Finding possibilities puzzle

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Question

The answer: 2

Hi guys, I'm doing the practice papers for an examination, and got stuck on this question. I ended up getting the right answer, but I'm not sure if my thinking is correct. I would love someone else's opinion on it.

My thinking -- >

"Statue to fountain, always pass the bandstand" The bandstand can only be the * in the middle, because that is the only place where going from one star to another star, the same star must always be crossed.

"Going from the lake to the bowling green, I never pass the fountain unless I pass the bandstand twice."

Not quite sure how to make that one out.

I ended up somehow getting at 2, but can't even seem to replicate my thinking in writing, which makes me think that it was more of a guess.

Would really appreciate other people's thinking on this!

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The star in the southeast has to be either the statue or the fountain, right? So lake and the bowling green must be west of the bandstand. If the lake, the bowling green, and the fountain were all on the circle west of the bandstand, you could certainly go from lake to fountain to bowling green without going past the bandstand more than once. So the fountain must be the star in the southeast.

That's two stars identified. Among the other three, no way of telling which is which.