993   #4181      #1988       #                      dukdiamond2     # 97767 FNBP C21.m/M2.3.30618        #3415      #2151       #                      weekender2      # 98798 FNBP C21.m/M2.1.170586       #2274      #1557       #                      weekender1      # 98824 FNBP C21.m/M3.108.4920       #3806      #2178       # `

Canonical versions for reference
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`Cloudy Bay      #020050000007100006090003000006700800030002000900005000000000407004600010000000608#Bronze Medalian #100400080000009200000030005000000900070800040006020003004700060710000000800005000#Silver Plate    #100006000050700003009020000040500300000090050000000074070800040600000800002001000#Platinum Blonde #003050009400100000080007000030005008000030920000000060005060002700004000810000000#Tungston Rod    #020000700006080100700003004000060000300005010008200000005000090000500040900001300#Golden Nugget   #020000700400080030009100000000005003000000064600030800005900000800040007010002000#dukdiamond1     #020400009000080030000003100000005800009200004000010050062000000074000000900600007#dukdiamond2     #000000780007100006000000150200030000030004000008500600006800500040090000900002000#weekender2      #000006080000100200090070004000008600300040005005200000030000000740000010900030007#weekender1      #020006700006000000708010000040500030010090000600004200004007800000000090000030005#`
coloin

Posts: 1733
Joined: 05 May 2005

champagne wrote:
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`1     5789   6    |3578  23579  23578   |24a789 2379   234A89 789   2      589  |4     13579  13578   |789    6      389   4     789    3    |678   2679   278     |5      279    1      ---------------------------------------------------------------2379  4      1259 |1357  8      6       |1279   123579 2359   2367  1357   125  |1357  4      9       |1267   8      2356   36789 135789 1589 |2     1357   1357    |14679  13579  34569 ---------------------------------------------------------------5     189    7    |168   126    4       |3      129    2689  238   6      128  |9     12357  123578  |128    4      258   2389  1389   4    |13568 12356  12358   |12689  1259   7     `

In that map, we have a typical SK loop (at least for me), exactly in the place where it stays normally. It is not a pattern with 3 candidates per cell, but it is a SK loop.

I don't know if it is an SK loop, as "SK loop" has never been defined formally.
But it satisfies undoubtedly both of the two interpretations I've given of it (belts of crosses and x2y2-belts), here: http://forum.enjoysudoku.com/viewtopic.php?t=5894
And it answers positively one of the questions that remained open about these interpretations: can the optional candidates I have introduced in my patterns appear in real puzzles?
denis_berthier
2010 Supporter

Posts: 1259
Joined: 19 June 2007
Location: Paris

denis_berthier wrote:
I don't know if it is an SK loop, as "SK loop" has never been defined formally.

I defined very simply my own specification for the SK loop here

http://forum.enjoysudoku.com/viewtopic.php?t=5624

in the chapter dedicated to "virus patterns".

A SK loop is a virus patterns chain that loops. (I do not see a key difference with denis's description. )

To answer another remark stating that it is not a true loop, I would be very reluctant to rally such statement.

As noticed Denis, the chain linking "virus patterns" is an AIC. To find the loop, my solver re use the process of Nice Loops, and the probe for the clearing of the SK loop can be done applyng exactly the same process as for a Nice loop.
champagne
2017 Supporter

Posts: 6542
Joined: 02 August 2007
Location: France Brittany

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