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