The New Sudoku Players' Forum

[champagne]

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

[Mathimagics]

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

[tarek]

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

Tarek

[1to9only]

http://forum.enjoysudoku.com/maximum-number-of-clues-for-a-given-se-rating-t6210-120.html#p281374

[Mathimagics]

Sorry for the meaningless diversion ... I seem to have gotten all my pearls in a jam

[tarek]

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?

[Mathimagics]

getting your leopard deaf?

Hysteriacal!

[Pupp]

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"?

[mith]

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.

[1to9only]

From: http://forum.enjoysudoku.com/patterns-game-t6290.html

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.

[m_b_metcalf]

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

[Pupp]

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)

[mith]

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?

[Pupp]

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.

[1to9only]

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.
.