Mr. Fortescue dies in his office poisoned by taxine (extracted from yew trees) and his entire family is suspect: his too young wife, her young handsome lover, his stuffy son, his son's self-absorbed wife, his fanatically religious sister-in-law, even the butter-won't-melt-in-her-mouth housekeeper. The wild adventurous black sheep son of the family shows up with a new wife in the middle of these tensions just as two more murders are committed. One of these deaths becomes very personal for Jane Marple who gets involved.
Probably, arguably, the best of the Marple episodes (I would put it side by side with "4:50 from Paddington") as Christie's masterfully reveals and at the same time obscures the identity of the murderer. I think all will find the solution to the puzzle intriguing while enjoying the excellent performances: look for a young Tom Wilkinson as well as Selina Cadell. Annette Badland (as of this writing starring in Midsomer Murders) is also very good as the dim-witted maid who knows too much and whose fate brings Jane Marple (her former employer) into the fray.
And best of all the nursery rhyme (from which the title comes), rather than a conceit, is a vital part of the mystery and its solution.