The New Sudoku Players' Forum

[blue]

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

The good news is that as the yield rate falls, the newly discovered grids will shift towards the "high cost" end of the spectrum.
That's is in line with what Mathimagics was saying about what might happen with the "crossover" point, I think.

This problem is predicted to be much worse for the 18C .

Since most grids (~82%) don't have an 18C, and since most that do, only have one 18C (~11%) ... "much worse" may be an understatement.

Interestingly a {-2+1} on our 1000 19C generated [slowly] almost as many [750] 18Cs ... so we wont be short of seeds ....

Yes ... interesting !

Cheers,
Blue.

[blue]

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

Here are the 19C counts for 99 random grids.
(The 100th grid was an outlier, with 20207 19C puzzles)

Code: Select all

                             below average (72) | (27) above avg.
------------------------------------------------+-----------------
   53   233   369   573   702   904  1264  1593 | 2237  3781  6102
   69   235   456   578   716   959  1270  1599 | 2296  4012  6133
   82   237   479   588   718   994  1319  1608 | 2567  4110  6521
  105   310   480   607   721  1008  1359  1633 | 2632  4364  6803
  122   314   485   613   758  1036  1413  1659 | 2666  4532  6954
  124   342   488   613   768  1076  1429  1815 | 2735  5164  7156
  142   354   496   634   813  1145  1446  1903 | 2977  5318  7339
  177   361   505   655   835  1146  1463  1951 | 3250  5812  8782
  213   366   543   671   892  1228  1578  2170 | 3417  6078  9409

@Mathimagics: After the next update, please PM a list of 100 random grids without a known 19C (or smaller).

[blue]

The 19C counts for the 100 grids from Mathimagics, are:

Code: Select all

    32   145   252   405   501   619   845  1035  1214  2007  2961  9907
    94   163   291   405   515   666   872  1060  1296  2069  2995
   106   170   303   412   528   678   881  1066  1330  2084  3664
   109   184   306   418   529   704   902  1078  1385  2172  3815
   114   192   321   434   553   751   926  1089  1400  2300  4044
   116   194   340   442   553   761   946  1127  1565  2313  4393
   128   196   362   447   554   775   950  1132  1751  2402  4678
   134   231   387   451   582   783  1001  1159  1875  2426  5971
   143   251   401   493   603   824  1002  1183  1964  2460  8077

The average is down to 1238 per grid -- to be compared with Afmob's result of ~2200 per grid across all grids.
There's still plenty of low hanging fruit, though.

Interestingly(?), there's still a 73:27 ratio between grids that are below-vs-above the current average.

[blue]

Wwe are less likely to get these of course.....
suppose same analysis on the found 19C grids we need to see ? [ am worried now]

If Mathimagics sends another 100, I'll give them a try.
I won't be able to get to them for a few hours, and they'll probably take a lot(?) longer to count. [ I'm worried too ! ]
I think there will be a fair number of low count grids in the mix, though.

[blue]

Counts for a random 100 of the grids known to have a 19C:

Code: Select all

   51   486   773  1120  1486  1936  2526  3085  3623  4779  8688 22640
   81   518   799  1125  1601  1991  2573  3097  3650  5231  8840
  286   529   823  1178  1648  2009  2618  3111  3962  5243  9497
  328   553   862  1211  1660  2053  2649  3127  4379  5647 10356
  345   577   901  1240  1697  2054  2684  3161  4455  6044 10548
  370   689   986  1273  1715  2154  2692  3262  4459  6057 10942
  393   705  1001  1304  1719  2155  2726  3403  4537  6996 12503
  439   723  1088  1352  1730  2175  2799  3472  4687  8451 13199
  441   744  1100  1391  1848  2200  2894  3551  4759  8561 13918

The average is 3317.

I think there will be a fair number of low count grids in the mix

Fewer than I expected, but not too bad.

[blue]

It looks like the "relative yield" -- (% yield)/(% unresolved) -- has stabilized at ~30%.
That's good !

--

Updated Blue19 :

Blue19-new.zip

(137.96 KiB) Downloaded 296 times

Blue18.zip

(91.31 KiB) Downloaded 273 times

[blue]

It looks like the "relative yield" -- (% yield)/(% unresolved) -- has stabilized at ~30%.
That's good !

I was wrong, I see.
It's under 25% now.

[blue]

FWIW: After another 15 million samples, my revised estimate is 250-281K

[blue]

And there is another (as yet) unaccounted factor, call it X. There was a fire in Band 6 - some records towards the end of the file were burned. Something nasty happened on the USB drive transfers from Jill to Jack, which only became apparent when I investigated the alignment between the LCTP catalogs on both machines. The file error was, naturally, not reported by Win10.

This was all quietly repaired while you all slept. But LCT19X had already progressed well past Band 6, and so its reported counts (R) only include what it found at the time. So X = F(6) - R(6), and F(all) will be R + 4814 + X, ok?

" " ... Yes: I am totally confused.

Want to know what X is? I do have that figure around here somewhere ...

Yes, please, and more:

• What band 6 data exists on each machine ?
  What's missing where, at this point (if anything) ?
• What got trashed ?
• Job files were produced from a good or a bad catalog ? (Does it matter ?)
• What do the recent R values reflect, exactly ?
• How (exactly) is it, that they end up short by some amount X (in addition to the 4815) ?
• [ You're positive that X represents a shortage, and not overage ? ]

I don't doubt that you have a handle on everything, but my curiosity for details, raised the itch to ask.

Cheers,
Blue.

[champagne]

Well .... I knew this exercise might be coming ....
However .... I think most of the Ed grids will have a 19 ( or an 18 )
It might be more worthwhile to generate and register the 19 grids first
And then individually check the missing ? 50k solution grids

And of course in a true morphing process.... if the pattern is kept the same ..... all puzzles generated will be from different solution grids ( excluding 8/9 clue swops ) ( excluding automorphic )

and the "best process" described by our friend is very expensive in the range 18/19 clues.
If one wants really qualify a solution grid for the lowest possible number of clues, IMO, the start must be 18 clues (assuming that all 17s are known)

[champagne]

The 20 clues area has been searched for hardest I have some 20 to share from my seeds file (more than in he file of potential hardest)
I have also a small number of 18 clues, likely redundant with other files.
I hope to get in the near future (mid august ??) a collection of 18 clues with a band having 2 clues

Will tell you more soon via pm

PS BTW, the file of potential hardest is available with puzzles of 20 clues and more

[champagne]

ive been looking at a grid "which has an 18" but i've been struggling to find the 18 puzzle from scratch ....
this grid

Code: Select all

347981256582476193169523874896245317754318962213769485925137648478692531631854729

how long does your program take to confirm one 18-puzzle ? [ and how many 19s ? !]

5.4 seconds to confirm "only one" 18, and 213 seconds to find 2709 19's (including the 63 non-minimals).
(Any confirmation(s) of the 2709 number ?)

Confirming 1x18 + 2709x19.
188 and 4000 seconds. Your code is both fast and correct.

Good challenge. So far I have nothing to do that, but after the results of the search of 18s having a band with 2 clues I see
a possible alternative design for the 17 clues search, this is for to-morrow
a possible design to explore a solution grid in the area 18-20 if the first idea works

[champagne]

Bad news about Blue19 app/dll:
It's very slow on grids with no 19.
250 random such grids, took ~3.33 seconds each, on average, to process.

Still a little too early to deliver numbers, but this seems the order of magnitude of the search of 17 distribution 665 on a solution grid known to have such a 17.( with the fresh code in test).
The 18 case would be worse in such a process

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

EDIT 2 same average 6 seconds with 1000 puzzles (running the 8 cores in parallel all of them working on the search of 17s)

[champagne]

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

My first idea when I worked on blue's proposal for the search of 17's was to do in the same pass the 566;656;665 search.
Blue's warned me that the 665 pass could be very expensive, just due to the fact that we have many more valid 66 valid sub puzzles.
This is for the search of 17's and explain why there is a special pass with the relevant entry file to change the 665 pass in another 656 pass.

Showing that a solution grid can produce a 18/19 is quite a different case. You can stop at the first valid 18/19, so yes, here you can use the process for the distribution 666/667 in bands.
The same process can be applied for any distribution likely then assuming {clues band 1 <= clues band 2 <= clues band 3}; using if necessary a permutation of bands.

[champagne]

Since most grids (~82%) don't have an 18C, and since most that do, only have one 18C (~11%) ... "much worse" may be an understatement.

And this is also be very bad to apply the 17 search process for the first 18 search