Jonathan Dandle wants to keep his dying sister from leaving a sizable bequest to her crackpot religion in her will, but in order to do that needs to convince her of his own state of enlightenment.
This is an enormously weak story, in that the puzzle turns on knowing Edgar Allen Poe’s poetry reasonably well plus a bit of astronomic folklore. Asimov himself mentions in the afterword that he had his doubts as to Dandle’s moral scruples, but that wasn’t a problem for me—the weakness of the puzzle itself was.