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 Laser Glue? by broll)

I think that too many times we have some reviewers and some solvers disregard "the spirit" of a problem; true there are times when such 'nitpicking' is in order, may be "by stacking" could have been a better phrase but then someone's going to query "air-gap".

I realise that you are not "nitpicking" but making an observation.

Posted by brianjn on 2010-06-03 05:02:07