## The hardest sudokus

Everything about Sudoku that doesn't fit in one of the other sections
Well, if it is the new hardest Sudoku, we should think of a name for it which signalizes its difficulty
I'm not very good at creating names, but here are some suggestions:
"Ocean's Peril"
"Ocean's Evil Fairy"
"Ocean's Trial of Courage"

Maybe you can think of better ones ;-)
Karlson

Posts: 26
Joined: 14 May 2006

tarek wrote:2 in r6c3 would lead to a contradiction (Complex Contradiction elimination)

Gave that one a try and found this error net.
Code: Select all
`*-----------------------------------------------------------------*| 3679   5689   3789  | 36789  46789  1     | 4678   45689  2     || 679    1      5789  | 6789   2      4679  | 4678   3      45789 || 4      23689  2389  | 5      6789   3679  | 17     689    1789  ||---------------------+---------------------+---------------------|| 1239   2359   4     | 1789   5789   279   | 37     258    6     || 269    7      59    | 2689   3      2469  | 248    1      458   || 8      2356   123   | 1267   456    2467  | 9      245    37    ||---------------------+---------------------+---------------------|| 5      2349   17    | 23679  679    8     | 12346  2469   1349  || 239    23489  2389  | 2369   1      5     | 23468  7      489   || 17     2389   6     | 4      79     2379  | 5      289    1389  |*-----------------------------------------------------------------*r6c3=1=r7c3-1-r7c79=1=r9c9  (implying r9c9<>3)    =1=r4c1    -2-r45c1=2=r8c1=3=r1c1-3-r13c3=3=r8c3-3-r9c2                          -3-r1c4=3=r3c6-3-r9c6... eliminating all the 3s in r9 and implying r6c3<>2.`

tarek wrote:I also came accross this wonderful step
[...]
Eliminating 8 from r1c4(ALS-XZ A=46789 in r1379c5 B=48 in r1c7 x=4 z=8, a classic VWXYZ wing)

[edit: Your grid shows the exclusion r1c3<>8 instead.]

daj95376 wrote:Very late in my solution, there's a Swordfish exposed in [r369] for <3>.

How is that possible when r1c3=3 is ultimately the correct placement?
Last edited by ronk on Wed Aug 16, 2006 6:15 pm, edited 1 time in total.
ronk
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Location: Southeastern USA

[Edited: deleted] Incorrect !!!
Last edited by daj95376 on Wed Aug 16, 2006 7:24 pm, edited 1 time in total.
daj95376
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daj95376 wrote:Ocean updated his puzzles before anyone posted a reply. Thus, there is no  showing. This may be why we're talking about different puzzles. It would be a good idea if everyone checked the puzzles they're using!!!

Huh? I was using the starting grid from your post.
ronk
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Location: Southeastern USA

Thank you all for comments, analysis and compliments! Interesting that the puzzle with Explainer rating 10.0 also seems to be among the most challenging for other solvers!
maria45 wrote:But, if I might ask you for numbering your puzzles now, as your number 1 yesterday is now number 2. Just for sake of reference, I'd like to indicate the right puzzle if I post a solution. Thank you.
The numbering/ordering of the puzzles is now stabilized, since puzzles are referenced outside the post. Normally Ravel will give reference numbers for those puzzles that qualify for his list. Sorry if the stepwise buildup of the post was confusing - caused by a stepwise search, queing of candidates for rating by Explainer, and the highest ER-rated puzzle occuring late in the process. Rather than adding late puzzles at the end, the puzzles are 'normalized' (123...) and sorted numerically - but split in two rating groups and the two patterns separated. [Exception: #16,#17,#18 are not properly numerically sorted - but because of external references the order will be kept as it is now].
Ocean

Posts: 442
Joined: 29 August 2005

ronk wrote:
tarek wrote:I also came accross this wonderful step
[...]
Eliminating 8 from r1c4(ALS-XZ A=46789 in r1379c5 B=48 in r1c7 x=4 z=8, a classic VWXYZ wing)

[edit: Your grid shows the exclusion r1c3<>8 instead.]

Typo corrected. Thanx

tarek

tarek

Posts: 2650
Joined: 05 January 2006

It might be interesting to note which of these show their "adamantine" quality right away before even one digit can be placed ... To Ocean's first group I've added a column on the right, which is Sudoku Explainer's rating of the "most-difficult" of the moves used to place the first digit:

""""""""""""""""""""
# M21/D21:
#
.....1..2.1..2..3.4..5.......4.....6.7..3..1.8.....9..5....8.......1..7...64..5.. # ER=10.0 # 1.2
.....1..2.1..3..4.5..6.......4.....1.7..8..3.2.....6..9....2.......4..7...35..8.. # ER=9.9 # 9.9
.....1..2.1..3..4.5..6.......4.....1.7..8..3.2.....9..9....2.......4..7...35..8.. # ER=9.9 # 9.9
.....1..2.1..3..4.5..6.......4.....1.7..8..3.2.....9..9....2.......4..7...37..8.. # ER=9.5 # 1.2
.....1..2.1..3..4.5..6.......4.....1.7..8..3.6.....8..2....6.......5..7...39..5.. # ER=9.4 # 1.2
.....1..2.1..3..4.5..6.......7.....8.9..4..1.8.....5..6....2.......1..9...87..3.. # ER=9.4 # 9.4
.....1..2.3..2..4.5..6.......4.....7.8..3..2.9.....5..1....9.......4..8...75..9.. # ER=9.4 # 9.4
.....1..2.3..2..4.5..6.......7.....3.1..4..8.6.....5..9....6.......7..3...85..9.. # ER=9.4 # 1.2
.....1..2.3..4..5.1..6.......5.....7.8..3..4.6.....1..9....6.......5..7...42..9.. # ER=9.4 # 1.2
.....1..2.3..4..5.6..2.......5.....3.7..8..4.2.....9..9....4.......5..7...41..6.. # ER=9.8 # 1.2
.....1..2.3..4..5.6..2.......5.....7.7..3..4.2.....6..1....8.......7..9...46..8.. # ER=9.5 # 1.2
.....1..2.3..4..5.6..7.......4.....8.9..5..3.8.....6..1....7.......3..9...82..4.. # ER=9.4 # 9.4
.....1..2.3..4..5.6..7.......5.....4.7..8..3.2.....6..1....6.......5..7...39..8.. # ER=9.5 # 1.2
.....1..2.3..4..5.6..7.......5.....4.8..2..9.7.....3..1....4.......5..8...96..7.. # ER=9.8 # 9.8
""""""""""""""""""""

A 1.2 on the right corresponds to a simple hidden single, while a 9.4+ corresponds to the most intricate of typically numerous intricate forcing chains. So in the latter, we're immediately "up against the wall" -- these are extreme examples of a type of puzzle that's been called a "pearl" (see Gurth's G811 below), some earlier examples of which are ...

Vidar's monsters
#2 http://forum.enjoysudoku.com/viewtopic.php?t=3198
#4 http://forum.enjoysudoku.com/viewtopic.php?p=23605

Ocean's M20 #10111
http://forum.enjoysudoku.com/viewtopic.php?p=31735#p31735

Gurth's pearls
#G811 http://www.sudoku.org.uk/cgi-bin/discus/show.cgi?tpc=29&post=5951#POST5951
#G816 http://www.sudoku.org.uk/cgi-bin/discus/show.cgi?tpc=29&post=6034#POST6034

Ruud is also in the midst of a "String of Pearls week" for his Daily Nightmares ...
http://www.sudocue.net/daily.php

It would be really neat to find a pearl whose very first placement requires a move rated 10.

[EDIT] Or, alternatively, to find a pearl requiring a first move rated 10. (Ocean's pearls above allow first moves rated 9.3 or less.)

EDIT: Added Ocean's M20 #10111; improved formatting
Last edited by r.e.s. on Thu Aug 17, 2006 10:27 am, edited 5 times in total.
r.e.s.

Posts: 337
Joined: 31 August 2005

ronk wrote:
daj95376 wrote:Ocean updated his puzzles before anyone posted a reply. Thus, there is no  showing. This may be why we're talking about different puzzles. It would be a good idea if everyone checked the puzzles they're using!!!

Huh? I was using the starting grid from your post.

My mistake and apology for not properly checking that the latter Swordfish did not align with what I'd highlighted in my example. Thanks ronk for catching this!!!
daj95376
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### Tough (or impossible) pattern.

Ocean, or anyone else who cares to try.

This pattern may not allow a puzzle but if it does I bet Ocean's generator is the one to tame it.

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`

I can get puzzles if I add a clue or two to the empty boxes, and they are generally hard puzzles when I do get ones. Interesting pattern.
fermat

Posts: 105
Joined: 29 March 2006

### Re: Tough (or impossible) pattern.

fermat wrote:This pattern may not allow a puzzle but if it does I bet Ocean's generator is the one to tame it.

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`

Have a look at this recent post.

JPF
JPF
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Location: Paris, France

Modest analysis of Ocean's 10.0 puzzle.

Code: Select all
`.....1..2.1..2..3.4..5.......4.....6.7..3..1.8.....9..5....8.......1..7...64..5..r8c6    =  5     Hidden Single    b6  -  2458  Naked  Quad    b7  -  17    Hidden Pairr25     -  5     X-Wing`

At this point, my solver finds seven simple and four complex Forcing Chains/Nets. I then forced each elimination in turn and observed the subsequent solutions. Except for the following elimination, all of the subsequent solutions were essentially the same ... and a little longer.

Code: Select all
`r4c5    <> 9 (4) [r4c5]=9 => [r3]=INVALID *`

Note: (4) = number of candidates in the cell, and * indicates a complex Forcing Chain/Net.

At this point, I tried the same approach on the simple/complex Forcing Chains/Nets following this elimination. This time, all of the subsequent solutions were essentially the same. (No, my solver doesn't list the specifics of Forcing Chains/Nets.)
daj95376
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### Re: Tough (or impossible) pattern.

JPF wrote:
fermat wrote:This pattern may not allow a puzzle but if it does I bet Ocean's generator is the one to tame it.

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`

Have a look at this recent post.

JPF

OK, Ocean has tried it and there seems to be no puzzle in this clue set.
Thanks!
fermat

Posts: 105
Joined: 29 March 2006

If it must solve harder than forcing trains at the first step,
the puzzles whose clue are less than 30 might be a challenge and hard.

Whether this kind sudoku exists?
Eioru

Posts: 182
Joined: 16 August 2006

Hello Ocean,

Ocean wrote:The Explainer Rating 10.0 is probably a new "record" - provided that puzzle has enough steps. Maybe a suitable challenge for you, Maria?

I solved this ER10.0 puzzle last friday. I don't know if I should post it, spoiling the fun for the other manual solvers?

Somehow disappointingly, it was not the hardest puzzle in terms of solving strategy. My solution has gone quite straightforward. It also didn't needed more than 10 contradictions, so that's equal to the #07/18 puzzle with ER9.9.

The strategy was clear because of the two hidden pairs and their being interconnected. Eliminate most of the possible candidates 3, then the puzzle must either break up into either two simple alternating chains, the one chain with the candidates 1, the other chain with the candidates 3, or some of the cells with candidates 1 or 3 will be solved...

Perhaps this are enough clues to other manual solvers?

Greetings, Maria
maria45

Posts: 54
Joined: 23 October 2005

maria45 wrote:I don't know if I should post it, spoiling the fun for the other manual solvers?

Since it seems, that Carcul is on holidays and the summer is not rainy enough in Norway, i dont know about any other solver who would try it manually, so please post it (i also noticed that solutions to toughies are often very different).
ravel

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Joined: 21 February 2006

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