Hi, here I have a problem with how to travel across a shape without going alone the same line twice. Capitalization and 'lower case-alization' of single letters (except I) are intentional in this question. Capitals represent a destination, lower case represents a path between two destinations.

In question 1) below, a path of c, b*, b, c* will start at 'B', follow path 'c' etc and follow 'c*' back to B. This means it uses 4 paths.

1)

What is the longest trail possible on this and why does it need to start on 'B' or 'C'?

2)

Prove that the longest track possible is '5', when you start at 'A'

3)

What is the longest continuous trail possible, justifying your reason.

Thanks for any help and advice.