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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)

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Some Thoughts Divisibility | Comment 4 of 7 |

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
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