dukuso wrote:

123456789

456789123

789123456

231564897

564897231

897231564

312645978

645978312

978312645

uses gangsters 1,1,1 - 1,1,1 so I think it's the most canonical.

It could also be the one requiring the most clues, since gangster1 stands for 1728 bands, the most of all gangsters.

So now I tested whether there is a 18-clues sudoku whith that grid as unique solution.

18 clues are required at least, as we have seen before and these must be arranged such that 2 clues solve each of the 18 3*3 latin subsquares.

This gives only 1296 possible configurations of the 18 clues and none of them give a sudoku with unique solution.

We have :

18 configurations with 413108 solutions

108 configurations with 141917 solutions

36 configurations with 47479 solutions

18 configurations with 44148 solutions

162 configurations with 41224 solutions

162 configurations with 22245 solutions

18 configurations with 16740 solutions

324 configurations with 15156 solutions

162 configurations with 9258 solutions

108 configurations with 4914 solutions

162 configurations with 411 solutions

18 configurations with 96 solutions

it seems that we have 18-fold symmetry here.

With 19 clues however there are uniquely solvable sudokus over this grid.

- Code: Select all
`.........`

..6.8.1..

7....3.52

..1.6.8..

.....7.3.

...2.....

3....5.7.

.4.......

..8...6.. EDIT this does not have a unique solution !

EDIT

This is wrong

It does NOT have a 19-clue puzzle !!!!!!!