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?

(In reply to re(3): Extension (A deeper question) by Charlie)

Yeah, that was a typo - it should have been 25 and not 23. Luckily you can't get much past Charlie =)

I guess a start for proving or disproving if there are any numbers that yield more than two solutions would be SilverKnight's Floor-Ceiling approach. It would probably still need a Brute Force factor to it, though.

Hmmmmm...

Posted by nikki on 2004-02-05 16:32:41