The minimum number of colours to required paint all sides of a cube that no two adjacent faces may have the same colour is.

The correct option is 3.

Let us understand why 3 is the minimum number of colours required to paint the faces of a cube such that no two adjacent faces share the same colour.

A standard cube has 6 faces in total. These 6 faces are arranged in 3 pairs of opposite faces:
1. Top and Bottom faces
2. Front and Back faces
3. Left and Right faces

By definition, any face of a cube is adjacent to exactly 4 other faces. The only face it is not adjacent to is its opposite face. For example, the Top face is adjacent to the Front, Back, Left, and Right faces, but it is not adjacent to the Bottom face.

To satisfy the condition that no two adjacent faces have the same colour, we can assign the same colour to faces that are not adjacent to each other. Since opposite faces are the only non-adjacent pairs, we can paint each pair of opposite faces with the same colour:
- Paint the Top and Bottom faces with Colour 1.
- Paint the Front and Back faces with Colour 2.
- Paint the Left and Right faces with Colour 3.

In this arrangement:
- The faces sharing Colour 1 (Top and Bottom) are opposite and do not touch.
- The faces sharing Colour 2 (Front and Back) are opposite and do not touch.
- The faces sharing Colour 3 (Left and Right) are opposite and do not touch.

Thus, no two adjacent faces share the same colour. Since a cube has 3 pairs of opposite faces, we require exactly 3 different colours. It is impossible to do it with fewer than 3 colours because any group of 3 mutually adjacent faces (for example, Top, Front, and Right) must all have different colours to avoid sharing a colour between adjacent faces.