In a cube, one pair of opposite faces is painted in Red, the second pair of opposite faces is painted Greeen and the third pair is in Blue. This cube is now cut into 729 smaller but identical cubes.
(i) How many small cubes are there with at least two different colors on their faces??
(Ans. 92)
(ii). How many small cubes are there with exactly one face painted red???
(Ans. 98)

please explain in detail.

• let a cube of dimension 9*9*9 is cut into 729 smaller cubes of dimension 1*1*1
  1) consider a face of cube
  there is a 9*9 square sheet in which 9+8+8+7=32 cubes are painted with at least two different colors (4 cubes are painted with 3 colors,28 are painted with 3 colors).
  now cosider opposite face of this face
  there also 32 cubes are painted with at least two different colors
  now consider 4 corners,not included in these two faces
  there are 7 cubes at each corner painted with two colors
  so no. of cubes painted with at least two different colors on their faces = 32+32+4*7=92
  2)consider a red painted face of cube there is a 9*9 square sheet in which
  7*7 cubes are there with exactly one face painted red
  there also 7*7 cubes are exactly one face painted red
  so total no. of cubes exactly one face painted red=7*7+7*7=98
• 11 years agoHelpfull: Yes(2) No(0)