# Answers to Knot X explained — A Tangled Tale

> Chapter companion for A Tangled Tale by Lewis Carroll.

## What happens

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 three sons given relational conditions over time). The author critiques various incorrect or incomplete answers submitted by correspondents, using playful and satirical commentary, and awards class rankings to the solvers.

## Themes in this chapter

### Mathematical Reasoning

The chapter focuses on solving two mathematical problems, emphasizing logical deduction, algebraic manipulation, and critique of flawed reasoning.

### Humor and Absurdity

The author uses witty and satirical commentary on incorrect solutions, such as comparing Delta's assumptions to a grim battlefield and Magpie's logical leaps to a bird's behavior.

### Competition and Achievement

The chapter ranks solvers into classes (e.g., 'first class,' 'honourable'), reflecting a competitive spirit in solving puzzles.

## Character check-ins

### Polar Star

Adopted solution for the Chelsea Pensioners problem, described as better than the author's own.

### Algernon Bray

Listed among solvers of the Chelsea Pensioners problem and the Sons' Ages problem; also remonstrates the author's logical assertion.

### Dinah Mite

Listed among solvers for both problems; criticized for tentative solution in the Sons' Ages problem.

### Jane E.

Listed among solvers for both problems; criticized for leaving the second occasion unnoticed in the Sons' Ages problem.

### Simple Susan

Listed among solvers for both problems; described as 'anything but simple' and her solution as clumsy and roundabout.

### White Sugar

Listed among solvers for both problems; praised for detecting an oversight regarding the son's age of majority.

## Key lines

> Adding the wounds together, we get 70 + 75 + 80 + 85 = 310, among 100 men; which gives 3 to each, and 4 to 10 men. Therefore the least percentage is 10.

By summing the percentages of wounds, we find 310 wounds per 100 men, meaning each man averages 3 wounds, with 10 men having 4 wounds, so at least 10% lost all four.

_Solution to the Chelsea Pensioners problem._

> Let the ages at first be x , y , ( x + y ) . Now, if a + b = 2 c , then ( a − n ) + ( b − n ) = 2 ( c − n ) , whatever be the value of n. Hence the second relationship, if ever true, was always true.

If two ages sum to double a third, subtracting the same number from each preserves the relationship, so the condition holds at all times if it holds at any time.

_Key logical step in solving the Sons' Ages problem._

> I have received more than one remonstrance on my assertion, in the Chelsea Pensioners’ problem, that it was illogical to assume, from the datum '70 p. c. have lost an eye,' that 30 p. c. have not.

Several readers objected to my claim that knowing 70% lost an eye does not logically imply the remaining 30% did not.

_Author defends his logical point against criticism._

## Links

- HTML: https://www.betterreads.online/discover/a_tangled_tale_se/chapters/answers-to-knot-x
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- All chapters: https://www.betterreads.online/discover/a_tangled_tale_se/chapters