How many minimum number of colours will be required to paint all the sides of a cube without the adjacent sides having the same colours ?

The number of ways of painting the faces of a cube with six different colours is

The number of ways of painting the faces of a cube with six different colours is

The number of ways of painting the faces of a cube with six different colours is

Each of the six squares in the strip shown in the fig., is to be coloured with anyone of ten different colours so that no two adjacent squares have the same colour. Find the number of ways of colouring the strip.

A new flag is to be designed with six vertical strips using some or all of the colours yellow, green,blue and red.Then,the number of ways this can be done such that no two adjacent strips have the same colour is

A new flag is to be designed with six vertical stripes using some or all of the colour yellow, green, blue and red. Then, the number of ways this can be made such that no two adjacent stripes have the same colour is