Imagine a rectangular solid that is made up of smaller unit cubes. The solid measures x by y by z. Now imagine building a shell of unit cubes around the entire solid.
First question: what is an equation for the number of unit cubes in the shell, in terms of x, y, and z?
Second question: for what x, y, and z is the number of cubes in the rectangular solid equal to the number of cubes in the shell?
The original cube has xyz unit cubes.
The new one has
So the shell alone has
Well, when the shell equals the original cube, then
Uh, not easily solved. Suggestions?