- Find how many smaller cubes can be drawn in a larger cube of dimension nxnxn.
Here is a mild diversion. Given a cube of dimensions nxnxn, how many smaller cubes can be drawn within it. All cubes are integer dimensions and are drawn on the grid lines if you imagine the larger cube as a 3D graph paper. For example, in a 2x2x2 cube one can draw one 2x2x2, eight 1x1x1's. Try working it out for a 4x4x4 cube. Try and derive the general formula and use it for a 10x10x10 cube. Or a 100x100x100 cube. Have fun.