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Hexomino corral



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#1 bonanova

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Posted 10 July 2013 - 07:57 AM

If a domino is two squares joined at a common edge, then a hexomino is a similar plane figure comprising six squares. Since a cube has six square sides, it follows that certain hexominos can be folded into a cube. Here is one: Col 173

 

+----+----+----+
|              |
+----+====+----+
=== =|= ==|

==== + ===+
=== =| ===|
==== + ===+
==== | ===|
=== =+----+

 

There are others, of course. So this puzzle has two(+) parts.

  1. Count them.
    Counting as a single hexomino all shapes that differ only by rotation
    and/or reflection, sketch all the hexominos that will fold into a cube.
    How many are there?

     
  2. Corral them.
    Now fit them, without overlap, inside a rectangle or square.
    What is the smallest perimeter of that enclosure?
    Extra credit: what is the smallest area of that enclosure?

     

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#2 TimeSpaceLightForce

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Posted 11 July 2013 - 11:33 AM   Best Answer

Spoiler for squared


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#3 bonanova

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Posted 14 July 2013 - 08:47 AM

Kudos to TSLF.
Nicely done!
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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