SudokuPX (SudokuP + Diagonal)

For fans of Killer Sudoku, Samurai Sudoku and other variants

Re: SudokuPX (SudokuP + Diagonal)

Postby Leren » Thu Sep 06, 2018 11:35 am

The latest news I have on the SudokuPX front is that Mathimagics now has a stash of 206,059 puzzles solving to 88,114 EDPX grids. The number is rising slowly, as MM is working furiously on the SudokuP 12 clue project, and I'm finding about a hundred puzzles a day with my spreadsheet approach, although I suspect that if MM got back on this project the number of puzzles would rise very quickly. The 9 clue puzzle count is stalled at 3.

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Re: SudokuPX (SudokuP + Diagonal)

Postby creint » Thu Sep 06, 2018 9:07 pm

eleven wrote:I guess your single chains can't resolve single digit patterns like the ones i posted above.

With your hardest step:
An ALS gets reduced by a chain, but that chains contains 2 subchains that each result in a reducing it to a Locked set.
For the extra eliminations in cell r9c9, you use yet another chain to proof 3 or 5.
How far should a solver go, with depth or trying extra chains?

I did not use sets in my solving net nor did i use subchains, so it would have never found this. But still my solver would solve up to SE 9, i think.
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Re: SudokuPX (SudokuP + Diagonal)

Postby Mathimagics » Thu Sep 06, 2018 11:47 pm

.
OK, we started with SudokuP, found the absolute minimal puzzles (11 clues), and these turned out to be P&P solvable without too much difficulty.

But when we add the X constraints, we find that 9-clues is the new minimum, and these puzzles are clearly challenging.

I think that tarek has confirmed that the same situation applies to SudokuW (Windoku), which after all is simply SudokuP with a different set of "windows" (PSET's). The 9-clue puzzle I posted there there is similarly challenging, it seems.

One of the reasons I find Kakuro so absorbing is that it has enormous range in difficulty levels (wrt P&P solving), from easy to impossible. I conjectured once that Sudoku was less interesting because it had a much narrower range.

But here we have demonstrated, I think, that these variants extend the difficulty range considerably.

I think this is a good thing! 8-)
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Re: SudokuPX (SudokuP + Diagonal)

Postby Leren » Thu Nov 22, 2018 12:28 am

Well, I done nothing else for the last couple of months apart from searching for 10 clue PX puzzles. I now have a collection of about 149,000.

In doing so I appear to have come across 3 new 9 clue puzzles. Here they are in minlex format with their corresponding solutions.

Code: Select all
................1.....2............3......2....45............6.7.........8.......      128745936347869512965123847851692473693471285274538691519287364736954128482316759
...............1......2....3..........4...........56...1...............7.......8.      789163425245789163163524798396871542524396871871245639918637254632458917457912386
...........1....2.....3............4...........25............6.7.........8.......      639712548471958623258634719397286154514397286862541397923875461745169832186423975

It would be nice if one of resident geniuses could confirm/refute the correctness of this.

Leren

<edit>

Following blue's observation below, I have found my minlexing bug, so no new 9 clue puzzles and my EDPX puzzle count has dropped to about 149,000. Ouch !!! :oops:
Last edited by Leren on Fri Nov 23, 2018 8:18 am, edited 3 times in total.
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Re: SudokuPX (SudokuP + Diagonal)

Postby blue » Thu Nov 22, 2018 7:14 am

Hi Leren,

It's "refute", unfortunately.
It looks like your "minlexing" process, isn't taking the E-transformation into account.
The puzzles, can be transformed to match Mathimagics's three puzzles, like this:

Code: Select all
Leren #1: E-transform,                          relabel --> Mathimagics #3
Leren #2: E-transform, (left <-> right) mirror, relabel --> Mathimagics #1
Leren #3: E-transform,                          relabel --> Mathimagics #2
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Re: SudokuPX (SudokuP + Diagonal)

Postby Leren » Thu Nov 22, 2018 8:12 am

OK blue, thanks for that. Leren
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Re: SudokuPX (SudokuP + Diagonal)

Postby Mathimagics » Sun Dec 09, 2018 1:26 pm

.
We've found many, many 10-clue SudokuPX puzzles, by various non-rigorous means.

One rigorous (ie. complete) enumeration we CAN easily do is to use the 10-clue symmetric puzzle enumerator (see here)

I ran it on SudokuPX and found just 32 cases of symmetric 10-clue puzzles:

Hidden Text: Show
Code: Select all
.1.2.....3.....4.....5.....................................4.....6.....2.....7.8.
.1.2.....3.....4.....5.....................................6.....5.....7.....3.8.
.1.2.....................3.4.3.....................5.1.6.....................7.8.
.1.2.....................3.4.5.....................6.7.6.....................8.4.
.1.......2...............3.4.3.....................5.1.6...............7.......8.
.1.......2...............3.4.5.....................6.7.6...............8.......4.
.1.............2.........3.4.3.....................5.1.6.........7.............8.
.1.............2.........3.4.5.....................6.7.6.........8.............4.
.1...................2...3.4.3.....................5.1.6...7...................8.
.1...................2...3.4.5.....................6.7.6...8...................4.
...1.....2.....3.....4...5.............................6...3.....7.....1.....8...
...1.....2.....3.....4...5.............................6...7.....4.....8.....2...
...1.....2.....3.....4.....5.........................6.....3.....7.....1.....8...
...1.....2.....3.....4.....5.........................6.....7.....4.....8.....2...
...1.....2.....3.....4.......5.....................6.......3.....7.....1.....8...
...1.....2.....3.....4.......5.....................6.......7.....4.....8.....2...
.....1.2...3.....4.....5.................................3.....1.....6...7.8.....
.....1.2...3.....4.....5.................................6.....7.....5...8.4.....
.....1.2...........3.............3.4.........2.5.............6...........7.8.....
.....1.2...........3.............4.5.........6.7.............7...........5.8.....
.....1.....2.....3.4...5.................................2...6.1.....7.....8.....
.....1.....2.....3.4...5.................................6...7.8.....5.....3.....
.....1.....2.....3.....4.........5.............6.........2.....1.....7.....8.....
.....1.....2.....3.....4.........5.............6.........7.....8.....4.....3.....
.....1.....2.....3.....4...........5.........6...........2.....1.....7.....8.....
.....1.....2.....3.....4...........5.........6...........7.....8.....4.....3.....
.......1...2.......3.............3.4.........1.5.............6.......7...8.......
.......1...2.......3.............4.5.........6.7.............7.......8...5.......
.......1.........2.3.............3.4.........1.5.............6.7.........8.......
.......1.........2.3.............4.5.........6.7.............7.8.........5.......
.......1...........2...3.........2.4.........1.5.........6...7...........8.......
.......1...........2...3.........4.5.........6.7.........8...7...........5.......


Note that these aren't canonicalised, so there are probably many equivalences wrt CF grids/puzzles in this set.
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