Can a certain board be covered in Tetrominoes

Question

Prove that a $15x8$ board cannot be covered by $2$ L-tetrominoes and $28$ skew tetrominoes.

This is a coloring proof and I have tried a variety of colorings, from stripe colorings to other unique colorings with no luck in obtaining a contradiction. Any help would be greatly appreciated.

Answer 1

Horizontal stripes should do it.

The 15 rows divide into 8 red rows (with 64 squares in total) and 7 green rows (with 56 squares in total).

Each skew pentomino covers two squares of each color no matter how it's oriented, so the 28 skew pentominoes together use up all of the green squares.