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A cube is coloured red on two opposite faces, blue on two adjacent faces and yellow on the two remaining faces. It is then cut into two halves along the plane parallel to the red faces. One piece is then cut into four equal cubes and the other one into 32 equal cubes
Let's take the original side length of the cube to be 2a
Cutting the square parallel to the red faces, would give us:
Let's say we cut the upper piece into four equal squares.
The upper piece is a cuboid with dimensions (2a, 2a, a)
To make four cubes we can cut it into equal halves along is height and length.
To cut the lower piece into 32 equal pieces, we can put 3 cuts along its length, 3 cuts along its height and breadth
All the cubes from the upper half have at least one face coloured.
In the lower half, the cubes on the bottom, frontleft, and right would have one face coloured.
The only cubes that will not have any face coloured would be the four cubes that form the inner portion of the upper face.
Therefore, 4 is the correct answer.
