If a cube is coloured red on all faces and cut into 64 smaller cubes of equal size, then which of the following are correct? I. Sixteen small cubes have no face coloured. II. Twenty four small cubes…
Question and options
If a cube is coloured red on all faces and cut into 64 smaller cubes of equal size, then which of the following are correct?
I. Sixteen small cubes have no face coloured.
II. Twenty four small cubes have only one face coloured.
III. None of the cubes can have its opposite faces coloured red.
IV. There are eight cubes which have three faces coloured.
I. Sixteen small cubes have no face coloured.
II. Twenty four small cubes have only one face coloured.
III. None of the cubes can have its opposite faces coloured red.
IV. There are eight cubes which have three faces coloured.
- I, III and IV only
- I, II and III only
- I and IV only
- II, III and IV only
Answer and explanation
Correct answer: D - II, III and IV only
4x4x4 cut: no face coloured = 2^3 = 8 (so I is false); one face = 6 x 2^2 = 24 (II true); opposite faces of a small cube are never both painted when n > 2 (III true); corner cubes with 3 faces = 8 (IV true).
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