The hardest sudokus

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

Postby Eioru » Fri Sep 08, 2006 4:25 pm

Do sudoku solving techniques have this "Dynamic Double Forcing Chains(+)"

All kind of "Forcing Chains" in my record list are :
6..4..5......2......5..1..62..7..4...9.....8...6..9..37..8..2......5......1..3..5 ~4 Forcing X-Chains
..........4..8..5...3..1..8...9..5...9..6..2...1..8..4...3..7...6..2..9...5..7..1 ~31 Forcing Chains
1.......2.3..4..5...6...7.....1.4....8..2..4....5.8.....2...6...4..3..8.7.......1 ~8 Nishio Forcing Chains
5..2..9......7......6..1..46..9..3...8.....4...7..2..18..3..5......4......1..6..9 ~9 Cell Forcing Chains
1.......2.3..4..5...6...7.....1.4....8..2..4....5.8.....2...6...4..3..8.7.......1 ~23 Region Forcing Chains
1.......2.3..4..5...6...7.....1.4....8..2..4....5.8.....2...6...4..3..8.7.......1 ~12 Dynamic Cell Forcing Chains
1.......2.3..4..5...6...7.....1.3....8..6..3....9.4.....7...1...4..5..8.2.......9 ~2 Dynamic Cell Forcing Chains(+)
..1.....2.3..4....5..6..3....4..7..1....8..3.9..2..6.......8..9.7..2..4.2..1..8.. ~36 Dynamic Contration Forcing Chains
1.......2.3..4..5...6...7.....1.4....8..7..4....5.8.....7...6...5..3..8.2.......1 ~19 Dynamic Contration Forcing Chains(+)
1.......2.3..4..5...6...7.....1.3....4..6..8....4.5.....2...9...8..5..4.7.......1 ~4 Dynamic Double Forcing Chains
None ~0 Dynamic Double Forcing Chains(+)
.....1..2.3..2..4.5..6.......6.....7.7..1..3.8.....5..7....5.......3..2...98..6.. ~27 Dynamic Region Forcing Chains
1.......2.3..4..5...6...7.....1.3....8..7..4....4.6.....2...6...5..3..8.9.......1 ~10 Dynamic Region Forcing Chains(+)
Eioru
 
Posts: 182
Joined: 16 August 2006

Postby Ocean » Fri Sep 08, 2006 11:40 pm

daj95376 and ronk wrote:Is there some sort of super fish here??? (...) Very interesting observation. (...)

daj/ron: I'm happy to see the observations and discussions... Hopefully the puzzle set contains some new material for joy and analysis!

Eioru wrote:Can I ask you
what time did you spend completing a pattern ( find all puzzles rated over 9.0 )
and what program to use finding these super hard puzzles?
Hi Eioru - Glad to see yours and tareks contributions lately.
The X-pattern is not searched exhaustively. Some subsets of the pattern were searched, each search lasting several hours. Useful observation: Puzzles in the X-pattern that satisfy all of the following conditions - 1. All digits in upper band differ (= first seven nonzero digits). 2. All digits in lower band differ (= last seven digits). 3. All digits in left stack differ (= the three left columns). 4. All digits in right stack differ (= the three right columns). 5. Suexrating > 400. - More than 90% of such puzzles were rated 9.0 or above by Explainer (of the about 200 checked). Very effective screening criteria for finding hard puzzles, once it was established.
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby JPF » Sat Sep 09, 2006 7:35 am

Ocean wrote:Useful observation: Puzzles in the X-pattern that satisfy all of the following conditions - 1. All digits in upper band differ (= first seven nonzero digits). 2. All digits in lower band differ (= last seven digits). 3. All digits in left stack differ (= the three left columns). 4. All digits in right stack differ (= the three right columns). 5. Suexrating > 400. - More than 90% of such puzzles were rated 9.0 or above by Explainer (of the about 200 checked). Very effective screening criteria for finding hard puzzles, once it was established.
Thanks Ocean for this clever observation.

I generated 3 X-pattern puzzles randomly.
Two of them are following the rules => ERR 9.4 and 9.0 :
Code: Select all
900000004020060010003000800000109000010040050000203000007000900060010020400000003
900000007020060010003000800000109000010040050000207000007000900050010020400000003

This one has 2 common digits in stacks 1 and 3
Code: Select all
 3 . . | . . . | . . 8
 . 5 . | . 2 . | . 4 .
 . . 6 | . . . | 7 . .
-------+-------+-------
 . . . | 8 . 4 | . . .
 . 4 . | . 1 . | . 5 .
 . . . | 7 . 6 | . . .
-------+-------+-------
 . . 3 | . . . | 6 . .
 . 2 . | . 9 . | . 1 .
 8 . . | . . . | . . 7


singles only. (14 steppers)

JPF
JPF
2017 Supporter
 
Posts: 6139
Joined: 06 December 2005
Location: Paris, France

Postby ronk » Sat Sep 09, 2006 12:35 pm

Can anyone point me to publicly available software ... preferably command line rather than GUI ... which generates permuted puzzles from a given?

TIA, Ron
ronk
2012 Supporter
 
Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Postby gsf » Sat Sep 09, 2006 2:21 pm

ronk wrote:Can anyone point me to publicly available software ... preferably command line rather than GUI ... which generates permuted puzzles from a given?

my solver
if you just want 99 equivalent copies (plus the original first):
Code: Select all
-J99 -qFN -f%v original.dat

and yes I'm almost out of option letters
gsf
2014 Supporter
 
Posts: 7306
Joined: 21 September 2005
Location: NJ USA

x-pattern

Postby claudiarabia » Sat Sep 09, 2006 11:08 pm

Ocean wrote:
Code: Select all
 *-----------*
 |1..|...|..2|
 |.3.|.4.|.5.|
 |..6|...|7..|
 |---+---+---|
 |...|1.4|...|
 |.8.|.7.|.4.|
 |...|5.8|...|
 |---+---+---|
 |..7|...|6..|
 |.5.|.3.|.8.|
 |2..|...|..1|
 *-----------*



I'm getting nostalgic to see this ocean-beauty. With this shape I made my first trial to construct a sudoku on my own one year ago - with paper and pencil. I've forgotten how many numbers I had to add till I finally had a valid one. I know you generate this easily with your program. I still stick to SS and SE while combining them in my efforts and having much joy when I finished one.:)

Cheers

Claudia[/code]
claudiarabia
 
Posts: 288
Joined: 14 May 2006

Re: Try that online sudoku solver 20clues-puzzle

Postby claudiarabia » Sat Sep 09, 2006 11:18 pm

Jon wrote:Here is a free online sudoku solver ....BTW, here is the hardest Sudoku I ever found:
{ 0, 0, 2, 0, 9, 0, 1, 0, 7 },
{ 0, 3, 8, 6, 0, 0, 0, 0, 0 },
{ 4, 0, 0, 0, 0, 0, 0, 0, 0 },
{ 0, 0, 0, 0, 0, 5, 0, 0, 0 },
{ 0, 0, 9, 0, 1, 0, 3, 0, 0 },
{ 0, 0, 0, 4, 0, 0, 0, 0, 0 },
{ 0, 0, 0, 0, 0, 0, 0, 0, 4 },
{ 0, 0, 0, 0, 0, 7, 9, 2, 0 },
{ 8, 0, 6, 0, 3, 0, 7, 0, 0 },


Dear Jon

Thank you for this nice 20-cluer (if r9c7 is omitted) SE rated 2.0!
claudiarabia
 
Posts: 288
Joined: 14 May 2006

Re: Try that online sudoku solver 20clues-puzzle

Postby JPF » Sun Sep 10, 2006 12:18 am

claudiarabia wrote:Thank you for this nice 20-cluer (if r9c7 is omitted) SE rated 2.0!

Claudia,
this puzzle is minimal and is rated 8.4 by SE

JPF
JPF
2017 Supporter
 
Posts: 6139
Joined: 06 December 2005
Location: Paris, France

Re: Try that online sudoku solver 20clues-puzzle

Postby claudiarabia » Sun Sep 10, 2006 1:30 pm

JPF wrote:
claudiarabia wrote:Thank you for this nice 20-cluer (if r9c7 is omitted) SE rated 2.0!
Code: Select all
 *-----------*
 |..2|.9.|1.7|
 |.38|6..|...|
 |4..|...|...|
 |---+---+---|
 |...|..5|...|
 |..9|.1.|3..|
 |...|4..|...|
 |---+---+---|
 |...|...|..4|
 |...|..7|92.|
 |8.6|.3.|7..|
 *-----------*
Claudia,
this puzzle is minimal and is rated 8.4 by SE JPF

Thank you,

I would have missed my favorite construction-SE-level otherwise!
But let me give an excuse for this. When I entered the grid in SE manually, I missed the right place for the 4 in row 7. Instead of putting the 4 correctly in r7c9 I put it in r7c8. Checking out validity SE presented me one unique solution - a rare coincidence which let me believe that I typed everything correctly. And now you can delete the 7 in r9. Anyway I checked solvers in the internet which are not able to solve some hard sudokus so I thought Jon had presented a very bad one or just made a joke. So here is the light-version:
Code: Select all
 *-----------*
 |..2|.9.|1.7|
 |.38|6..|...|
 |4..|...|...|
 |---+---+---|
 |...|..5|...|
 |..9|.1.|3..|
 |...|4..|...|
 |---+---+---|
 |...|...|.4.|
 |...|..7|92.|
 |8.6|.3.|7..|
 *-----------*
Sorry
With best wishes

Claudia
claudiarabia
 
Posts: 288
Joined: 14 May 2006

Re: Try that online sudoku solver 20clues-puzzle

Postby r.e.s. » Sun Sep 10, 2006 11:15 pm

claudiarabia wrote:So here is the light-version:
Code: Select all
 *-----------*
 |..2|.9.|1.7|
 |.38|6..|...|
 |4..|...|...|
 |---+---+---|
 |...|..5|...|
 |..9|.1.|3..|
 |...|4..|...|
 |---+---+---|
 |...|...|.4.|
 |...|..7|92.|
 |8.6|.3.|7..|
 *-----------*

Hmmm ... it's very "light" on solutions -- it has none.:)
r.e.s.
 
Posts: 337
Joined: 31 August 2005

Re: Try that online sudoku solver 20clues-puzzle

Postby claudiarabia » Mon Sep 11, 2006 12:19 pm

r.e.s. wrote:Hmmm ... it's very "light" on solutions -- it has none.:)


If you make one mistake, it will become a mistake-chain, a forcing one, I fear. I did not only put Number four in row 7 on the wrong place, but also the Nr 7 in Row 9 wich I placed in c8 instead of c7. I saw then that c7 only contained the 5 as a candidate and decided to eliminate the 7 because I assumed the 7 in r8 to be enough to define. And it worked. That's how I came to the 2.0 solution.

Code: Select all
 *-----------*
 |..2|.9.|1.7|
 |.38|6..|...|
 |4..|...|...|
 |---+---+---|
 |...|..5|...|
 |..9|.1.|3..|
 |...|4..|...|
 |---+---+---|
 |...|...|.4.|
 |...|..7|92.|
 |8.6|.3.|.7.|
 *-----------*
[/quote]
claudiarabia
 
Posts: 288
Joined: 14 May 2006

Postby Eioru » Tue Sep 12, 2006 8:24 am

Are there sudoku puzzles satisfied any of these?
1. 5 x Dynamic Double Forcing Chains(+)
2. 10 x Dynamic Double Forcing Chains
3. 10 x Dynamic Cell Forcing Chains(+)
4. 2 x Jellyfish
5. 5 x Swordfish
the more numbers, the better:D
These five are rare solving methods.
Eioru
 
Posts: 182
Joined: 16 August 2006

Postby maria45 » Tue Sep 12, 2006 5:45 pm

Hi Eioru,

is this meant as e.g.

1. > 4 Dynamic Double Forcing Chains(+)
maria45
 
Posts: 54
Joined: 23 October 2005

Postby Ocean » Wed Sep 13, 2006 7:44 am

Eioru wrote:Do sudoku solving techniques have this "Dynamic Double Forcing Chains(+)"

Here is a puzzle where Explainer applies Dynamic Double Forcing Chains (+). The clue pattern is new for this hardness level (Explainer rating 9.7).
Code: Select all
 *-----------*
 |..1|...|2..|
 |.3.|...|.4.|
 |5..|.6.|..7|
 |---+---+---|
 |...|1.8|...|
 |..4|.3.|8..|
 |...|9.4|...|
 |---+---+---|
 |6..|.2.|..3|
 |.7.|...|.5.|
 |..9|...|1..|
 *-----------*
Ocean
 
Posts: 442
Joined: 29 August 2005

Postby Eioru » Wed Sep 13, 2006 12:51 pm

Ocean wrote:Here is a puzzle where Explainer applies Dynamic Double Forcing Chains (+). The clue pattern is new for this hardness level (Explainer rating 9.7).
Code: Select all
 *-----------*
 |..1|...|2..|
 |.3.|...|.4.|
 |5..|.6.|..7|
 |---+---+---|
 |...|1.8|...|
 |..4|.3.|8..|
 |...|9.4|...|
 |---+---+---|
 |6..|.2.|..3|
 |.7.|...|.5.|
 |..9|...|1..|
 *-----------*


Thanks Ocean, and I find on this topic's first page
Ocean #5/M21/D21
.....1..2.1..3..4.5..6.......4.....1.7..8..3.2.....9..9....2.......4..7...35..8..
rated 9.4
also has 1xDynamic Double Forcing Chains (+)

and I feel the ranking is Double=>Cell=>Region=>Contration of average difficulty.

maria45 wrote:is this meant as e.g.
1. > 4 Dynamic Double Forcing Chains(+)

Yes, though I just find 1 Dynamic Double Forcing Chains(+),
so, it can be done from 2 to more.
Other four are also rare to satisfied.

Eioru wrote:All kind of "Forcing Chains" in my record list are :


I renew it
5 Forcing X-Chains ~ .1....2.......3..45...2..1.2...6..5...7..8....9.3..........48....49....36......2.
31 Forcing Chains ~ ..........4..8..5...3..1..8...9..5...9..6..2...1..8..4...3..7...6..2..9...5..7..1
11 Nishio Forcing Chains ~ ....6......62.13...278.456..61...45.4.......6.52...13..184.672...47.28......8....
23 Region Forcing Chains ~ 1.......2.3..4..5...6...7.....1.4....8..2..4....5.8.....2...6...4..3..8.7.......1
9 Cell Forcing Chains ~ 5..2..9......7......6..1..46..9..3...8.....4...7..2..18..3..5......4......1..6..9
36 Dynamic Contration Forcing Chains ~ ..1.....2.3..4....5..6..3....4..7..1....8..3.9..2..6.......8..9.7..2..4.2..1..8..
27 Dynamic Region Forcing Chains ~ .....1..2.3..2..4.5..6.......6.....7.7..1..3.8.....5..7....5.......3..2...98..6..
14 Dynamic Cell Forcing Chains ~ .....1..2.1..3..4.5..6.......4.....1.7..8..3.6.....8..2....6.......5..7...39..5..
4 Dynamic Double Forcing Chains ~ 1.......2.3..4..5...6...7.....1.3....4..6..8....4.5.....2...9...8..5..4.7.......1
19 Dynamic Contration Forcing Chains(+) ~ 1.......2.3..4..5...6...7.....1.4....8..7..4....5.8.....7...6...5..3..8.2.......1
10 Dynamic Region Forcing Chains(+) ~ 1.......2.3..4..5...6...7.....1.3....8..7..4....4.6.....2...6...5..3..8.9.......1
2 Dynamic Cell Forcing Chains(+) ~ 1.......2.3..4..5...6...7.....1.3....8..6..3....9.4.....7...1...4..5..8.2.......9
1 Dynamic Double Forcing Chains(+) ~ ..1...2...3.....4.5...6...7...1.8.....4.3.8.....9.4...6...2...3.7.....5...9...1..
Eioru
 
Posts: 182
Joined: 16 August 2006

PreviousNext

Return to General