The New Sudoku Players' Forum

[Leren]

After another day of searching, we are up to 525 ED grids, 646 ED 10 clue puzzles.

Leren

[Mathimagics]

.
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 . . | . . . |
  +-------+-------+-------+


[blue]

Confirmed.

Congratulations

[coloin]

... if you dont look you wont find !
Excellent ..... unfortunately i cant see the first move to solve it..

[Mathimagics]

Excellent ..... unfortunately i cant see the first move to solve it..

That's good! It's a "real" puzzle, not some trivial singles-only knock-up!

Here are the three CF puzzles I've found, on 3 different grids:

Code: Select all

.................2.....8.........8....7......9............4.....1....5.....6.....: 123456789456789132879321456231698574698574321745132698312945867967813245584267913
.................6.....1........85...........2............4.....3....8.....9.....: 123456789459287136786931245631845972942673518578129463214568397365794821897312654
.................6.....9........1.....4......2............4.....8....5.....7.....: 123456789457918362986723451862347915794185623315269874671594238239871546548632197


I have to thank Leren for doing such a good job on the 10-clue search. Showing that there were 100's of puzzles to be found, led me to revisit my Morph Walker, where I found a bug. Fixing this led to 1000's of 10C grids, and some of these turned out be non-minimal.

Our ED 10-clue SudokuPX catalog now has 3418 grids, 6268 puzzles.

[coloin]

blue's little processors ...... i can sense them whirring !!!

[eleven]

Congratulations, Mathimagics !

Seems to be a tough one indeed.

[blue]

Excellent ..... unfortunately i cant see the first move to solve it..

Added: there's an 8 locked in the diagonal in box 1, followed by ...
There's a chain of 5 hidden singles for 8's, but I can't see anything after that.

Here are the three CF puzzles I've found, on 3 different grids:

The solutions are minlex, but the clues don't line up with the solutions.

[Mathimagics]

The solutions are minlex, but the clues don't line up with the solutions.

Ah, now here's the thing ... I was told that the canonicalisation function should return the minlex puzzle which might not match the minlex solution ... so I did that.

Have I been misinformed? Or have I just misunderstood ...

In any case, here are the CF-solution aligned puzzles:

Code: Select all

...........6..........2............4......3....51............6.9.........8.......: 123456789456789132879321456231698574698574321745132698312945867967813245584267913
................3....9.....6....5...........8......4...1.....................2.5.: 123456789459287136786931245631845972942673518578129463214568397365794821897312654
.....6.....7.......8........................3.....9......5.....2......4.....3....: 123456789457918362986723451862347915794185623315269874671594238239871546548632197


[blue]

Maybe neither ...

In any case the puzzles aren't minlex either. They don't have a '1' in the first non-empty cell.
They have the same shapes as the minlex versions, but the wrong "(re)labeling".

Some people (maybe most) like puzzles to be in ("puzzle only") minlex form.
gsf's tool, was probably used may times, to put a puzzle in minlex form, before checking if it appeared in the list of "known 17's".

If you post a puzzle and solution grid together, though, (IMO) the grid should be the solution to the puzzle, and not the minlex form of its solution.

I see where you're coming from though. People like a minlex form for the puzzle, and you've been interested in reporting the number of ED solution grids, associated with with the puzzle lists that you've been keeping. I imagine then, that you have a database that pairs minlex puzzles with the minlex forms of thier solutions.

[Mathimagics]

In any case the puzzles aren't minlex either. They don't have a '1' in the first non-empty cell.
They have the same shapes as the minlex versions, but the wrong "(re)labeling".

Right. I simply looped through the 32 transformations, applied to both puzzle and solution, and chose the puzzle with "least" value. What I should be doing is choosing the puzzle with the earliest clue position, then relabelling so that clue becomes a '1'.

Does that sound right?

If you post a puzzle and solution grid together, though, (IMO) the grid be the solution to the puzzle, and not the minlex form of its solution.

Yes, I agree.

I imagine then, that you have a database that pairs minlex puzzles with the minlex forms of thier solutions.

For the 12-clue SudokuP's, I catalog the puzzles in the form returned by your SudokuP canonicaliser (puzzle+solution) function.

For PX puzzles, I have reverted to using the strict matching form, ie the solution is morphed to minlex CF, and the puzzle is morphed the same way, so it always matches the solution. If anybody wants minlex puzzle forms, I can do that separately.

[blue]

What I should be doing is choosing the puzzle with the earliest clue position, then relabelling so that clue becomes a '1'.

Does that sound right?

No. Don't worry (explicitly) about the clue positions, or the solution grid.

You should do something equivalent to this:
1) Transform the puzzle, without relabeling.
2) Flag digits 1-9 as "unmapped", map 0 to 0, and flag 0 as mapped (assuming 0 means "empty cell").
3) Set a "next available" value at 1.
4) Loop over the cells in the usual order.
5) For each one, look at the cell value, and check whether it has already been mapped.
6) If not, flag it as mapped, map it to the "next available" value, and increment the "next available" value.
7) Update the cell value using the map, and move on to the next cell.
8) When finished, check if transformed relabelled puzzle beats "best case", and update the best case as needed.

If you wanted to map the solution grid too, rather than just using the solver on the final puzzle,
then whenever you update the "best case" for the puzzle, you should:
1) Make sure that all 9 (possible) cell values have been mapped ... in case the puzzle used only 8 clue values.
2) Transform the original solution in the same way as the puzzle.
3) Relabel it using the (finalized) map.

[Mathimagics]

.
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!

[Mathimagics]

.
To get to an estimate of the number of PX grids with 10-clue puzzles, we'll follow blue's method, and begin with a breakdown of 10-clue grids by MCB.

We don't actually have exact MCB values for PX grids, but we can use the fact that all PX grids are firstly P grids, and try the distribution using the MCB values for SudokuP. We have found 7,163 grids so far with 10-clue puzzles, and here is our initial table:

Code: Select all

-----+----------+-------+-----------
 MCB |    grids |  10CG | 10CG/grids
-----+----------+-------+-----------
   0 |    1992  |  124  |  6.2249%
   1 |   16051  |  548  |  3.4141%
   2 |   69711  | 1436  |  2.0599%
   3 |  219352  | 2540  |  1.1580%
   4 |  438102  | 2934  |  0.6697%
   5 |  659108  | 2546  |  0.3863%
   6 |  803580  | 1952  |  0.2429%
   7 |  753617  | 1157  |  0.1535%
   8 |  561618  |  587  |  0.1045%
   9 |  377142  |  273  |  0.0724%
  10 |  215672  |   99  |  0.0459%
  11 |   28259  |   11  |  0.0389%
  12 |   49413  |   13  |  0.0263%
  13 |    6019  |    0  | 
  14 |    6738  |    1  |  0.0148%
  15 |      48  |    0  | 
  18 |    2028  |    0  | 
-----+----------+-------+-----------
     | 4208450  | 14221 |  0.3379%  (Puzzles = 28803)
-----+----------+-------+-----------


This seems like a useful starting point, as it clearly shows a distinct bell-curve distribution, much as very similar to what we saw for SudokuP.

Now for the tricky bit, testing random samples in each MCB division with the HS test rig. This could take some time! Small sized PX mode UA's are even rarer here than with SudokuP. Around 80% of PX grids appear to have no more than 16 UA's of size 12 or less. More than 60% have 10 or fewer.

On the plus side, there are a lot less grids to test ...

Unfortunately I can't do any HS testing for at least a week, since all my CPU threads are under the hammer with 12-clue SudokuP "back-fill" operations

[Mathimagics]

unfortunately i cant see the first move to solve it..

Seems to be a tough one indeed.

I notice that even the mighty fsss2 is challenged by these puzzles.

For 11-clue minimal puzzles I get 1000 - 1500 solves per second, whereas for the 9-clue puzzles I get just 60 - 90

I've unleashed a monster ...