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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Re: SudokuPX (SudokuP + Diagonal)

Postby tarek » Sun Dec 15, 2019 10:25 am

I'm currently rating a list that Leren kindly provided with Sukaku explainer v1.14.5

tarek wrote:started with Leren's PX list … I'm not sure if the list is a collection of random 10 clue puzzles or not but from the 1st 1000 puzzles it appears on average to have difficult puzzles and non singles puzzle. already there is an ER=10.6
Code: Select all
.....................................1.....23.4..5.......1.....4.6...7.....8..... 10.6/1.5/1.5 DCFC+FC/HS/HS


Update:
We have breached the ER=11.0 barrier with the SudokuPX. It will be good to know if you think that these rated by v1.14.5 are as difficult as they would appear
Code: Select all
...................................1...........2....345.....6.....47....8.....9.. 11.5/4.3/2.9 DCFC+DFC/g2SK01/gI
...................................1......2....3.........4...5.6......4.27..8.... 11.3/1.2/1.2 DCFC+MFC/HS/HS
...................................1......2....34........5...4.6.....1...7...8... 11.0/2.9/2.9 DCFC+MFC/gI/gI
...................................1......2....34........53..6.7.........8..9.... 11.3/2.9/2.9 DCFC+MFC/gI/gI


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Re: SudokuPX: 10-clue search

Postby tarek » Sun Dec 15, 2019 10:51 am

eleven wrote:
Mathimagics wrote:So, guys & gals, how's the pencil-solving analysis coming along?

I have played around with it for a while.
It needs some practice to spot moves like
Code: Select all
 *------------------------------------------------------------------------------------*
 |b134679   125679  12345679  | 23467    235679  2345679  | 123479  8        124579   |
 | 134579   8       1234579   | 23457    2579    234579   | 123479  124579   6        |
 | 34567    24679   24679     | 8        2679    1        | 47      234579   234579   |
 |----------------------------+---------------------------+---------------------------|
 | 134679   1679    134679    |b123467  b123679  8        | 5       123679   123479   |
 | 1345679  145679  1345789   | 1234567  2679    234579   | 24679   124679   1234789  |
 | 2        145679  3456789   | 14567   b135679  345679   | 13467   134679   34789    |
 |----------------------------+---------------------------+---------------------------|
 | 8        125679  2679      |c12367    4       23567    |b123679  1235679  123579   |
 | 45679-1  3       24579-1   |d12567   d12567   257      | 8      a1245679  124579   |
 |e14567   e124567  24567     | 9        8       23567    |d13467  d1234567  23457    |
 *------------------------------------------------------------------------------------*

1r8c8 = 1r1c1,r4c4,r7c7 (pos 1) - r7c4 = r8c45 => -1r8c13
1r1c1,r4c4,r7c7 (diag) = r8c8 - r8c45 = r7c4 => (pos1) -1r1c7, r4c1

There were some some more complex more complex with single digits, and now i wonder, if it is only a monster in length, not in hard steps.
Maybe it can be solved with locked candidates, subsets and coloring (one digit moves) only.
Is there no solver around ?

I found this next move which could be of interest:
5:2 grouped strong links in *:Main diagonal and in %:Box 7 weakly linked by c6 r8c9<>5
Code: Select all
+----------+----------------------------------------------------------------------------+----------+
| 134679   | 125679     12345679   23467      235679     2345679    123479     8        | 124579   |
+----------+----------+                                                      +----------+----------+
| 134579   | 8        | 1234579    23457      2579       234579     123479   | 124579   | 6        |
|          +----------+----------+                                +----------+----------+          |
| 34567      24679    | 24679    | 8          2679       1        | 47       | 234579     234579   |
|                     +----------+----------+          +----------+----------+                     |
| 134679     1679       134679   | 123467   | 123679   | 8        | 5          123679     123479   |
|                                +----------+----------+----------+                                |
| 1345679    145679     1345789    1234567  | 2679     | 234579     24679      124679     1234789  |
|                                +----------+----------+----------+                                |
| 2          145679     3456789  | 14567    | 135679   |*345679   | 13467      134679     34789    |
|                     +----------+----------+          +----------+----------+                     |
| 8          125679   | 2679     | 12367      4         %23567    | 123679   | 1235679    123579   |
|          +----------+----------+                                +----------+----------+          |
| 145679   | 3        | 124579     12567     %12567     %257        8        |*1245679  | 12479-5  |
+----------+----------+                                                      +----------+----------+
| 14567    | 124567     24567      9          8         %23567      13467      1234567  |*23457    |
+----------+----------------------------------------------------------------------------+----------+
The overall rating is 9.6 so it really gets ugly from this point
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Re: SudokuPX (SudokuP + Diagonal)

Postby tarek » Sun Dec 15, 2019 4:47 pm

Progress is slow in rating this collection of 10-clue SudokuPX. I only managed 13,000+ puzzles to rate. It is worth checking if this version of Sukaku Explainer assessment is fair as it appears that the collection so far is non-singles & on average very tough puzzles.

I'll share the latest high scorers (11.0+) for your feedback in case there is something wrong with the rating. I'll be interested specifically to know what do you think of the highest rated one
Code: Select all
...................................1..2........3..4.......5..6..4.....7..8..9.... 12.2/12.2/2.9 DCFC+DFC/DCFC+DFC/gI
...................................1...........2....345.....6.....47....8.....9.. 11.5/4.3/2.9 DCFC+DFC/g2SK01/gI
...................................1......2....3.........4...5.6......4.27..8.... 11.3/1.2/1.2 DCFC+MFC/HS/HS
...................................1......2....34........5...4.6.....1...7...8... 11.0/2.9/2.9 DCFC+MFC/gI/gI
...................................1......2....34........53..6.7.........8..9.... 11.3/2.9/2.9 DCFC+MFC/gI/gI
...................................1......2.3..45........6...7.8.........9.....4. 11.1/1.2/1.2 DLFC+MFC/HS/HS
...................................1......2.34.56........7...4.8.........9....... 11.1/1.2/1.2 DCFC+MFC/HS/HS
...................................1..2........3..4.......5..6..7.....8..9..2.... 11.0/11.0/2.9 DCFC+MFC/DCFC+MFC/gI
...................................1..2.....3..4..........3..5..6.....7..8..9.... 11.0/11.0/2.9 DCFC+MFC/DCFC+MFC/gI
...................................1..2.....3..4..5.......3..6..7.....8..9....... 11.0/11.0/2.9 DCFC+MFC/DCFC+MFC/gI
...................................1..2...3.4..5..6.......2..7...........8..3.... 11.1/8.8/2.9 DCFC+MFC/DRFC/gI
...................................12..........34........5...4.6.......7.8...9... 11.4/2.9/2.9 DCFC+MFC/gI/gI
...................................12..........34.5......6...4..7........8..9.... 11.7/2.9/2.9 DCFC+DFC/gI/gI
...................................12....3.....45........6...5.7...8.....9....... 11.1/2.9/2.9 DCFC+MFC/gI/gI
..................................1..2..3........4..5.........6..4..7.....2.....8 11.2/2.3/2.3 DCFC+MFC/NS/NS
...............................1..2..3.......45....6.......75....8........9...... 11.3/2.3/2.3 DCFC+MFC/NS/NS
..............................1.2..3..4........5...6.........7..8........1.....9. 11.4/4.0/2.9 DCFC+MFC/Sky/gI
.............................1.....2...........3....4.5.....6.....17....8.....9.. 11.5/4.3/2.9 DCFC+DFC/g2SK01/gI
..........................1........2......3....41........5...6.7.........8..9.... 11.3/1.5/1.5 DCFC+MFC/HS/HS
..........................1.......2..3..4...........5......6.....7..8.........1.9 11.2/1.2/1.2 DCFC+MFC/HS/HS


[Edit:] I rated the 3 known 9 clue SudokuPX puzzles separately and they rated ER 10.2, 9.6 and 11.1
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Re: Interesting SudokuPX

Postby tarek » Tue Dec 17, 2019 10:01 pm

An interesting puzzle with a rare one step technique for this type of puzzle to solve it to stte. Can you spot it?
It is a SudokuPX but for convenience I'm showing the X diagonal regions only

Code: Select all
+-----+-----------------------------------------+-----+
| 17  | 8     2     57    19    39    4     6   | 359 |
+-----+-----+                             +-----+-----+
| 6   | 5   | 17    2     4     139   78  | 39  | 89  |
|     +-----+-----+                 +-----+-----+     |
| 4     39  | 39  | 58    6     78  | 57  | 2     1   |
|           +-----+-----+     +-----+-----+           |
| 3     4     16  | 69  | 2   | 19  | 58    7     58  |
|                 +-----+-----+-----+                 |
| 57    2     57    3   | 8   | 4     19    19    6   |
|                 +-----+-----+-----+                 |
| 89    19    68  | 17  | 5   | 67  | 3     4     2   |
|           +-----+-----+     +-----+-----+           |
| 19    13  | 4   | 68    39    68  | 2   | 5     7   |
|     +-----+-----+                 +-----+-----+     |
| 58  | 6   | 58    4     7     2     19  | 13  | 39  |
+-----+-----+                             +-----+-----+
| 2   | 7     39    19    13    5     6     8   | 4   |
+-----+-----------------------------------------+-----+

Original puzzle which comes from Leren's collection of 10 clue SudokuPX puzzles
Code: Select all
..........................1....2.....2.3............4...4....5..6..7...........8.
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Re: SudokuPX (SudokuP + Diagonal)

Postby 999_Springs » Wed Dec 18, 2019 3:55 am

bug+2 -9r1c56r2c89? lol
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
Pat wrote:prenyast
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Re: SudokuPX (SudokuP + Diagonal)

Postby tarek » Wed Dec 18, 2019 12:45 pm

999_Springs wrote:bug+2 -9r1c56r2c89? lol

There is a w-wing (not yet implemented in Sukaku explainer), a VWXYZ wing (2 of them) but I was after the BUG+2. Well done! :D

P.S. Because this is a SudokuPX you can also eliminate -9r4c6,r8c9
Last edited by tarek on Wed Dec 18, 2019 4:31 pm, edited 1 time in total.
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Re: 10-clue SudokuPX list rating update

Postby tarek » Wed Dec 18, 2019 12:58 pm

Leren's 10 clue SudokuPX list is slow to rate due to high on average difficulty which reflects on the time to rate per puzzle. I've stopped at 40,000.

The highest diamonds encounterd
Code: Select all
.........................1...2.....3..4...5.......6..7.8..........7.........9.... 10.6/7.8/7.8 CFC+FC/NFC/NFC
.........................1...2........3...4.....4....56.........7.5........8..... 9.8/7.8/7.8 DCFC+/NFC/NFC
.........................1...2........3...4.....4....5.6..........57........8.... 9.4/7.8/7.8 DCFC/NFC/NFC
.........................12..3........4...5.....5....6.7..........6.........8.... 9.4/7.8/7.8 DCFC/NFC/NFC
.........................1...2...3....45..........6..7.8..........7.........9.... 9.3/7.8/7.8 DCFC/NFC/NFC
.........................1...2.....3..4.........5.6..7...3........7.............8 9.2/7.8/7.8 DCFC/NFC/NFC
.........................1...2...3.4..56..........7..8..........4.8.............. 9.1/7.8/7.8 DRFC/NFC/NFC
.........................1...2........3...4.....4.5..67...........6........8..... 8.0/7.8/7.8 NFC/NFC/NFC
.........................1...2........3...4.....4.5..67...........6..........8... 7.8/7.8/7.8 NFC/NFC/NFC


Highest rated puzzles encountered
Code: Select all
...................................1..2........3..4.......5..6..4.....7..8..9.... 12.2/12.2/2.9 DCFC+DFC/DCFC+DFC/gI
.........................1....2....13..........45............6.......7...8.9..... 12.1/4.1/2.9 DCFC+DFC/2SK/gI
.........................1...23...........4..........5....6......7....8..8...9... 12.0/12.0/4.3 DCFC+DFC/DCFC+DFC/g2SK01
.........................1...23...........4..........5....6......7....8..2...9... 12.0/12.0/4.3 DCFC+DFC/DCFC+DFC/g2SK11
.........................12..3......4...........5....6....47....8...........2.... 12.0/7.9/2.9 DCFC+DFC/NFC/gI
.........................1...2..3.....4...5..........6....7......1....8......9... 12.0/2.9/2.9 DCFC+DFC/gI/gI
.........................1...2......3...........4..5.6....7.....8......5....9.... 12.0/2.3/2.3 DCFC+DFC/NS/NS
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Re: SudokuPX (SudokuP + Diagonal)

Postby tarek » Wed Dec 18, 2019 8:01 pm

Sukaku Explainer v1.14.7 release is out which supports SudokuPX

use the command line option if interested
Code: Select all
-X1 -D1 --techs=111110101110111111110111001101001111111
which uses the P and X constraints with the default variants techniques
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