A cube is painted green on all faces and divided into 125 smaller cubes of equal sizes .How many cubes are not painted on any face? The ans is 27.. Anyone explain me how
if you will divide a cube into 125 pieces each face will have 25 cubes ( to understand to divide a surface into 25 pieces you will need a 5x5 grid, hence for 3 dimensions i.e. cube you will have to find the cube-root of 125 i.e. 5 so each face will have 25 faces. ) out of which the one at edges will have at least 2 sides painted, then the remaining cubes will be 9 at the center of each face whose at least one face will be painted, if you will remove these painted cubes from each side, you'll get a cube with 3 x 3 cubes on each face multiplied by 3 by the same logic as before, you'll get 27 cubes which are not painted.