How we did it
Strategy and Solver Engine
This is a final result:
We made a Darwin Machine. The picture below shows the grid with a neutral sexehexes perimeter. This forces the edge (the yellow sexehexes). The program places the tiles in random mode. It finds the corners first, and then it follows the blue spiral until the center. If no sexehex enters in a place, the Darwin Machine start again.
After 3.147.955 attempts, we found this not-solution: the central place could be only covered with the piece "X" which it is already in use.
The sexehex "A" is different for a female edge only. We insert it, and then we exchange "C" and "D", "E" and "F", "H" and "I", "J" and "K", and finally "L" and "M".
If I use 127 full random sexehexes, the probability of inserting every piece is:
127 one-side sexehexes have many combinations of staying on this hexagonal grid:
There are ~10^110 solutions, but I must do 10^202 attempts to find one! Is it possible? Is it true? Am I saying mistakes? Am I lucky to find one solution? Is anybody on-line with answers?