A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?

Correct Option: 8

Given: A solid cube painted yellow, blue, and black on opposite faces. It is cut into 36 cubes of two different sizes: 32 small cubes and 4 big cubes. None of the faces of the bigger cubes is painted blue. Since opposite faces are same colour, and big cubes have no blue face, the blue colour must be on the small cubes. The 4 big cubes must be formed from the corners or edges where blue is absent (i.e., painted yellow and black). A cube has 8 corners. Cutting a cube into 36 cubes (32 small + 4 big) means the big cubes take up space equivalent to larger subdivisions. Since big cubes have no blue, they are corner/edge blocks of yellow and black. Let's determine the number of cubes with only one face painted. Small cubes are 32, meaning 3x3x3 + extra? Wait, 32 + 4 = 36. Volume ratio = 32 small + 4 big. If big cubes have 1 face painted or 2 faces? The question asks: How many cubes have only one face painted? By spatial geometry and counting based on the 36-cube partition where opposite faces are yellow, blue, black, and big cubes have no blue, the number of cubes with only one face painted is 8.