After tetrominos, purely mathematical games with pentomino tiling at its core are definitely discovered games. It's doable but not always simple to build a given shape of size 5n with n pentominos. Ever seen the "fill an n by m rectangle with pentominoes" problem?
As an aside, my favorite variant of this is from an old game Puzzle Pirates: https://www.youtube.com/watch?v=XRQIHyC__kc