perplexus.info :: Shapes : T-Hexomino Packing

T-Hexomino Packing (Posted on 2016-08-26)

A T-hexomino is depicted below:

+--+--+--+--+--+
|  |  |  |  |  |
+--+--+--+--+--+
      |  |
      +--+

Prove that this hexomino cannot tile any size rectangle.

Consider its 3-D counterpart. Show that 25 of them can pack a 5x5x6 box.

See The Solution Submitted by Brian Smith

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

Part 1 only

Comment 1 of 1

Part 1 is simple. To tile a rectangle you must be able to tile a corner. There's only one way to place the T into a corner. This forces the second at 90 degrees up against it. And then you're stuck.

I was going to wait to post until I cracked the 3D version but I can't find the solution.

Posted by Jer on 2016-08-28 21:34:17

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (17)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info