Consider the following image.
Within the grid the are a total of 19 cells.
We have one cell for zero leaving 18 cells.
Shading nine cells we create 2 sets of the digits 1 to 9. With one set being on the shaded cells and the other set being on the unshaded cells.
The shaded digits within all 15 straight lines running through the grid sum to the exact same total as the unshaded digits within the same line.
Is there a solution for all of the 19 different digits being the centre cell?
Example: In the above image the centre cell is a shaded 3 so is it possible to put a shaded 9 in the centre?
Ignoring rotations and reflections, how many different ways are there of arranging the numbers within the grid so that the shaded cells are equal to the unshaded cells in all 15 lines running through the grid?