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Question
A solid cube has been painted yellow, blue and black on pairs of opposite faces. The cube is then cut into 36 smaller cubes such that 32 cubes are of the same size while 4 others are of bigger sizes. Also no faces of any of the bigger cubes is painted blue.
How many cubes have at least two faces painted?
A solid cube has been painted yellow, blue and black on pairs of opposite faces. The cube is then cut into 36 smaller cubes such that 32 cubes are of the same size while 4 others are of bigger sizes. Also no faces of any of the bigger cubes is painted blue.
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Solution
The correct option is B 28
In the given statement, there are 36 cubes, 32 of which are of the same size and 4 other sure of bigger size. Clearly, each side of bigger cubes is twice as large as that of similar cubes. Also, since no face of any of the larger cubes is painted blue, so each one of the larger cubes has one face painted red, one is black and all other faces are unpainted.
There are no cubes having more than three faces painted. 8 cubes at the edges of the block have three faces painted and as calculated above, 20 cubes have two faces painted. Thus, 8+20=28 cubes have two or more faces painted.
In the given statement, there are 36 cubes, 32 of which are of the same size and 4 other sure of bigger size. Clearly, each side of bigger cubes is twice as large as that of similar cubes. Also, since no face of any of the larger cubes is painted blue, so each one of the larger cubes has one face painted red, one is black and all other faces are unpainted.
There are no cubes having more than three faces painted. 8 cubes at the edges of the block have three faces painted and as calculated above, 20 cubes have two faces painted.
Thus, 8+20=28 cubes have two or more faces painted.
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