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4x11 Grid Fill (Posted on 2010-03-21) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 1.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Divisibility | Comment 5 of 7 |
(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

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