Sorry, I didn't understood what it mean ambiguity in terms of paths, maybe its lingo diffs...

you will get to a junction. Do you turn left or right? You don't know...
What does it mean?

If I can go left (didn't stepped on this cell before) I'll try to go left, same for right...

can you please clarify this condition?:
"It must be possible to follow the line with no ambiguity"

Seems like I'm not the only1 struggling with this condition..

I read the discussions, and I still don't get why it's invalid test:

    +-+
    | |
    ++++
    ++++
   X+++
     +---X

there is only one path forward and backward, isn't it?

is it possible to pass on corner twice but to different directions?