20. As shown in the figure, the shape is composed of ten line segments. Now, we are to color the line segments using three colors, with the requirement that adjacent segments must be colored differently (line segments sharing a common endpoint are considered adjacent). If colors can be reused, how many different coloring methods are there in total?

The shape is composed of ten line segments. Now, we are to color the line segments using three colors, with the requirement that adjacent segments must be colored differently (line segments sharing a common endpoint are considered adjacent). If colors can be reused, how many different coloring methods are there in total?
【Analysis】Label the ten line segments. Segment 1 has 3 coloring methods, Segment 2 has 2 coloring methods, at this point, Segment 3 is adjacent to both Segment 1 and 2, so it has only 1 coloring method, Segment 4 is adjacent to both Segment 1 and 3, so it has only 1 coloring method, and it is the same color as Segment 2, Segment 5 is adjacent to both Segment 1 and 2, so it has only 1 coloring method, and it is the same color as Segment 3.
Considering Segment 6, Segment 6 has 2 coloring methods: it can be the same color as Segment 1 or the same color as Segment 5. If Segment 6 is the same color as Segment 1, i.e., different from Segment 5, at this point, Segment 7, which is adjacent to both Segment 5 and 6, has only 1 coloring method, the same color as Segment 2, Segment 8, which is adjacent to both Segment 5 and 7, has only 1 coloring method, the same color as Segment 1, Segment 9, which is adjacent to both Segment 6 and 7, has only 1 coloring method, the same color as Segment 3, Segment 10, which is adjacent to both Segment 8 and 9, has only 1 coloring method, the same color as Segment 2. In summary, in this case, there are \(3 \times 2 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1 \times 1 = 6\) coloring methods. If Segment 6 is the same color as Segment 5, at this point, Segment 7 has 2 choices, either the same color as Segment 1 or the same color as Segment 2, at this point, Segment 8, which is adjacent to both Segment 5 and 7, has only 1 choice, Segment 9, which is adjacent to both Segment 6 and 7, has only 1 choice, the same color as Segment 8, at this point, Segment 10 also has 2 choices, either the same color as Segment 7 or the same color as Segment 5, in this case, there are \(3 \times 2 \times 1 \times 1 \times 1 \times 1 \times 2 \times 1 \times 1 \times 2 = 24\) coloring methods. In summary, there are a total of \(24 + 6 = 30\) coloring methods.