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. Arthur B. Frost added illustrations when the series was printed in book form. 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. The ribbing of readers answering wrongly – giving their names – was not always well received (see Knot VI below ). In the December 1885 book preface Carroll writes: Describing why he was ending the series, Carroll writes to his readers that the Knots were "but a lame attempt". Others were more receptive: In 1888 Stuart Dodgson Collingwood wrote "With some people, this is the most popular of all his books; it is certainly the most successful attempt he ever made to combine mathematics and humour." They have more recently been described as having "all the charm and wit of his better-known works". Summary of Knots and solutions. 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. 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. 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. Knot VI, Her Radiancy. Two travellers appear in Kgovjni, a land referenced in earlier Knots. The ruler places them in "the best dungeon, and abundantly fed on the best bread and water" until they resolve a logical problem. Knot VII, Petty Cash. The aunt and niece encounter "by a remarkable coincidence" others who are travelling not only on the same train, but at the same station, on the same day, at the same hour . Lunch bills are muddled due to the aunt's reluctance in writing down numbers that could "easily" be memorised. Knot VIII, De Omnibus Rebus. The travellers of Knot VI are leaving Kgovjni with relief, when a mathematical problem occurs to one of them. Knot IX, A Serpent with Corners. The characters of Knot II, Balbus and his two students, return to give three problems loosely connected by a narrative. Knot X, Chelsea Buns. Mad Mathesis and her niece return, as well as Balbus and his two students. Changes after magazine publication. Changes were made when the stories were published in  book form. In the solution to Knot III reader AYR is dropped entirely from discussion. The change causes a comparison with same number of readers getting a perfect score on a previous Knot to be dropped: Other examples of changes in Knot III are "Mad Mathesis dragged her off" to "Mad Mathesis hurried her on", and Clair saying "If I may go the same way round, as I did last time" to "If I may choose my train".