Practice question
Question
A cube is painted black on two adjacent faces and on one opposite face, yellow on two opposite faces and green on the remaining face. It is then cut into 64 equal cubes. How many cubes have one black coloured face only?
Explanation
Four by four by four division yields face centers with single painted face. Black occupies three faces with two opposite, leaving only central squares of those faces uncontaminated by other colors. Counting four centers per black face minus shared edges totals twelve cubes.
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