Some unit cubes are assembled to form a larger cube. Some of the faces of the larger cube are then painted. The cube is taken apart and it is found that 217 of the unit cubes have paint on them. What is the total number of unit cubes?

First you must realize that the only way to come up with an odd number like that is to have 3 sides of the big initially get painted, with that information a 9-unit cube is the solution, yielding 729 blocks.

Posted by bs on 2004-02-03 00:42:30