chunk: Knot II, Eligible Apartments. Professor Balbus, named after a hero with "anecdotes whose vagueness in detail was more than compensated by their sensational brilliance", is given a problem by students. The number of guests for a party is described in puzzling terms. He in turn creates a mathematical problem for them: two answers are required of readers.
  Solution: The mathematical problem is solved with the aid of a diagram. Those employing "guesswork" are given partial credit. One reader suggests the genealogical problem can be solved by "intermarriages", to which Carroll replies, "Wind of the western sea, you have had a very narrow escape! Be thankful to appear in the Class-list at all!"
  Knot III, Mad Mathesis. Overbearing aunt Mad Mathesis bets her niece that she can select a train from London that will pass more trains than her niece's does. The niece loses, but thinks she has found a solution to win, a second time.