A Graveyard to Let by Carter Dickson
Published in 1949
Sir Henry Merrivale, the British detective known as H.M., made a fictional name for himself by solving complicated locked-room mysteries. In 1949 he took a trip to the United States (with a letter in hand for Harry Truman) and found himself competing with the New York police to crack a swimming pool vanishing. No, the pool itself has not disappeared but a man (H.M.’s old pal Frederick Manning) has jumped into it and left nothing of himself behind except a floating hat. The plot diverts from the main mystery to show us H.M. toying with an Irish cop in the subway and knocking a baseball out of ball field and into a cemetery. The puzzle becomes a bit more serious when the vanished man turns up stabbed nearly to death and his dead-for-decades wife reappears, looking quite unlike a corpse.