For this puzzle, we have a grid and 4 elements of fences.
For the 4 levels that I propose, the principle is the same :
2) Surround the polyiamond with fence elements :
The fence elements are black but, to better distinguish them in this example, we represent them in yellow.
3) Place the fence on the grid :
4) Place the RayMag pieces on the grid, inside the fence :
In the example above we did not use the fence element d ; this is used when there is a hole in the polyiamond or a reentrant angle of 300°.
This is the case for the hexiamond heart :
In this level, we will only use the 10 smallest polyiamonds, to be reconstitued, each one, using only the small pieces of RayMag.
The 9 small pieces of RayMag :
Among these 10 polyiamonds, only one has no solution at this level.
For this level, we can look for a solution for each polyiamond going from the monoiamond (1) to the tridecaiamonds (13) ; there are there fore 14 475 possible searches.
For the first polyiamonds (from the monoiamond to the octiamonds), it is quite easy because one of the pieces of de RayMag (RayMag 9a) is a basic triangle.
This level is the same as level 2 except that we cannot use RayMag 9a, which makes research much more interesting :
However, we are limited to the dodecaiamonds (which still makes 5 240 searches).
For this level, we add a constraint ; to understand this constraint, let’s look at the following 3 solutions from the same octiamond :
In the solution above on the left, we do not use RayMag 9a : it is therefore a possible solution at level 3. But we can see, on the right, that this solution is divided into of a solution of the triamond (in orange) and a solution of a pentiamond (in green).
In the solution above, we cannot separate the solution into 2 solutions of polyiamonds ; this is the constraint that we add for level 4 : find a solution that cannot be divided into solutions of polyiamonds of lower order.
Below we see that a solution of position 1 is also a solution for the positions 3, 5, 7, 9 and 11 :
But this is not a solution for the other positions.
I think this remark is valid for all polyiamonds.
On the tray :