The New Sudoku Players' Forum

[blue]

I know, it's terrible
What a POS

I couldn't resist playing with Colin's idea.

Here's the beginning of the table:

Hidden Text: Show

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    N |     grids | Bands with N 5-clue puzzles
------+-----------+----------------------------
    0 |        17 |   1 224 237 254 307 413
   63 |        31 |  33  48
   78 |        35 | 101
   90 |        67 |  45  67 225
  108 |       103 | 247
  156 |       106 | 289
  168 |       109 | 104
  177 |       116 | 219
  213 |       122 | 240
  244 |       126 | 183
  252 |       245 |   4 415
  258 |       253 | 105
  300 |       266 | 100
  301 |       288 |  83
  309 |       311 | 133
  312 |       327 |  72
  324 |      2293 |   2 412 414
  326 |      2582 | 140
  331 |      2915 | 238
  374 |      3003 | 122
  378 |      3158 |  54
  410 |      3486 |  93
  421 |      3789 | 116
  485 |      4379 | 220
  490 |      4896 |  74
  499 |      5225 | 109
  527 |      5638 |  84
  529 |      6682 | 223
  539 |      7244 | 232
  540 |      7966 | 233
  543 |      8385 | 115
  546 |      8810 |  32
  594 |      8926 | 302
  692 |      9238 | 259
  777 |      9778 | 241
  852 |     10585 | 253 309
  864 |     13649 | 252 305
  972 |     13775 |  16
 1107 |     14014 |   8
 1131 |     17386 | 160 294
 1225 |     27243 | 152 218 226 230
 1275 |     32397 | 217 260
 1531 |     41776 | 222 229
 1577 |     45779 |  92
 1614 |     50774 |  39
 1626 |     57414 | 256 306
 1781 |     62505 | 119
 1783 |     67799 | 171
 1850 |     71996 | 245
 1858 |     89258 |  47 127
 1859 |    102558 |  46 124


I'll extract & test the first million grids, sometime soon.

Blue.

[coloin]

Gentlemen !
To Mathimagics .... if it finds the 20 ... job is done...whats the problem !
may be rotating the puzzle and scanning the other bands would be a sort of double check ....? ah EDIT i see blue has done that

To blue yeah it seemed a good one ! well maybe just do the grids with 665 ? how many are there of those ?
Anyway work in progress !

[blue]

Hi Colon,

well maybe just do the grids with 665 ? how many are there of those ?
Anyway work in progress !

I'm not really sure what you mean by "665".
Do you mean every grid where two bands don't have 5-clue puzzles, but the 3rd one does ? ... but doesn't have 4-clue ?

I did run the first ~1M where every band & stack had low 5-clue counts.
The display said I should have had (961565-961319) = 246 grids with no 668, but I only had 19, and some were duplicates.
I think I accidentally had two processes going at the file at the same time, and I Ctrl^C's out of one, and it trashed the file.
I'm running it again, but I'll be away for several hours now.

Later,
Blue.

[coloin]

yes - a 665 would mean that the clues in band count are at least 665 . or more than 554 in each repective band.
as ony a few of the 416 bands need 6 clues maybe there wont be that many grids !

[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

[dobrichev]

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

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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.

[Mathimagics]

His name should be Ozymandias: "Look at my run times, fellow coders, and despair ... "

[blue]

No, don't say that.
I couldn't stand that character.
I'm more the Rorschach/Comedian type.

Cheers.

[blue]

Hi Colin,

This shows the counts you were interested in (I hope).

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666/xxx 666/666 yyy/666 |      47519 |         17 |         17
665/xxx 665/665 yyy/665 |     228185 |         20 |         26
664/xxx 664/664 yyy/664 |     194843 |         11 |         36
663/xxx 663/663 yyy/663 |      62706 |          0 |          1
662/xxx 662/662 yyy/662 |         39 |          0 |          0
655/xxx 655/655 yyy/655 |    2591055 |        514 |        790
654/xxx 654/654 yyy/654 |   13528622 |       8971 |      13552
653/xxx 653/653 yyy/653 |    4567942 |        704 |       6676
652/xxx 652/652 yyy/652 |      10560 |          0 |          5
644/xxx 644/644 yyy/644 |   44030211 |      94448 |     185704
643/xxx 643/643 yyy/643 |   30838250 |      40804 |     222895
642/xxx 642/642 yyy/642 |      20553 |          0 |        165
633/xxx 633/633 yyy/633 |    6360840 |       1754 |      61338
632/xxx 632/632 yyy/632 |       8232 |          0 |         76
622/xxx 622/622 yyy/622 |         54 |          0 |          8
555/xxx 555/555 yyy/555 |   14411818 |      15455 |     173345
554/xxx 554/554 yyy/554 |  214493467 |    2211750 |    4632166
553/xxx 553/553 yyy/553 |   76484734 |     260697 |    2532325
552/xxx 552/552 yyy/552 |      65144 |          1 |       2198
544/xxx 544/544 yyy/544 | 1257024445 |   89415895 |  142418480
543/xxx 543/543 yyy/543 |  820360406 |   48904321 |  219150672
542/xxx 542/542 yyy/542 |     544118 |         36 |     181854
533/xxx 533/533 yyy/533 |  148019477 |    1862491 |   55362798
532/xxx 532/532 yyy/532 |     197632 |          1 |      78186
522/xxx 522/522 yyy/522 |        130 |          0 |        113
444/xxx 444/444 yyy/444 | 1750050402 |  409386989 | 1244946479
443/xxx 443/443 yyy/443 |  989657965 |  528186529 | 2410287584
442/xxx 442/442 yyy/442 |     318847 |        238 |    1984425
433/xxx 433/433 yyy/433 |   97372976 |   77655487 | 1221627908
432/xxx 432/432 yyy/432 |      27715 |        119 |    1726413
422/xxx 422/422 yyy/422 |         20 |          0 |        690
333/xxx 333/333 yyy/333 |    1211625 |    1206487 |  166800598
332/xxx 332/332 yyy/332 |          6 |          6 |     332752
322/xxx 322/322 yyy/322 |          0 |          0 |        257
222/xxx 222/222 yyy/222 |          0 |          0 |          6

[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 ?

[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

[blue]

Hi Mladen,

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

Thanks for the confirmation.

[blue]

Hi Colin,

Quite a bit of catching up to do, from my end ...

Anyway work in progress !

The grids with low 5-clue counts, didn't produce anything new.
The only cases in the first ~1M, with no 668, were the 4+15 cases with automorphisms.
--4 with no 20C at all, and the other 15 listed in the "Grids containing a 21 but no 20" thread.
The next batch, bringing the total to ~10M tested, produced nothing.
The same 4+15 cases, came in testing the 666 and 665 grids.
I ran the 664 and 655 grids too (~2.8M grids) ... no hits.

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 !

There are 983,959,110 ED double bands.
The 44 classes that you have in mind, can be partitioned into 913,393 smaller classes too, going by the mini-column/"gangster-like" signatures in the filled bands. Canonical cases can be defined as having a (true) gangster signature in the missing band, and "gangster-like" signatures in the other bands that are minlex with respect to automorphisms of the signature in the missing band.

The MC grid has 6+6+27's:

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12...6......7....3.......5....5...9..64......8....1...312645978645978312978312645

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

No. Here's one with only the trivial automorphism, and a triple 224 in the stacks:

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123456789456789123789123456214365897365897214978214365541632978632978541897541632