Can 250 bricks each having dimension 1x1x4 be packed into a 10x10x10 box?
If so, show how.
If not, explain why is it not possible.

Not possible.

Imagine filling the box with 125 2x2x2 smaller boxes, colored in a checkerboard pattern black and white with black at a corner.  Black will be at every corner.  There will be 63 black boxes and 62 white.
Total volume 63*8=504 black bits, 62*8=496 white bits.

The four bits of the 1x1x4 bricks will always cover exactly two white and two black bits.  250*2=500 black and 500 white.  There will be some untiled bits.

Posted by Jer on 2015-08-28 14:00:30