This question is based on the following information: The six faces of cube are painted in a manner that no two adjacent faces have the same colour. The three colours used in painting are red, blue…
Question and options
This question is based on the following information: The six faces of cube are painted in a manner that no two adjacent faces have the same colour. The three colours used in painting are red, blue and green. The cube is then cut into 36 smaller cubes in a manner that 32 cubes are of one size and the rest of a bigger size and each of the bigger cube has no red side. How many cubes only have one side coloured?
- 0
- 16
- 4
- 8
Answer and explanation
Correct answer: D - 8
Take a 4x4x4 cube: four 2x2x2 cubes (volume 32) plus 32 unit cubes makes 36 pieces. Opposite faces share a colour. The big cubes avoid red only if they fill the middle two layers between the red top and bottom faces, so the 32 unit cubes form the red top and bottom layers. Each 4x4 layer has 4 centre cubes with only one painted face, giving 4 x 2 = 8. The big cubes each show two faces.
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