The New Sudoku Players' Forum

[Maq777]

Hello,

I'm looking for more examples of orbitals with 62208 models. I have these six; does anyone know of any more?

If you have them and could share them, I would greatly appreciate it.

Best regards

Code: Select all

  Familia 62208 - A            Familia 62208 - B            Familia 62208 - C
  -------------------------    -------------------------    -------------------------
  | 1 2 3 | 4 5 6 | 7 8 9 |    | 1 2 3 | 4 5 6 | 7 8 9 |    | 1 2 3 | 4 5 6 | 7 8 9 |
  | 7 8 9 | 1 2 3 | 4 5 6 |    | 7 8 9 | 1 2 3 | 4 5 6 |    | 9 7 8 | 1 2 3 | 4 5 6 |
  | 4 5 6 | 7 9 8 | 1 2 3 |    | 4 5 6 | 7 8 9 | 1 2 3 |    | 4 5 6 | 8 9 7 | 1 2 3 |
  -------------------------    -------------------------    -------------------------
  | 3 1 2 | 6 4 5 | 9 7 8 |    | 3 1 2 | 6 4 5 | 9 7 8 |    | 3 1 2 | 6 4 5 | 8 9 7 |
  | 9 7 8 | 3 1 2 | 6 4 5 |    | 9 7 8 | 3 1 2 | 6 4 5 |    | 7 8 9 | 3 1 2 | 6 4 5 |
  | 6 4 5 | 8 7 9 | 3 1 2 |    | 6 4 5 | 8 9 7 | 3 1 2 |    | 6 4 5 | 9 7 8 | 3 1 2 |
  -------------------------    -------------------------    -------------------------
  | 2 3 1 | 5 6 4 | 8 9 7 |    | 2 3 1 | 5 6 4 | 8 9 7 |    | 2 3 1 | 5 6 4 | 9 7 8 |
  | 8 9 7 | 2 3 1 | 5 6 4 |    | 8 9 7 | 2 3 1 | 5 6 4 |    | 8 9 7 | 2 3 1 | 5 6 4 |
  | 5 6 4 | 9 8 7 | 2 3 1 |    | 5 6 4 | 9 7 8 | 2 3 1 |    | 5 6 4 | 7 8 9 | 2 3 1 |
  -------------------------    -------------------------    -------------------------
 
  Familia 62208 - D            Familia 62208 - E            Familia 62208 - F
  -------------------------    -------------------------    -------------------------
  | 1 2 3 | 4 5 6 | 7 8 9 |    | 1 2 3 | 4 5 6 | 7 8 9 |    | 1 2 3 | 4 5 6 | 7 8 9 |
  | 7 8 9 | 1 2 3 | 4 5 6 |    | 9 7 8 | 1 2 3 | 4 5 6 |    | 7 4 9 | 1 2 8 | 3 5 6 |
  | 4 5 6 | 7 8 9 | 1 2 3 |    | 6 4 5 | 9 7 8 | 1 2 3 |    | 8 5 6 | 7 3 9 | 1 2 4 |
  -------------------------    -------------------------    -------------------------
  | 8 1 2 | 6 3 5 | 9 7 4 |    | 3 1 2 | 6 4 5 | 9 7 8 |    | 3 1 7 | 2 4 5 | 9 6 8 |
  | 9 7 4 | 8 1 2 | 6 3 5 |    | 8 9 7 | 3 1 2 | 6 4 5 |    | 9 6 4 | 8 1 7 | 2 3 5 |
  | 6 3 5 | 9 7 4 | 8 1 2 |    | 5 6 4 | 8 9 7 | 3 1 2 |    | 2 8 5 | 9 6 3 | 4 1 7 |
  -------------------------    -------------------------    -------------------------
  | 2 4 1 | 5 6 8 | 3 9 7 |    | 2 3 1 | 5 6 4 | 8 9 7 |    | 6 3 1 | 5 7 4 | 8 9 2 |
  | 3 9 7 | 2 4 1 | 5 6 8 |    | 7 8 9 | 2 3 1 | 5 6 4 |    | 4 9 2 | 6 8 1 | 5 7 3 |
  | 5 6 8 | 3 9 7 | 2 4 1 |    | 4 5 6 | 7 8 9 | 2 3 1 |    | 5 7 8 | 3 9 2 | 6 4 1 |
  -------------------------    -------------------------    -------------------------


[Serg]

Hi, Maq777!
What does it mean "62208 orbital model"? What property of Sudoku solution grids do you mean?

Serg

[Maq777]

Hi, Maq777!
What does it mean "62208 orbital model"? What property of Sudoku solution grids do you mean?

Serg

Hi Serg,

I'm referring to this line which indicates that there are 11 different orbits with 62208 patterns. I have already identified 6 of those 11 orbits, and I was wondering if anyone has already identified Sudoku examples of the other 5 that I am missing.

Code: Select all

#ORBIT   COUNT       MODELS
1        1           5184
2        1           20736
3        3           31104
4        2           46656
5        11          62208  <----
6        15          93312
7        2           124416
8        85          186624
9        92          279936
10       42          373248
11       29          419904
12       1257        559872
13       2826        839808
14       7336        1119744
15       548449      1679616
16       5472170387  3359232


[champagne]

like 'Serg' still don't see what is the property

[Serg]

Hi, Maq777!
If I understood you correctly, you want to get the list of Sudoku solution grids having exactly 54 (3359232/62208) automorphisms under the group of VPT (validity preserving transformations, such as swapping rows in a band, swapping stacks, transposing, etc.). You expect to find 11 such solution grids, but found 6 of them only, right?

Serg

[Maq777]

Hi, Maq777!
If I understood you correctly, you want to get the list of Sudoku solution grids having exactly 54 (3359232/62208) automorphisms under the group of VPT (validity preserving transformations, such as swapping rows in a band, swapping stacks, transposing, etc.). You expect to find 11 such solution grids, but found 6 of them only, right?

Serg

Exactly !!!


I've just found one more.

Code: Select all

62208 - G
-------------------------
| 1 2 3 | 4 5 6 | 7 8 9 |
| 7 8 9 | 1 2 3 | 4 5 6 |
| 4 5 6 | 7 8 9 | 1 2 3 |
-------------------------
| 6 1 8 | 9 4 2 | 3 7 5 |
| 3 7 5 | 6 1 8 | 9 4 2 |
| 9 4 2 | 3 7 5 | 6 1 8 |
-------------------------
| 5 9 1 | 2 6 7 | 8 3 4 |
| 8 3 4 | 5 9 1 | 2 6 7 |
| 2 6 7 | 8 3 4 | 5 9 1 |
-------------------------


[Serg]

Hi, Maq777!
Here is the list of automorphic Sudoku solution grids having 27 or more automorphisms (posted by gsf in 2007).

Serg

[Maq777]

Serg,

Thank you so much, this was exactly what I was looking for.