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.
(In reply to Divisibility
by Brian Smith)
George Edward Martin, in "Polyominoes: a guide to puzzles and problems in tiling", provides a proof showing that L-tetrominoes of 4 unit squares covering an h x w unit-square rectangle can only occur if hw is divisible by 8, and that the h x w unit-square rectangle must be either (1) an 8m x n unit-square rectangle with n odd or (2) a 2m x 4n unit-square rectangle. As 4 x 11 is neither in the form of 8m x n nor 2m x 4n unit-squares, the L-tetromino of 4 unit squares can not cover a 4 x 11 unit-square rectangle.
Posted by Dej Mar
on 2010-03-23 01:41:02