Love Miss Marple. Love that a dithering old lady can figure out what's going on before most.
This one has Miss Marple in the Caribbean thanks to her nephew Raymond. He sends her to a warmer climate to help her health. While talking with an old military man, Miss Marple sort of pays attention to his stories. As he begins to tell her one about a murderer who got away and wants to show her a photo, he notices someone over her shoulder. Quickly changing the subject and putting his wallet away, Miss Marple never gets the full story. The next day he's dead, making Miss Marple suspicious and then she's even more suspicious when the photo seems to have disappeared. Two more deaths and Miss Marple has the killer. Along the way she makes friends with rich invalid who gives her the nickname Nemesis.