1. Scientists are puzzled as to why the whale had swum to the shore.

1-2. Scientists are puzzled as to why the whale has swum to the shore.

2. Scientists are puzzled about why the whale had swum to the shore.

3.Scientists are puzzled concerning why the whale had swum to the shore.

4. Scientists are puzzled regarding why the whale had swum to the shore.
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Do we have to use 'had swum' or 'has swum'? Can we use 'about' etc. instead of 'as to'?

Yes to all your questions. "has" or "had" do not quite mean the same thing, though. "has" is present tense, meaning the whale is still near the shore. "had" is past tense, so it means the whale may no longer be near the shore.

Maybe she swam away again. :)

When discussing the past action of the whale swimming to the shore, we can use either "had swum" or "has swum" depending on the context.

If the sentence is describing a past event, such as when scientists recently discovered the beaching of the whale and are currently discussing it, we can use "had swum." For example:

- Scientists are puzzled as to why the whale had swum to the shore. (Describing a past event)

If the sentence is expressing a current situation, where scientists are actively discussing the whale's presence on the shore, we can use "has swum." For example:

- Scientists are puzzled as to why the whale has swum to the shore. (Describing a current situation)

So, both "had swum" and "has swum" can be used, depending on whether the focus is on a past or current event.

Regarding the use of "as to," it is a more formal and precise phrase that can be replaced with similar phrases like "about," "concerning," or "regarding." All four options you provided (about, concerning, as to, regarding) are suitable and convey the same meaning. You can choose the one that sounds the best to you or fits the overall style or tone of your writing.