creint wrote:Yes that is an 8x8, but strangely I see box constraints in the 3rd dimension.

It is now unclear because you cannot fit 1-4 in a row 8 cells. Where are the constraints?

In your picture I see now box constraints in the 3rd dimension.

The box constraint in the 3rd dimension you're talking about is the container. If it wasn't clear, the container is a 3D version of a traditional "9x9" box.

sw478 wrote:The size/number of cells in each box (I call boxes containers), row, and column (I call rows and columns span) would be the product of all container dimensions, and the total number of cells in the sudoku is containerSize^n, where n is the number of dimensions.

In the [2, 2, 2], you're trying to fit the numbers 1-8 in each container and each span[0] (row), span[1] (column), and span[2]. Not 1-4. The length of each span is 8 and the size of the containers is 8, which makes 8 the relevant number for a [2, 2, 2].

If you look at an 8x8x1 slice of the [2, 2, 2], that wouldn't ever be a sudoku. And you're not guaranteed to (most likely not unless designed) find any valid [2, 2] "4x4" sudokus in the [2, 2, 2].

creint wrote:[2,2,] but somewhere it get transformed into a 4x4 puzzle. [3,3] = 9x9

[2,2,1] gives 3 extra puzzles = 1 cube, [2,2,2] gives 31 extra puzzles = 8 cubes, [2,2,3] gives 107 extra puzzles = 27 cubes. But I still don't see how they are linked.

In a [2, 2, 1], since the third dimension is 1, this is a special case where you can get split the [2, 2, 1] sudoku at the third dimension and get 4 valid [2, 2] sudokus. You can't meaningfully transform a [2, 2] to a [2, 2, 2], or split a [2, 2, 2] into [2, 2] sudokus to get extra puzzles.