A T-hexomino is depicted below:
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Prove that this hexomino cannot tile any size rectangle.
Consider its 3-D counterpart. Show that 25 of them can pack a 5x5x6 box.
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