Question

A cube painted red on two adjacent faces and black on the face opposite to the red faces and green on the
remaining faces is cut into 64 smaller cubes of equal size. How many cubes are there which have no face
painted?​

Answer 1

Answer:

Thus, there are two edges where the faces painted red and black meet, and each edge has four cubes. Thus, there are totally 88 smaller cubes on each face. So, there are 32 smaller cubes which have at least one of their faces green. The remaining 64 - 32 = 32 smaller cubes have none of their faces green.

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