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?

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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.

Posted by Brian Smith on 2010-03-22 23:25:00