# A Tangled Tale — Chapters explained

> Chapter companions for A Tangled Tale by Lewis Carroll.

- [Epigraph](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/epigraph.md): A brief Latin epigraph introduces the book, inviting the reader to accept it as it is.
- [To My Pupil](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/to-my-pupil.md): A poetic dedication praising a pupil's mastery of arithmetic and encouraging them to pursue lasting fame in mathematics, even surpassing Euclid.
- [A Tangled Tale](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/a-tangled-tale.md): The chapter presents a series of mathematical puzzles and logical conundrums wrapped in whimsical narratives, featuring characters like Clara, Balbus, and Mad Mathesis as they engage in playful yet challenging problems i
- [Knot I: Excelsior](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/knot-i-excelsior.md): Two knights descend a mountain at different speeds, discussing their pace and the time of day. The younger knight struggles with arithmetic as the elder challenges him to guess the time they stood on the peak, promising 
- [Knot II: Eligible Apartments](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/knot-ii-eligible-apartments.md): Hugh and Lambert search for lodgings in Little Mendip with their tutor Balbus, encountering a series of landladies offering single back rooms with cabbages. They also puzzle over a riddle from their father about a dinner
- [Knot III: Mad Mathesis](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/knot-iii-mad-mathesis.md): Clara and her aunt Mad Mathesis visit the Charing Cross Metropolitan Station and engage in two train-meeting matches. The first match involves counting trains met while traveling opposite directions around a circular rou
- [Knot IV: The Dead Reckoning](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/knot-iv-the-dead-reckoning.md): Two travelers, having completed a holiday trip and shed their knightly disguises, are aboard a ship near the Equator. They observe native fishermen from Mhruxi carrying money in sacks, which are accidentally swept overbo
- [Knot V: Oughts and Crosses](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/knot-v-oughts-and-crosses.md): Clara and her aunt Mad Mathesis engage in a match of marking pictures at an art gallery, using crosses for good marks and oughts for bad marks under complex scoring conditions. Clara struggles with the rules and her choi
- [Knot VI: Her Radiancy](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/knot-vi-her-radiancy.md): Balbus and Norman arrive in Kgovjni and are taken to the palace, where they meet the Governor and are presented to Her Radiancy. The Governor explains that they must judge a competition among three scarf-makers—Lolo, Mim
- [Knot VII: Petty Cash](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/knot-vii-petty-cash.md): Clara struggles to remember the cost of her luncheon while her aunt Mad Mathesis insists on recording it in her petty cash tablets. They encounter two old sisters at the train station who share the same predicament, lead
- [Knot VIII: De Omnibus Rebus](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/knot-viii-de-omnibus-rebus.md): The Governor escorts Balbus and Norman out of the Imperial presence, explaining the grurmstipths (omnibuses) that run to the harbour. They witness the Commander-in-Chief struggling to arrange twenty-four pigs in four sti
- [Knot IX: A Serpent with Corners](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/knot-ix-a-serpent-with-corners.md): Hugh and Lambert are on the beach at Little Mendip, where Hugh experiments with buckets to test the principle of displacement. He is puzzled when the displaced water seems less than the bucket's bulk. At dinner, Hugh pre
- [Knot X: Chelsea Buns](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/knot-x-chelsea-buns.md): Clara and her aunt Mad Mathesis encounter a Chelsea bun seller while discussing a morbid arithmetic problem about wounded soldiers. Later, they join Clara's father, his three sons, and Balbus for a tense family gathering
- [Appendix](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/appendix.md): Alice expresses a desire to help untangle a knot, setting a playful and curious tone for the appendix.
- [Answers to Knot I](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/answers-to-knot-i.md): The chapter presents the solution to a puzzle about two travelers walking on level ground, up a hill, and back down, calculating the total distance walked and the time of reaching the hilltop. It includes a detailed solu
- [Answers to Knot II](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/answers-to-knot-ii.md): This chapter provides solutions to two problems from Knot II: the Dinner Party Problem and the Lodgings Problem. The Dinner Party Problem asks how many guests the Governor of Kgovjni must invite given a set of relationsh
- [§1: The Dinner Party](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/1-the-dinner-party.md): The Governor of Kgovjni attempts to host a small dinner party, inviting four relatives who turn out to be the same person. The chapter presents the puzzle, discusses various answers received, and lists the class of corre
- [§2: The Lodgings](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/2-the-lodgings.md): Balbus presents a mathematical problem about a square with 20 doors on each side, numbered consecutively from a corner. The task is to determine which of four numbered doors (9, 25, 52, 73) minimizes the sum of distances
- [Answers to Knot III](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/answers-to-knot-iii.md): This chapter presents the solution to a railway meeting problem involving two travellers going opposite ways around a circular railway, with trains starting every 15 minutes in each direction. The answer for the first pa
- [Answers to Knot IV](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/answers-to-knot-iv.md): The chapter presents the solution to a mathematical problem involving five sacks with given pairwise and triple weights, solved via arithmetic. The author then categorizes and comments on the ninety-seven answers receive
- [Answers to Knot V](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/answers-to-knot-v.md): This chapter presents the solution to a puzzle about marking pictures with crosses and oughts, aiming to minimize the number of pictures marked while maximizing the total marks. The answer is 10 pictures with 29 marks, a
- [Answers to Knot VI](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/answers-to-knot-vi.md): This chapter provides solutions to two problems from Knot VI. The first problem involves A and B increasing their wealth from £1,000 to £60,000 by using zeros to transform numbers at the Bank of England. The second probl
- [Answers to Knot VII](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/answers-to-knot-vii.md): The chapter presents the solution to a mathematical problem involving the cost of lemonade, sandwiches, and biscuits, and discusses the methods used by various competitors. It includes a class list of solvers, critiques 
- [Answers to Correspondents](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/answers-to-correspondents.md): The author responds to correspondents regarding Knots II and VI, clarifying assumptions about house numbering and defending the mathematical reasoning behind the Double Rule of Three problems. He addresses criticisms of 
- [Answers to Knot VIII](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/answers-to-knot-viii.md): This chapter provides solutions to two puzzles: the Pigs Problem, which involves placing pigs in sties to satisfy a numerical condition, and the Grurmstipths Problem, an omnibus overtaking puzzle solved using relative sp
- [§1: The Pigs](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/1-the-pigs.md): The chapter presents a puzzle about placing twenty-four pigs in four sties such that, when going round and round, the number in each sty is nearer to ten than the number in the last. The answer given is 8, 10, 0, 6. Only
- [§2: The Grurmstipths](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/2-the-grurmstipths.md): This chapter presents a mathematical problem involving omnibuses and a traveller, exploring the relative speeds and times of meeting and overtaking. The solution is derived using algebraic reasoning, and several submitte
- [Answers to Knot IX](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/answers-to-knot-ix.md): This chapter provides solutions and commentary on three problems: the Buckets Problem, Balbus' Essay Problem, and the Garden Problem. The author evaluates various submitted answers, highlighting errors and correct reason
- [§1: The Buckets](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/1-the-buckets.md): The chapter presents a puzzle about a small bucket floating in a larger one, challenging Lardner's statement that a solid displaces an equal bulk of fluid. Various correspondents offer flawed explanations, and the author
- [§2: Balbus’ Essay](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/2-balbus-essay.md): Balbus poses a puzzle about a solid immersed in water, where the water rises through an infinite series of decreasing distances (2 inches, 1 inch, 1/2 inch, etc.), and he concludes the water will rise without limit. The 
- [§3: The Garden](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/3-the-garden.md): A mathematical problem about an oblong garden with a spiral gravel walk is posed and solved. The solution involves setting up a quadratic equation based on the area of the garden equaling the length of the walk. The chap
- [Answers to Knot X](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/answers-to-knot-x.md): This chapter presents solutions to two mathematical problems: the Chelsea Pensioners problem (finding the minimum percentage of soldiers who lost all four body parts) and the Sons' Ages problem (determining the ages of t
- [§1: The Chelsea Pensioners](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/1-the-chelsea-pensioners.md): This chapter presents a mathematical problem about the minimum percentage of Chelsea pensioners who must have lost all four body parts (eye, ear, arm, leg) given the percentages who lost each. The solution is 10%, derive
- [§2: Change of Day](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/2-change-of-day.md): The narrator postpones a geographical problem indefinitely, citing a lack of statistics and personal confusion, and questions their own ability to judge others when uncertain of their own standing.
- [§3: The Sons' Ages](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/3-the-sons-ages.md): This chapter presents a mathematical problem about three sons' ages, where the relationships between their ages at two different times lead to a solution. The narrator critiques various incorrect or incomplete solutions 
- [Endnotes](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/endnotes.md): The chapter contains brief endnotes clarifying the meaning of the Pigeon-English term 'Maskee' and acknowledging a deceased friend as the source of the preceding essay.
- [List of Illustrations](https://www.betterreads.online/discover/a_tangled_tale_se/chapters/list-of-illustrations.md): This chapter lists the illustrations included in the book, specifically mentioning a musical score for 'Chelsea Buns,' a genealogy diagram for a dinner party, and a diagram of a square with its doors.

HTML index: https://www.betterreads.online/discover/a_tangled_tale_se/chapters