I’ve been thinking about variations on the problem of cycling through all twelve pentominoes by moving a single cell at a time. (I wrote about this in a previous post.) Constraining the way that the squares are allowed to move led to something almost like a chess problem.
Starting with the above position, take five turns as follows:
A turn consists of moving one white knight, then moving one black knight, according to standard chess rules.
After each turn, the squares occupied by the ten knights must form two separate pentominoes.
After the fifth turn, all twelve pentominoes must have appeared exactly once. (This includes the two that are present in the starting position.)
[I may make a separate post discussing and spoiling the puzzle later.]