dyitto wrote:Very interesting!

Could you post the grids?

What's the minimal definition of your variant?

(Which properties are derived from the others? The same-total property is a consequence of the cycles I guess.)

I will describe how I developed the concept.

First of all, I defined 2 attributes for each cell value: range (small={123},medium={456},large={789}) and modulo of 3 (1={147}, 2={258}, 0/3={369}).

The reason I did that was to create an elegant graphical representation of Sudoku, which you can find in the "One for the X'mas" thread in this forum.

So I wanted to see with this concept if it was possible to establish a very concise and elegant variant rule. Immediately one came up:

Neighbours have different attributes.With this fundamental rule the solution space is much refined already. Note that with this constraint, all 3x3 nonets automatically become semi-magic squares (or Euler squares if you consider the 2 attributes). Then once the

disjoint group constraints are applied, it is further "restrained" (as HATMAN, one of the experts in Sudoku variants, love to say). I believe only 2 essentially different solutions exist, if we can freely swap the cell values based on their attribute structures.

So what's remaining is to fix the contextual and positional aspect. I do this by adding 2 extra constraints:

3. The central 3x3 nonet must be a full magic square (essentially saying R5C5=5).

4. The mini-rows must be cycles of 1-5-9/2-6-7/3-4-8 (left to right). The mini-columns must be cycles of 1-6-8/2-4-9/3-5-7 (top to bottom). This fix the reflection/rotation unstability.

(Alternatively, one can bypass constraints 3 and 4 by specifying the cell values of N5 as the [834159672] full magic square.)

With these 4 constraints, there are only 2 valid solutions and as I said above, they form a pair of 9-9 revealing twins!

I'm sure using a simple solver software (e.g. JSudoku) anyone can find the 2 grids within seconds. But if people still want it, I will post the grids next time.