Drjsguo wrote:The San and Chuan Sudokus I posted earlier are not having more than three restrictions. They each have only three rules. E.g. San Sudoku: each block, Plum positions, and San (三) shaped three-line groups are limited to have nine different digits. There is no row or column restriction for San Sudoku at all. Here is an example:

4,5,7,3,4,9,9,3,4

6,1,8,5,7,1,8,6,5

9,3,2,8,2,6,2,1,7

6,9,8,5,8,1,2,1,5

2,5,3,9,2,6,4,9,7

7,4,1,3,7,4,6,8,3

1,2,3,7,6,2,8,7,6

7,4,9,3,8,4,1,3,2

5,6,8,1,5,9,4,9,5

Row and column constraints are no longer required here.

I think what you describe here is just another representation of our plain Vanilla Sudoku. Try to transform boxes 1,2,3,4,5,6,7,8,9 to rows 1,4,7,2,5,8,3,6,9. Your example then becomes this grid:

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`4 5 7 6 1 8 9 3 2`

6 9 8 2 5 3 7 4 1

1 2 3 7 4 9 5 6 8

3 4 9 5 7 1 8 2 6

5 8 1 9 2 6 3 7 4

7 6 2 3 8 4 1 5 9

9 3 4 8 6 5 2 1 7

2 1 5 4 9 7 6 8 3

8 7 6 1 3 2 4 9 5

Which is just a simple Vanilla Sudoku grid.

Drjsguo wrote:Same is for Chuan Sudoku. I do not think they are not new types of Sudoku. I also believe 17 could be the lowest given to solve them logically.

Similarly, the "Chuan Sudoku" is just another representation of a normal Vanilla Sudoku grid if you do the transformation boxes 1,2,3,4,5,6,7,8,9 to columns 1,2,3,4,5,6,7,8,9. Also, if you simply transpose the grid a "Chuan Sudoku" is essentially the same as a "San Sudoku". That's why 17 is the (conjectured) minimum number of givens to these puzzles. They're essentially the same as Vanilla Sudoku puzzles.

Drjsguo wrote:BTW, it seems that Row and Column are also transformable to San (三) and Chuan (川). For example, if Row transformed into San, the Column would be transformed to Chuan. Meanwhile the Blocks (Boxes) remain the same but move to different locations. With constraints included only San, Chuan, Block and nothing else, it is also another new type of Sudoku.

This transformation is essentially boxes 1,2,3,4,5,6,7,8,9 to boxes 1,4,7,2,5,8,3,6,9. Again I wouldn't call it "a new type of Sudoku", but just "a different representation of an existing Vanilla Sudoku grid".