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RayMag and the Polyiamonds

For this puzzle, we have a grid and 4 elements of fences.

For the 4 levels that I propose, the principle is the same :

1) Choose a polyiamond ; for the example, we choose the hexiamond crown :

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 :

Level 1

In this level, we will only use the 10 smallest polyiamonds, to be reconstitued, each one, using only the small pieces of RayMag.

The 10 smallest polyiamonds (each containing 1 to 5 basic triangles) :

The 9 small pieces of RayMag :

Among these 10 polyiamonds, only one has no solution at this level.

Level 2

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.

In this level, we can use all pieces of RayMag :

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.

Level 3

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).

Level 4

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, we use RayMag 9a : it is therefore a level 2 solution.

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.

Notes :

• Look at solutions for the first pentiamond ; this pentiamond has 12 possible positions on the grid :

    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.

Below we see that a solution of position 2 is also a solution for the positions 4, 6, 8, 10 and 12 but is not a solution for the other positions :

I think this remark is valid for all polyiamonds.

• Some dodecaiamonds can be done on the tray ; for example :

On the tray :

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Shapes on grid             Off-grid shapes