## SudokuPX (SudokuP + Diagonal)

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Re: SudokuPX (SudokuP + Diagonal)

Mathimagics wrote:.
Thanks, blue!

My minlex-puzzle results for the 3 x 9C grids above:
Code: Select all
`.................1.....2.........2....3......4............5.....6....7.....8.....: 619578324527349681348612579196783245273495816485261937831957462962134758754826193.................1.....2........34...........5............6.....7....3.....8.....: 257641938634987521981352674192573486763498152548126793325764819876219345419835267.................1.....2........3.....4......5............4.....6....7.....8.....: 359471862827695341641382957186723594274958136593164278938247615462519783715836429`

That looks better!

But now for the pencil/paper solvers... What methods must be used to solve this 9-clue puzzle?
(No Bruteforce/Backtrack of course)

Hajime

Posts: 1022
Joined: 20 April 2018
Location: Netherlands

### Re: SudokuPX (SudokuP + Diagonal)

.
I have updated the 10-clue grid distribution above.

I've been running the morph-walker now for just 24 hours, and we have found 14,221 grids with 10-clue puzzles.

This is 0.34% of the total grids, compare this figure (which will certainly at least double, and probably increase by much more than that) with the 0.11% of SudokuP grids estimated to have 12-clue puzzles.

In terms of puzzle counts, SudokuP grids with 12-clue puzzles on average have 5 or 6, while SudokuPX 10-clue grids have around 2.

Mathimagics
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Location: Canberra

### Re: SudokuPX (SudokuP + Diagonal)

Hi all,

{Edit: I got my constraints messed up, corrected now]

tarek

tarek

Posts: 3759
Joined: 05 January 2006

### Re: 9-clue SudokuPX found?

Hi, Mathimagics!
Mathimagics wrote:.
I have found the first 9-clue puzzle!

Unless my solver is dodgy, of course. I think not, but will wait for Leren or blue to confirm this.

Code: Select all
`  +-------+-------+-------+  | . . . | . . . | . . . |  | . . . | . . . | . . 6 |  | . . . | . . 1 | . . . |  +-------+-------+-------+  | . . . | . . 8 | 5 . . |  | . . . | . . . | . . . |  | 2 . . | . . . | . . . |  +-------+-------+-------+  | . . . | . 4 . | . . . |  | . 3 . | . . . | 8 . . |  | . . . | 9 . . | . . . |  +-------+-------+-------+`

Congratulations for finding 9-clue SudokuPX puzzle! You came to "essential bound" for Sudoku-like puzzles - valid puzzle must have not less than 8 clues (and have not less than 8 different digits).

Serg
Serg
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### Re: SudokuPX (SudokuP + Diagonal)

Hi Serg!

I was actually hoping SudokuPX might produce an 8-clue puzzle, but that now seems highly unlikely. We have found over 30,000 grids with 10-clue puzzles, but all of these puzzles (except for those on the 3 grids above) are minimal.

It seems that we can only get 8-clue puzzles by varying the PSETS (cf: my "Contiguous Psets" example).

Cheers!

Mathimagics
2017 Supporter

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Joined: 27 May 2015
Location: Canberra

### Re: SudokuPX (SudokuP + Diagonal)

Hajime wrote:But now for the pencil/paper solvers... What methods must be used to solve this 9-clue puzzle?

I guess, only very advanced ones would do it. After resolving the five 8's (using the lock in the main diagonal, as blue mentioned), it looks like this:
Code: Select all
`+-------------------------------+-------------------------------+-------------------------------+| 8         125679    12345679  | 23467     235679    2345679   | 123479    123579    1234579   || 134579    124579    1234579   | 23457     2579      234579    | 123479    8         6         || 34567     245679    2345679   | 8         235679    1         | 347       234579    234579    |+-------------------------------+-------------------------------+-------------------------------+| 134679    1679      134679    | 123467    123679    8         | 5         123679    123479    || 1345679   145679    1345789   | 1234567   125679    234579    | 1234679   124679    1234789   || 2         145679    3456789   | 134567    135679    345679    | 13467     134679    34789     |+-------------------------------+-------------------------------+-------------------------------+| 1679      8         125679    | 12367     4         23567     | 123679    1235679   123579    || 145679    3         124579    | 12567     12567     257       | 8         1245679   124579    || 14567     124567    24567     | 9         8         23567     | 13467     1234567   23457     |+-------------------------------+-------------------------------+-------------------------------+`

I tried, but could not eliminate any candidate here. But ok, i have never solved a SudokuPX ...
eleven

Posts: 2805
Joined: 10 February 2008

### SudokuPX: 10-clue search

.
We have passed an interesting milestone - a rather astonishing 2% of SudokuPX grids have been found to have 10-clue puzzles:

Code: Select all
`-----+----------+-------+----------- MCB |    grids |  10CG | 10CG/grids-----+----------+-------+-----------   0 |    1992  |   848 | 42.5703%   1 |   16051  |  3686 | 22.9643%   2 |   69711  |  8901 | 12.7684%   3 |  219352  | 16174 |  7.3735%   4 |  438102  | 17807 |  4.0646%   5 |  659108  | 14950 |  2.2682%   6 |  803580  | 10733 |  1.3356%   7 |  753617  |  6171 |  0.8189%   8 |  561618  |  3144 |  0.5598%   9 |  377142  |  1339 |  0.3550%  10 |  215672  |   509 |  0.2360%  11 |   28259  |    36 |  0.1274%  12 |   49413  |    76 |  0.1538%  13 |    6019  |     4 |  0.0665%  14 |    6738  |     5 |  0.0742%  15 |      48  |     0 |  0.0000%  18 |    2028  |     0 |  0.0000%-----+----------+-------+-----------     | 4208450  | 84383 |  2.0051%  (Puzzles = 199352)-----+----------+-------+-----------`

The random morph walkers are not yet fatigued, not even laboured breathing, so this count will certainly rise even further.

There have been no further 9-clue discoveries, it looks like there might only be those 3 reported above.

So, guys & gals, how's the pencil-solving analysis coming along? I see the dog ate tarek's homework ...

Mathimagics
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Location: Canberra

### Re: SudokuPX: 10-clue search

Mathimagics wrote: I see the dog ate tarek's homework ...

I wanted to check the validity 1st but messed up my constraints. I then managed to verify all of them. Congratulations on the 9-clue puzzles. You know I have interest in theses 8-clue constrained puzzles from before.

My solving unfortunately finished abruptly very quickly. Although I can see some of the easier solving techniques even in the variant mode, I can't do that with the more advanced ones. Variant fishes and almost locked sets are more difficult unless you solve these variants on a regular basis.

I will try to put them through my solver to check ... alternatively it may need a variant sudoku solver elesewhere to advance it.

I can certainly see your next project coming up: "Windoku X"

tarek

tarek

Posts: 3759
Joined: 05 January 2006

### Re: SudokuPX: 10-clue search

tarek wrote:I can certainly see your next project coming up: "Windoku X"

I have configured a solver and basic toolset for SudokuW, SudokuWX (ie Windoku, WindokuX) and will report on the preliminary results in a separate thread.

Mathimagics
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Location: Canberra

### Re: SudokuPX: 10-clue search

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 ?
eleven

Posts: 2805
Joined: 10 February 2008

### Re: SudokuPX: 10-clue search

eleven wrote:Is there no solver around ?

I could provide an "X" option for my (Dobrichev) SudokuP fsss solver (for Windows), But I don't see how that would help with solver-strategy development.

If it's the solution you want, it is given above (item 2 of the 3 grids listed) ...

Mathimagics
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### Re: SudokuPX: 10-clue search

I thought of a techniques solver with coloring (nishio) implemented. I think, it would have good chances to to it without guessing.
I know the solution, but there will be many steps to come there, so it is time consuming, to do all that without solvers help, if i want to find a good solution.

[Added:] If it can be solved with coloring, i would not spend more time on it. If not, i would like to see, where it is stuck.
eleven

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Joined: 10 February 2008

### Re: SudokuPX (SudokuP + Diagonal)

Probably SE > 9, can't solve it with single chains. Maybe set chains/fish or deadly patterns/complex logic.
But it still removed 20 candidates.
creint

Posts: 340
Joined: 20 January 2018

### Re: SudokuPX (SudokuP + Diagonal)

I guess your single chains can't resolve single digit patterns like the ones i posted above. : no, it should, but not patterns like full swordfish.
I arrived at a solution after about 70 steps (i guess, many were not necessary), but i am not sure, that i have not made mistakes (more probably i did).

This was my hardest step (after a couple of other eliminations), from units box 8, position 6 and diagonal 1.
Code: Select all
` *-------------------------------------------------------------------* | 137  .  .        | .      .      .       | .     .       .        | | .    8  135-2479 | .      .     #2479+35 | .     .       6        | | .    .  24679    | .      .      .       | .     .       .        | |------------------+-----------------------+------------------------| | .    .  .        | 12347  .      .       | .     .       .        | | .    .  1358-479 | .      2679  #2479+35 | .     .       138-2479 | | .    .  .        | .      .     a34579   | .     .       .        | |------------------+-----------------------+------------------------| | .    .  .        | 12367  4     B23567   | 2679  .       .        | | .    . #2479+5   |A12567 A12567 #27+5    | .    b124579 #2479     | | .    .  .        | 9      8     B23567   | .     .       35-247   | *-------------------------------------------------------------------*`

2479 must be in r25c6,r8c369 (# marked cells in pos 6 unit):
Otherwise both 3 and 5 must be there, but a 3 implies, that there is no 5:

3r25c6 - r*679c6 = r7c4 - 3r1c1,r4c4,*r6c6 = (3-5) r9c9 =
{[5r6c6 - r25789c6 = r8c45 - r8c3] | [5r8c8 - r8c3456 = r79c6 - r258c6] }
(in both cases not in # cells, but in aA or bB)

From the other side, if -5r9c9, both 5r6c6 and r8c8 kill the 5's in the marked cells => 3r25c6 -> 3r9c9
=> -2479r2c3,r5c39, -247r9c9
eleven

Posts: 2805
Joined: 10 February 2008

### Re: SudokuPX (SudokuP + Diagonal)

Hm, when i tried to shorten my solution path, i saw that at least one step after the one above was wrong. Not in the outcome, but i would need a complex network to prove it.
I have spent too much time on it to look for alternatives now, and it is very cumbersome without a technique solvers help. With the 11 additional groups and the lot of steps needed, you can hardly avoid mistakes.
So i can't recommend it for p&p players ...
eleven

Posts: 2805
Joined: 10 February 2008

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