A Tangled Tale

A Tangled Tale is a collection of 10 brief humorous stories by Lewis Carroll (Charles Lutwidge Dodgson), published serially between April 1880 and March 1885 in The Monthly Packet magazine. The stories, or Knots as Carroll calls them, present mathematical problems. In a later issue, Carroll gives the solution to a Knot and discusses readers' answers. The mathematical interpretations of the Knots are not always straightforward.

Knot I, Excelsior. Two knights discuss the distance they will have travelled that day, uphill and downhill at different speeds. The older knight obscurely explains the mathematical problem.

Carroll's Solution: As with most of the Knots, the solution includes: a simplified restatement of the problem, a method to arrive at the solution, the solution, a discussion of readers' solutions, then readers' grades. In his discussion, Carroll relates that one reader accuses the senior knight of untruthfulness (this is rebutted by Carroll, using the knight's tone). Another reader answers the problem by extending the story (this is quoted). The poem of two readers answering the problem is also quoted.
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.

Knot IV, The Dead Reckoning. The two knights of Knot I, in a modern guise, are party to a dispute about the weight of passengers' bags lost overboard from a ship.

Knot V, Oughts and Crosses. The aunt and niece from Knot III are in an art museum. Trading snipes as before, the aunt evades her niece's logical problem: the niece's preceptress had told her girls "The more noise you make the less jam you will have, and vice versa." The niece wants to know if this means that if they are silent, they will have infinite jam. Instead, her aunt responds with her own logical problem.