A Tangled Tale · Chapter
Answers to Knot VII explained
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.
What happens
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 of incorrect or incomplete solutions, and a digression on logic and reasoning.
Themes in this chapter
Mathematical Reasoning
The chapter provides a detailed algebraic solution to a system of equations and discusses methods for solving problems with multiple unknowns.
Humor and Absurdity
Includes playful commentary on competitors' mistakes, such as the 'dreamy remark' and the absurdity of assuming sandwiches cost nothing.
Social Critique
Critiques the reasoning of various solvers and the nature of competition, with a digression on logic and arguing with a lady.
Characters to notice
- Clara
Referenced in the context of her luncheon cost problem.
- Balbus
Mentioned for his general principle about ascertaining the cost of a luncheon.
- Simple Susan
Thanked for kind words of sympathy.
- Old King Cole
Listed in the class sections for his solution.
- Hecla
Shared highest honours for using a method certain to produce the answer or prove impossibility.
- Martreb
Shared highest honours for the same reason as Hecla.
Key passages
“If it is all his own, he will make a good algebraist in the time to come.”
If Little Jack's solution is original, he shows promise as a future algebraist.
Praise for a competitor's algebraic reasoning.
“The two Kings are fearfully deliberate! I suppose walking quick, or taking shortcuts, is inconsistent with kingly dignity.”
The two kings' solutions are extremely slow, perhaps because haste is beneath their royal status.
Humorous critique of the slow pace of certain solvers.
“In logical language, in order to disprove a 'universal affirmative,' it is enough to prove its contradictory, which is a 'particular negative.'”
To disprove a statement that applies to all cases, one only needs to show a single counterexample.
Explanation of logical reasoning used to challenge Balbus's principle.