Question 23
The diagram below shows a regular hexagon that is divided into six congruent triangular regions $A,B,C,D,E,F$. Two triangular regions are adjacent if they share a common side. For example, $A$ and $B$ are adjacent but $A$ and $C$ are not adjacent. In how many ways can we colour these regions $A,B,C,D,E,F$ using six different colours such that the adjacent regions do not receive the same colour? (Note that not all six colours need to be used in colouring the six regions and non-adjacent regions can receive the same colour).
