you have a 9x9x9 sided cube made up of 1 squaree inch squares. If all sides are painted how many cubes have no paint on any side?

Since cubes on all sides are painted, I believe that you would need to eliminate a cube from each side, so I think that the answer is 7x7x7 = 343

To add in general for nXnXn cube the answer is (n-2)X(n-2)X(n-2)

I agree with John's answer, but the wording is terrible. You have to assume that the cube is built from 9^3 one inch cubes. Then the problem becomes simple to visualize and solve. I hope the interview explained the problem clearer than this poster.

Eric, calm yourself. Im guessing he means that all sides (like he said) are painted. i.e. only the cubes on the outside of the cube. So the way to solve would be think of an 8x8x8 cube inside of a 9x9x9 cube, where are all of the 8x8x8 cube pieces have no paint on them. I think the answer is 8 cubed or 512 then, but dont quote me on that.

shuld be one ?, 3 cubes on on x axis, 2 on y side , 2 on z side , if all sides are painted..we will only be left with middle cube which is common cube and cannor be painted,,