The number of ways in which the diagram in Fig. 6.1 can be coloured so that each of the smaller triangle is painted with one of the three colours yellow, pink or green and no two adjacent regions are painted with the same colour, is
24
12
36
16
This can be done in the following ways:
(i) paint the central triangle with one of the three col-
ours;
(ii) paint cach of the remaining triangles with any one of the two remaining colours. Thus, the required number of ways
.
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