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 agree that there seems to be no solution. A quibble: the pieces could be better described as "J" shaped (an "L" shape would be a disallowed "reflection"). Two will fit together to form a 2x4 rectangle. A construction would prove the contrary, but I do not know what form an impossibility proof might take.