Let the initial vertex = A, implying that the ant must travel to G.
Let's divide the journey into 3 stages and count the number of options for each stage.
First stage;
Since the ant can travel from A to B, D, or E, the number of options for the first stage = 3.
Second stage:
Whether the ant is at B, D or E, it has 2 options for the next stage.
If the ant is at B, it can travel next to F or C.
If the ant is at D, it can travel next to C or H.
If the ant is at E, it can travel next to F or H.
Thus:
The number of options for the second stage = 2.
Third stage:
Wherever the ant ends in the second stage, it can then travel to G by a short route, a medium route, or a long route, for a total 3 options.
For example:
If the ant travels A-B-F in the first 2 stages, it can then travel to G as follows:
Short route = F-G.
Medium route = F-E-H-G.
Long route = F-E-H-D-C-G.
Thus:
The number of options for the third stage = 3.
To combine the options for each stage, we multiply:
3*2*3 = 18.
The correct answer is
C.
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