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I was given an exercise in which my task is to partition this geometric object into 16 equal pieces(both by area and shape). How can someone accomplish this task?

EDIT: We also need to partition the inside.

enter image description here

Rohcana
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McLinux
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  • Do you have some details about the dimensions of geometric object? – Harish Chandra Rajpoot Sep 24 '15 at 14:07
  • Not very many, I only know that this object is 2 dimensional, everything else is in the picture above. – McLinux Sep 24 '15 at 14:10
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    I think the solution is four of these back to back:

    http://math.stackexchange.com/questions/1420433/is-there-more-than-one-way-to-divide-the-l-shaped-tromino-into-four-congruent/1442518#1442518

     – Colm Bhandal Sep 24 '15 at 14:34
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    @McLinux You might want to consider whether or not the thick perimeter is important. If it is, I recommend stating it in the question. If it's not, I recommend re-drawing the image to exclude it. – Colm Bhandal Sep 24 '15 at 15:11

2 Answers2

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I don't know if I understand your question correctly, but I think this is a valid solution: ?!

enter image description here

Alex
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Update: This is not really a solution, because of the specific dimensions of the shape in the question. See comments.

I'm not sure if this is a valid solution, it depends on the dimensions of the object. But if your object is essentially four squares cut out of the corner of a big square, the following works:

enter image description here

I base my solution heavily on another question about the L-tromino.

Community
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Colm Bhandal
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  • But the dimensions don't work. The missing corners aren't a quarter of the whole thing. Also, you are treating the outside and inside the same. (I don't know if this is allowed though) – Alex Sep 24 '15 at 14:48
  • @Alex Yes, I'm not sure if this is allowed, but the rules for partitioning aren't clear, so I'm posting it as a possibility. Also, the missing corners, by my crude finger measurements, do seem to be a quarter of the whole area... are you sure they're not? – Colm Bhandal Sep 24 '15 at 14:53
  • Well, the whole thing is 11 blocks wide and the corners are only 2 blocks wide. – Alex Sep 24 '15 at 14:55
  • @Alex yes good point. I'll make a note of that in my answer. – Colm Bhandal Sep 24 '15 at 15:02
  • @Alex, you might also want to consider whether or not the thick perimeter is important. If it is, I recommend stating it in the question. If it's not, I recommend re-drawing the image to exclude it. – Colm Bhandal Sep 24 '15 at 15:06
  • @ColdBhandal I didn't ask the question, but yes, I think McLinux should clarify the question a bit. – Alex Sep 24 '15 at 15:09
  • @Alex- you are right indeed. You both have an 'x' in your name, which threw me off. I'll put my comment in the main question. – Colm Bhandal Sep 24 '15 at 15:11