Show how ten 3x3x3 cubes can be packed in a cubical box having edge length 8.9

Place one cube in each of the 4 bottom corners and a fifth at the bottom center rotated 45º.  A second layer of 5 can sit on top of these.

The smallest box that can be filled the way would have edge length 6+1.5√2≈8.1213

And if the box need not be a cube the height could be merely 6.

Posted by Jer on 2014-05-29 15:18:16