How to solve the cable bridge problem using an algorithm?

Question

I was wondering if it is possible to solve this problem with a bridge bridge by searching for a graphical search algorithm:

Feeling brushes says DFS, but how should I determine the state? (That is, if DFS is even the way to go.)

Rope bridge

Answer 1

This problem must be solved without a computer.

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Answer 2

EWD 1255.