The hardest sudokus (new thread)

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Re: The hardest sudokus (new thread)

Postby champagne » Thu Aug 13, 2020 5:55 am

Mathimagics wrote:Thanks, Tarek!

Sampling 10 million 18C minimal puzzles suggests 1 in ~900 are pearls, BTW. That's pretty close to the 17C case (57, or 1 in 862)

Are there any instances of non-minimal pearls?

Hi Mathimagics,

just considering the definition or a pearl and of a diamond, taking a puzzle and making simplest moves first, you reach the position where the remaining puzzle is a diamond. You are in basically in a pearl position when you have done all moves rated below 2.3 if you take this as start.

Hope this is the right answer to your point
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Re: The hardest sudokus (new thread)

Postby Mathimagics » Thu Aug 13, 2020 8:03 am

What I meant was, can a Pearl (no singles available) have redundant clues?

Conversely, can we add clues to a Pearl and still get a Pearl? It seems that we can:
Code: Select all
....56...4......23...1......1..7.3...6......4...3....8.........8.2..4.........56.   18c
....56...4......23...1......1..7.3...6......4...3....8.........8.2..4.........562   19C

And we can add even more, the max on this puzzle is 37 clues:
Code: Select all
....567.94..7...23..91.3...21..7.39..6.9..274.9.3.2..8.........8.2..493.94.8.7562   37C
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Re: The hardest sudokus (new thread)

Postby tarek » Thu Aug 13, 2020 11:15 am

I’m not sure where all of the is leading to. If you are solving using resolution rules that have singles at the bottom. Then each time you use a non single technique you are technically in a Pearl position

I’m not sure where to find it now but somebody has a thread with puzzles having the maximal number of clues for each SE rating which is impressive

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Re: The hardest sudokus (new thread)

Postby Mathimagics » Thu Aug 13, 2020 1:30 pm

Sorry for the meaningless diversion ... I seem to have gotten all my pearls in a jam :?
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Re: The hardest sudokus (new thread)

Postby tarek » Thu Aug 13, 2020 3:07 pm

Mathimagics wrote:Sorry for the meaningless diversion ... I seem to have gotten all my pearls in a jam :?
surly that is still better than getting your leopard deaf?
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Re: The hardest sudokus (new thread)

Postby Mathimagics » Thu Aug 13, 2020 3:14 pm

tarek wrote:getting your leopard deaf?

Hysteriacal! 8-)
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Re: The hardest sudokus (new thread)

Postby Pupp » Thu Aug 13, 2020 8:21 pm

champagne wrote:
Mathimagics wrote:Thanks, Tarek!

Sampling 10 million 18C minimal puzzles suggests 1 in ~900 are pearls, BTW. That's pretty close to the 17C case (57, or 1 in 862)

Are there any instances of non-minimal pearls?

Hi Mathimagics,

just considering the definition or a pearl and of a diamond, taking a puzzle and making simplest moves first, you reach the position where the remaining puzzle is a diamond. You are in basically in a pearl position when you have done all moves rated below 2.3 if you take this as start.

Hope this is the right answer to your point


What's a "Pearl" or a "Diamond"?
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Re: The hardest sudokus (new thread)

Postby mith » Thu Aug 13, 2020 8:45 pm

As I understand it, a pearl is a puzzle where the hardest rated move is required before you are able to place a digit, while a diamond is a puzzle needs its highest rated move to eliminate a candidate. (Though I think I've seen it also used for puzzles where the moves required for placing a digit / eliminating a candidate are above a certain threshold?)

SE gives a pearl and diamond rating, which is the rating required to place a digit or eliminate a candidate, respectively... at least for the techniques SE supports.
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Re: The hardest sudokus (new thread)

Postby 1to9only » Thu Aug 13, 2020 8:57 pm

From: http://forum.enjoysudoku.com/patterns-game-t6290.html
g.r.emlin wrote:Patterns Game ratings are the tuple ER/EP/ED:
  • ER (explainer rating): the higest Sudoku Explainer rating of the methods leading to the puzzle solution
  • EP (pearl rating): the higest Sudoku Explainer rating of the methods leading to the first cell placement
  • ED (diamond rating): the higest Sudoku Explainer rating of the methods leading to the first candidate elimination
Ratings sort numerically from left to right, low to high. A pearl or diamond must have ER > 2.3.

Pearl, ER=EP, e.g. ED=4.0/4.0/1.2. Diamond, ER=EP=ED, e.g. ED=5.0/5.0/5.0.
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Re: The hardest sudokus (new thread)

Postby m_b_metcalf » Thu Aug 13, 2020 9:36 pm

1to9only wrote:Pearl, ER=EP, e.g. ED=4.0/4.0/1.2. Diamond, ER=EP=ED, e.g. ED=5.0/5.0/5.0.

Small nit, I don't think 4.0/4.0/1.2 exists. Try 4.0/4.0/2.6.

Regards,

Mike
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Re: The hardest sudokus (new thread)

Postby Pupp » Sat Aug 15, 2020 8:41 pm

Just curious, but are there puzzles that would rate beyond 12 on Sudoku Explainer?

I had it crunch a puzzle off this thread and it clocked in at 11.9, and had Dynamic Region Forcing Chain, with a Dynamic Forcing Chain nested inside of it. (Not to mention many other steps that it seems only would be usable with puzzles at the Ludicrous level.)

12.3.....
4.....3..
..3.5....
..42..5..
....8...9
.6...5.7.
..15..2..
....9..6.
.....7..8

Difficulty rating: 11.9 (Dynamic Region Forcing Chains (+ Dynamic Forcing Chains))
This Sudoku can be solved using the following logical methods:
55 x Hidden Single
1 x Direct Hidden Pair
3 x Naked Single
7 x Pointing
1 x Claiming
1 x Hidden Pair
2 x Naked Triplet
1 x Skyscraper
1 x Two-string Kite
1 x XY-Wing
1 x XYZ-Wing
1 x WXYZ-Wing 137
1 x VWXYZ-Wing 1412
1 x VWXYZ-Wing 2411
1 x VWXYZ-Wing 139
2 x Forcing Chain
1 x Nishio Forcing Chains
4 x Cell Forcing Chains
3 x Region Forcing Chains
6 x Dynamic Cell Forcing Chains
21 x Dynamic Contradiction Forcing Chains
6 x Dynamic Region Forcing Chains
1 x Dynamic Region Forcing Chains (+)
2 x Dynamic Contradiction Forcing Chains (+)
11 x Dynamic Contradiction Forcing Chains (+ Forcing Chains)
1 x Dynamic Region Forcing Chains (+ Forcing Chains)
3 x Dynamic Contradiction Forcing Chains (+ Multiple Forcing Chains)
5 x Dynamic Contradiction Forcing Chains (+ Dynamic Forcing Chains)
3 x Dynamic Region Forcing Chains (+ Dynamic Forcing Chains)

The most difficult technique (ER): Dynamic Region Forcing Chains (+ Dynamic Forcing Chains)
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Re: The hardest sudokus (new thread)

Postby mith » Sun Aug 16, 2020 4:07 am

11.9 is the highest found for regular sudoku - there are 9 such puzzles in the database. I think someone posted a few 12s for Sudoku X earlier in the thread?
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Re: The hardest sudokus (new thread)

Postby Pupp » Sun Aug 16, 2020 3:48 pm

mith wrote:11.9 is the highest found for regular sudoku - there are 9 such puzzles in the database. I think someone posted a few 12s for Sudoku X earlier in the thread?


Thanks. Just curious, but does anybody know the highest difficulty for normal sudoku puzzles they use in competition?

There has to be some sort of upper bound, since solvers have a time limit to solve a puzzle.
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Re: The hardest sudokus (new thread)

Postby 1to9only » Sun Aug 16, 2020 4:56 pm

Pupp wrote: anybody know the ... difficulty for normal sudoku puzzles they use in competition?

In the 14th World Sudoku Championship 2019, this was one sudoku puzzle, it solves with singles only:
Code: Select all
12.......34.5.79.....6...5..987...4...........6...321..8...4.....48.5.67.......89 ED=1.5/1.2/1.2

In sudoku competitions, solvers have limited time to solve about 10 sudoku variants, with points awarded for correct solutions.
If you want more info (a sampler of sudokus in the competition), visit https://wspc2019.de/wsc.php, and download the Instruction Booklet pdf.
.
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