Mary's mathematical studies at college eventually give her the clues needed to uncover - almost too late - the leader of a crime syndicate even more powerful than that of Holmes' old nemesis, the late Professor Moriarty. The nature of Moriarty's research into binomial theorems is elucidated somewhat, but not so much in the manner of a plot device, while bases other than ten play a more key role in a major puzzle (saying more would give away too much). Mathematicians are portrayed in varying ways, ranging from deranged to serene.