A 30x30x30 cube is made by gluing together 30³=27000 unit cubes. A square pyramid having each side of the base as 30 units and, height from base to the apex of the pyramid as 30 units is cut out of the cube by means of an infinitely thin laser-like cutting tool.

How many unit cubes will stay undamaged inside the pyramid?

Note: The apex of the pyramid is located perpendicularly above the center of the square base.

(In reply to instinct tells me.... by Dej Mar)

I agree: (2*28^2+2*26^2+2*24^2...2*2^2) but can we ever be sure that pesky laser won't just graze the cubes on those even numbered layers?

Posted by broll on 2010-06-02 12:19:18