All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes
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.)
Solution Proof. Comment 7 of 7 |
Lengthwise, you need to sum to 11. Now, 11=2+2+2+3=2+3+3+3. So there are two posibilities, each involving at least a three unit side.

But having a three unit side lengthwise is impossible. Here is why:

Suppose you lay out this way,
 _ _ _

Then, no configuration would fill up the squares in the 4 unit side. This would leave either a 2x2 gap, or a single square with a 3x1 gap, or a shape with is non-tetromino.

Note that any parts each of these 4x3 block must be filled in independently, otherwise it would affect other parts and results in gaps straight away.


  Posted by Vee-Liem Veefessional on 2010-03-24 02:23:30
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information