Pentomino tiling

Pentomino tiling is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

A pentomino is a polyomino that consists of 5 squares. There are 12 pentomino shapes, if you don't count rotations and reflections. Most pentominoes can form their own mirror image through rotation, but some of them have to be flipped over.

        I                                                                        
        I     L              N                                          Y        
 FF     I     L      PP     NN     TTT              V       W     X    YY      ZZ
FF      I     L      PP     N       T     U U       V      WW    XXX    Y      Z 
 F      I     LL     P      N       T     UUU     VVV     WW      X     Y     ZZ

A Pentomino tiling is an example of an exact cover problem and can take on many forms. A traditional tiling forms an 8 by 8 grid, where 4 cells are left uncovered. The other cells are covered by the 12 pentomino shapes, without overlaps, with every shape only used once.

The 4 uncovered cells should be chosen at random. Note that not all configurations are solvable.

The task: create an 8 by 8 tiling and print the result.

For instance:

F I I I I I L N
F F F L L L L N
W F - X Z Z N N
W W X X X Z N V
T W W X - Z Z V
T T T P P V V V
T Y - P P U U U
Y Y Y Y P U - U

Cf.

• Free polyominoes enumeration