question_answer

DIRECTIONS: A cube painted red on two adjacent faces and black on the faces opposite to the red faces and green on the remaining faces is cut into sixty-four smaller cubes of equal size. How many cubes are there which have no face painted?

A) 0                                 

B) 4

C) 8         

D) 16

Correct Answer: C

Solution :

    There are 8 cubes having no face painted. Here, Faces ABCD, BCFG are painted with red. Faces ADEH, EFGH are painted with red. Faces CDEF, ABGH are painted with green. No. of divisions on the faces of cubes = 4 Now, the figure may be analyzed by dividing it into four horizontal layers: In Layer I: Four central cubes only one face painted green, four cubes at the corners have three faces painted red, green and black. Out of the remaining 8 cubes, four cubes have two faces painted red and green and four cubes have two faces painted black and green. In layer II and III: Four central cubes have no faces painted, four cubes at the comers have two face painted red and black. Out of the remaining 8 cubes four cubes have only one face painted black and four cubes have only one face painted red. In layer IV: Four central cubes have only one face painted green, four cubes at the comers have three faces painted red, green and black. Out of the remaining 8 cubes four cubes have two faces painted green and black and four cubes have two faces painted red and green.