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: Extension (A deeper question) by nikki)

Sorry for wording my question so poorly.

I think you interpreted it right, I want numbers that yield multiple solutions.

91 does because there could be a 7x7x7 cube painted on two adjacent sides or a 6x6x6 cube painted on 3 sides that share a vertex.

I'm not sure 23 can be done in any way except a 3x3x3 cube painted on 4 sides not in a ring. I haven't checked the others.

Are there any numbers that do give _more_ than 2 possible solutions? (besides 1 and 8)

-Jer

Posted by Jer on 2004-02-05 09:42:47