Facom: what is it?
Nowadays, Facom is the name of a firm that sells tools. However, many years ago, Fujitsu made computers with the name Facom. As far as I remember, they used the pentomino puzzle to advertise their computers and one of my colleagues possessed this pentomino puzzle.
Prolog versus Fortran
It was in the time of the 4-th and even 5-th generation computer languages. One of them we had running on a CDC mainframe at SARA was Prolog which still exists.
I tried to use that language to solve the Facom puzzle: filling a 3x4x5 block with the 12 pentominoes. No success, probably more my inability then the possibilities of Prolog, therefore I decided to solve the puzzle using good old Fortran, a language that also still seems to exist ;-).
The Facom program
The Fortran version, baptised "Facom", works, it finds even the 3940 solutions it is supposed to find within 2 minutes or so, and the same program can also be used to solve the other configurations: 2x3x10, 2x5x6, 2x20, 4x15, 5x12 and 6x10. The program is not capable to find solutions for other configurations. In the output of the program the pentominoes are coded as in this picture:
Another generic pentomino solver
If you are interested have a look at http://puzzler.sourceforge.net/docs/pentominoes.html, there you find a generic pentomino solver, written in Python, so not as fast as my Facom. This project is very well done, you get even 3-d pictures of the solution.