A jewellery artisan has at his disposal Brazilian stones of three colours: red, blue and green. He intends to produce jewellery made of a metal alloy, based on a mould in the shape of a non-square rhombus with stones at its vertices, so that two consecutive vertices always have stones of different colours. The figure illustrates a piece of jewellery, produced by this artisan, whose vertices $A$, $B$, $C$ and $D$ correspond to the positions occupied by the stones. Based on the information provided, how many different pieces of jewellery, in this format, can the artisan obtain? (A) 6 (B) 12 (C) 18 (D) 24 (E) 36
A jewellery artisan has at his disposal Brazilian stones of three colours: red, blue and green.
He intends to produce jewellery made of a metal alloy, based on a mould in the shape of a non-square rhombus with stones at its vertices, so that two consecutive vertices always have stones of different colours.
The figure illustrates a piece of jewellery, produced by this artisan, whose vertices $A$, $B$, $C$ and $D$ correspond to the positions occupied by the stones.
Based on the information provided, how many different pieces of jewellery, in this format, can the artisan obtain?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 36