dukuso wrote:look at this sudoku grid:
147 258 369
583 691 724
926 734 581
691 582 473
734 916 258
258 347 916
375 169 842
862 473 195
419 825 637
jayanth wrote:1. The final result obtained by BF and FJ, after discounting for the 9! combos of B1, is NOT divisible by 12096, the number of possible combos for B2. That is (72^2 * 2^7 * 27704267971) is not divisible by 12096. If their result is correct, then not all B2 variants above are valid. I am not sure about this.
Yes, I get that too (as 6688224 * 2 * 6^5).dukuso wrote:look at this sudoku grid:
...
Is there a name for this ? Let me call it 3doku until someone
suggest a better name.
...
How many grids are there ?
I think, it's 104015259648.
That was easy to count with a straightforward backtracking program
with some symmetry reductions. Can someone confirm ?
I assume it's just the usual size 3359232 group crossed with (S_3)^4 instead of S_9. That is, you relabel digits within each set {123}, {456}, {789} and also switch the sets themselves. Since 104015259648 / (3359232 * 6^4) = 23.89, which is reassuringly a little less than an integer, I'd guess there are "essentially" only 24 3doku grids.dukuso wrote:What's the symmetry-group ? I haven't thought about it yet...
That's a task for Ed and Frazer.
coloin wrote:This is a grid which solves a "4 constraint puzzle" from tso at then end of the latin squares thread http://www.menneske.no/sudoku/dg/3/eng/
Every clue is in a unique position in every box.......I was wondering how many grids have this property.....
from to
01 02 03 04 05 06 07 08 09 01 28 55 04 31 58 07 34 61
10 11 12 13 14 15 16 17 18 10 37 64 13 40 67 16 43 70
19 20 21 22 23 24 25 26 27 19 46 73 22 49 76 25 52 79
28 29 30 31 32 33 34 35 36 02 29 56 05 32 59 08 35 62
37 38 39 40 41 42 43 44 45 11 38 65 14 41 68 17 44 71
46 47 48 49 50 51 52 53 54 20 47 74 23 50 77 26 53 80
55 56 57 58 59 60 61 62 63 03 30 57 06 33 60 09 36 63
64 65 66 67 68 69 70 71 72 12 39 66 15 42 69 18 45 72
73 74 75 76 77 78 79 80 81 21 48 75 24 51 78 27 54 81
AAAAAAAAA
BBBBBBBBB
CCCCCCCCC
DDDDDDDDD
EEEEEEEEE
FFFFFFFFF
GGGGGGGGG
HHHHHHHHH
IIIIIIIII
ABCDEFGHI
ABCDEFGHI
ABCDEFGHI
ABCDEFGHI
ABCDEFGHI
ABCDEFGHI
ABCDEFGHI
ABCDEFGHI
ABCDEFGHI
AAABBBCCC
AAABBBCCC
AAABBBCCC
DDDEEEFFF
DDDEEEFFF
DDDEEEFFF
GGGHHHIII
GGGHHHIII
GGGHHHIII
ABCABCABC
DEFDEFDEF
GHIGHIGHI
ABCABCABC
DEFDEFDEF
GHIGHIGHI
ABCABCABC
DEFDEFDEF
GHIGHIGHI
AAABBBCCC
DDDEEEFFF
GGGHHHIII
AAABBBCCC
DDDEEEFFF
GGGHHHIII
AAABBBCCC
DDDEEEFFF
GGGHHHIII
ADGADGADG
ADGADGADG
ADGADGADG
BEHBEHBEH
BEHBEHBEH
BEHBEHBEH
CFICFICFI
CFICFICFI
CFICFICFI
coloin wrote:This is a grid which solves a "4 constraint puzzle" from tso at then end of the latin squares thread http://www.menneske.no/sudoku/dg/3/eng/
I got an answer about 50 million times bigger a while back ...Dan Hoey wrote: I make it 8 * 6^4 permutations, or 8 * n!^4 permutations for the n^2 by n^2 grid. (That is before permuting the set of cell labels, which is another factor of n^2!.)