The pentaminos are the puzzle's pieces represented on the beside picture.
They are the 12 different pieces that you can obtain joining 5
identical cubes side by side.
The rule of the game is to reconstitute a given shape.
Most of the time, you have to put them into a 8 x 8 array,
in which 4 cases must stay empty.
Here are some examples:
but there are many others.
I decided on day to find the number of solutions, for a given array.
I realised a little program to do it, first in C, then in Objective
It is a backtracking algorithm, which stops whenever an area to fill
has a surface which is not a multiple of 5.
Some answers computed by the program.
You can download:
A variant consists in arranging the 12 pentaminos in a rectangle.
Here are the number of solutions (up to the 4 symmetries):
The Caml program
(formatted with yamlpp).