2

Consider the following two sentences:

Why can I not open the door?

and

Why can not I open the door?

Which is more common? What's the subtle difference between them?

2

The former is definitely more common; the latter sounds rather dated, and interpretations may vary depending on the different connotations that it could provoke. The second option is often found in its contracted form, though: Why can't I open the door?.

Have a look at this question on cannot versus can't and the wh-movement it references. Note that the example in that answer is nearly identical to yours, and it opts for the former or contracted form.

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