For the challenges, we shall take the soft diamonds on a reduced scale :
1) Challenges on the tray :
These are shapes using the 27 soft diamonds and the 18 small pieces.
I have already given a solution of the 2 challenges above ; there are other solutions.
The 6 challenges above have at least one solution.
On the other hand, for the 6 challenges below, I don’t know if there is a solution.
2) Hexiamonds challenges :
If we consider triangles of side 3, the shape on the tray is a hexiamond.
Hence the idea of looking for solutions for the other hexiamonds, for example :
So that makes 11 challenges : some have no solution but which ones have a solution ?
Speaking of hexiamonds, we can look, as exercises, for solutions for the 12 hexiamonds of side 2 or side 1, for example :
Again some have no solution : which ones ?