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.

My first impression is that this is not possible.

Two such tetrominoes can form a 2x4 rectangle. that means that 5 such rectangles will fill a 10x4 rectangle whilst 6 are accommodated within a 12x4.

It seems from my investigations that I am always left  with a 4x1 rectangle or a 2x2  square after I have placed  10 "L" shapes.

Proof?  :-(

Posted by brianjn on 2010-03-22 04:53:43