Question

If each side of a white cube is painted with a distinct colour such that no face is white and then the cube is cut into 64 identical cubes without any wastage, how many pieces will have at least three different Colours?.​ please answer don't spam

Answer 1

Given  : each side of a white cube is painted with a distinct color such that no face is white and then the cube is cut into 64 identical cubes without any wastage,

To Find : how many pieces will have at least three different Colours

Solution:

A cube is cut into 64 cubes

Hence cube is cut into 4 * 4 * 4

All faces have different color

so cubes at vertex will have 3 different colors + white color on internal face

Hence 4 colors

Vertex at edges will have 2 colors and white color on internal face

Hence 3 colors

so pieces will have at least three different Colours = 8 + 12 * (4 - 2)

= 8 + 24

= 32

Hence 32 pieces will have at least three different Colours

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