Can a 4x11 rectangular grid of square blocks be covered (having no overlaps), with multiple copies of the tetromino (including rotations, but not reflections) as shown below?
If so, give an example. If not, provide a proof that this cannot be achieved.
Note: Each of the 44 square blocks of the 4x11 grid has the same shape and size as each of the 4 square blocks of the tetromino.
I remember seeing a proof that if an L-tetromino can tile a rectangle then the rectangle has an area divisible by 8. 44 is not divisible by 8, so a 4x11 rectangle not tilable with L-tetrominos.
I'll update this post as soon as I or someone else finds a citation.