What makes Mr. Nuttel susceptible to Vera's story in "The Open Window"?

To me, there are a couple reasons why Framton Nuttel falls
for Vera's story.

The first has to do with Vera.  She is
clearly a very good actress and that is not something you would expect from some 15 year
old girl -- you wouldn't expect her to come up with a wild story and then tell it so
seriously.

But the second has to do with Nuttel.  We can
see from what we are told of him that Nuttel is not the most sophisticated or the most
social person around.  His sister predicted that

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you will bury yourself down there
and not speak to a living soul, and your nerves will be worse than ever from moping.

If he is that
sort of a person, he may not really be perceptive enough to realize when he is being
tricked.

So I think it's a combination of Nuttel's
gullibility and Vera's believability.