The New Sudoku Players' Forum

[coloin]

If you scan grids composed by intersecting the box 1 of the canonical representation of band #14 with the box 1 of stack #381, you get the ultimate answer of 42 17-clue puzzles, and no better combination exists.....
)

and i thought this was a joke reference to the old "hitchhiker" answer [42]

It took a super human search to find the minimum number of clues for a double band [7] [ range 7- ?12]

certainly all grids with a 3 X MCDB count of 35 cant have a 17 - but that wont be many

Im just reflecting on what i said a while back here

if we are looking for grids which are likely to not have a 20 [ or 19] [as opposed to a 17]

I casually queried whether the minimum number of clues for a double band [MCDB] was 12 .... but it could well be 13
and certainly those double bands which have both requiring 5 clues might well have a MCDB of > 10

we could look at the band 3 which go along with those high scoring band 1&2s double bands

if they have a high scoring double band in the vertical bands in the grid ... we could have potential for finding those solution grids without a 20 /19

[coloin]

Yes..it could well be MCDB =13 for some double bands

Code: Select all

1.....7.........23.891......3.5...9..6...72..........4....4......59......7...26..


Code: Select all

+---+---+---+
|1..|...|7..|
|...|...|.23|
|.89|1..|...|
+---+---+---+
|.3.|5..|.9.|
|.6.|..7|2..|
|...|...|..4|
+---+---+---+
|...|.4.|...|
|..5|9..|...|
|.7.|..2|6..|
+---+---+---+ the representative one 20-clue puzzle in the MC grid


I cant seem to get it down to 12 clues in a double band which would be good because .....

If all 3 double bands need 13 clues - as they are here all equivalent, then 3 X the MCDB of 13 = 39.
This covers 2 grids therefore 39/2 = 19.5 , therefore 20 clues [ more than 19.5] would be needed

EDIT, unfortunately this is not the case as there is a completion in 12 clues for the double band in the mc grid.....
thanks to blue below

[coloin]

Well thats pretty good .... stunning really

and maybe those grids at either end will have a tendancy to have low or high clues.... and those at the top i presume may include most of the automorphic grids already checked !

And a definite reminder - as if we needed one of how many solution grids there are ......

With regard to my last post .... please could you check that the MCDB of the MC grid is 13 ....

....and i believe that there is quite a big number of ED double bands .... but at least only 44 classes !

[coloin]

Code: Select all

  1,  1,  1,224,224,224       0,     0,     0,     0,     0,     0
  4,224,224,224,224,224     252,     0,     0,     0,     0,     0
224,224,224,254,254,413       0,     0,     0,     0,     0,     0
224,224,224,225,225,414       0,     0,     0,    90,    90,   324

All them had either all bands or all stacks having type 224.

Yes they all have the triple band 224 !

I presume that all grids with triple band 224 are automorphic ?

I wonder does that mean that all grids with double band 224,224 and their respective 3rd band are automorphic - and already tested ?

[coloin]

Thankyou !

Well it seems we will know eventually if there are any more 21 but no 20 grids.

And excellent computation with the double bands .....i knew it was big
I remember a contributor computing the 5e9 grids row by row, but i have failed to locate where it was in the forum - so we could confirm your calculation if it could be located

And its such a shame [ for me ] that the MC grid does have double band with 12 clues .....I will have to edit accordingly !

If there are any double bands which need 13 clues to complete they would surely be in the known grids with bands needing 6 clues.... and we know the status of these grids anyway.

[coloin]

Great ..
.. will blue’s magic program be slower or quicker at finding 667-19Cs .... just wondering !

[coloin]

Such is the scale of the task ....
Perhaps there are casual readers who could easily help out with spare unused computer time. !
Perhaps I could put up a software guide where some could email you zipped reliable batches of up to 1M puzzles at a time.. ?
I hope you dont mind ive done it here - to see if there is any interest !!

However the 18C as we know is the stumbling block.

I’ve been looking at /generating the remote ( untouchable) puzzles which are isolated (-1+1) or existing in small pockets of isolated groups ... as of course there is
The big group of 1 billion 18C puzzles which are connected (-1+1) are there to be found easily - but not easy to collate!

[coloin]

Yes i tend to agree with you
looking at the batch run a single 19C puzzle was generated x7 to 750,000 puzzles in 4 hours, but a breakdown of solution grids was only 250,000. So indeed your program is 15x quicker !!!
When the LCT-20 completes i will use your program ...

[coloin]

my oldish but not that old spare dual computor ...is 32 bit i will use it !!!

but my 4 core -64 reported no issues !!!

Code: Select all

Solver verified, ready for work!

....great !

well done in the cricket !

[coloin]

Excellent that did the trick.
Now up and running with the Gen19j.exe - 2 workers more.

[coloin]

Yep more stability in the program and a needed RAM upgrade means
That I have workers in the background churning out 19C

x3 on gen19c
x2 on gen19j

returning home from a trip - have got 19 batch files to zip and transfer ....

C

[coloin]

workers have done well this week .... uploading now ...
im sure there are others who could contibute !
C

[coloin]

EDIT I made a test on the first 100 known 17 with distribution 665.
I got an average 6 seconds per solution grid having killed temporarily three ways to speed up the code due to bugs in the implementation.

Running the program to find the first 18 clues should be much faster in average

just a thought .... wouldnt it be better just to test for a 666/666 18C if this is the case .... and do a quick non-minimality check
or rather a lack of a 666/666 18C means there is no 17C [665] too

[coloin]

The process that the "workers" use to generate grids with 19's -- {-1,+1} puzzle morphing -- is biased towards producing grids with "more 19's" than average. Think about it.

well i suppose we will just have to see .... it will be interesting to see at what point the yield starts to drop
certainly those grids which only have a small number or 19C, there will be much less chance to find these puzzles.... There are 19C puzzles which are remote to {-1+1} and these wont be found, but i suppose we are relying on the fact that there will be many other 19C in that particular solution grid. This problem is predicted to be much worse for the 18C .
Interestingly a {-2+1} on our 1000 19C generated [slowly] almost as many [750] 18Cs ... so we wont be short of seeds ....

[coloin]

Great to have you on board
I'm uploading my next batches soon .... and we will see if we are just generating puzzles in grids with a plethora of 19C ..... hope not !
If this is so and there are many grids out there with a paucity of 19C then maybe we need to somehow change our method of attack - as ever the sudoku space doesnt make it easy