Cube Color

There is a cube in which one pair of opposite faces is painted red; another pair of opposite faces is
painted blue and the third pair of opposite faces is painted pink. This cube is now cut into 216 smaller but identical cubes.
12. How many small cubes will be there with no red paint at all?
(A) 121 (B) 144
(C) 169 (D) 100
13. How many small cubes will be there with at least two different colours on their faces?
(A) 49 (B) 64
(C) 56 (D) 81
14. How many small cubes will be there without any face painted?
(A) 64 (B) 49
(C) 36 (D) 25
how to solve these types of questions

Interview Candidate
Jul 9th, 2017
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Anjali

Aug 18th, 2017

216 small cubes means assume each small cube having 1cm length.
12. small cubes without red=216-(8 cubes having 3 colors+red is with 8 edges *4+16*2)
=216-8-32-32=144
13. at least 2 face colors = cube with 2 face colors + cube with 3 colors
cube with 2 face color = 12*4 = 48
cube with 3 face color = 8
at least 2 face colors = 48+8=56
14. small cubes without face color = total small cubes - face with at least one color
cube with color on one face = 6*16=96
cube with color on 2 faces = 12*4 = 48
cube with color on 3 faces = 8
cube with no face painting = 216-96-48-8= 64