The hardest sudokus

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

Postby Karlson » Wed Aug 16, 2006 7:25 pm

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

Postby ronk » Wed Aug 16, 2006 7:59 pm

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
2012 Supporter
 
Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Postby daj95376 » Wed Aug 16, 2006 8:38 pm

[Edited: deleted] Incorrect !!!
Last edited by daj95376 on Wed Aug 16, 2006 7:24 pm, edited 1 time in total.
daj95376
2014 Supporter
 
Posts: 2624
Joined: 15 May 2006

Postby ronk » Wed Aug 16, 2006 8:52 pm

daj95376 wrote:Ocean updated his puzzles before anyone posted a reply. Thus, there is no [Edit] 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
2012 Supporter
 
Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Postby Ocean » Wed Aug 16, 2006 10:05 pm

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

Postby tarek » Wed Aug 16, 2006 11:11 pm

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
User avatar
tarek
 
Posts: 2607
Joined: 05 January 2006

Postby r.e.s. » Wed Aug 16, 2006 11:21 pm

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

Postby daj95376 » Wed Aug 16, 2006 11:22 pm

ronk wrote:
daj95376 wrote:Ocean updated his puzzles before anyone posted a reply. Thus, there is no [Edit] 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
2014 Supporter
 
Posts: 2624
Joined: 15 May 2006

Tough (or impossible) pattern.

Postby fermat » Thu Aug 17, 2006 5:53 pm

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.

Postby JPF » Thu Aug 17, 2006 6:17 pm

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
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby daj95376 » Thu Aug 17, 2006 9:40 pm

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 Pair
r25     -  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
2014 Supporter
 
Posts: 2624
Joined: 15 May 2006

Re: Tough (or impossible) pattern.

Postby fermat » Fri Aug 18, 2006 4:26 am

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

Postby Eioru » Sat Aug 19, 2006 9:30 am

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

Postby maria45 » Sun Aug 20, 2006 7:11 pm

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

Postby ravel » Sun Aug 20, 2006 7:52 pm

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
 
Posts: 998
Joined: 21 February 2006

PreviousNext

Return to General