# Answers to Knot VI explained — A Tangled Tale

> Chapter companion for A Tangled Tale by Lewis Carroll.

## What happens

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 problem compares the merits of three scarf-makers (L, M, Z) based on rapidity, lightness, and warmth, demonstrating that the correct method is to multiply proportional marks rather than add them. The chapter also includes a class list of solvers and commentary on common errors.

## Themes in this chapter

### Mathematical Reasoning

The chapter focuses on solving mathematical problems, emphasizing correct methods such as multiplication over addition for proportional marks.

### Competition and Achievement

The class list and commentary on solvers' errors highlight a competitive atmosphere and the pursuit of correct answers.

### Humor and Absurdity

The playful criticism of solvers' mistakes and the whimsical names (e.g., Addlepate, Old Hen) add a humorous tone.

## Character check-ins

### Balbus

Listed among the five winners for Problem 2, though noted for defective reasoning.

### Dinah Mite

Listed as a winner in the class list for Problem 2.

### Simple Susan

Mentioned as one of the wrongdoers who put the rightful winner last, beguiled by the Old Hen.

### Mrs. Sairey Gamp

Mentioned among the third set of wrongdoers; her reasoning is criticized as flawed.

### Vis Inertiæ

Addressed in the postscript regarding Knot V; she misunderstood the condition about filling columns with oughts and crosses.

### Old Hen

Mentioned as having beguiled Simple Susan with chaff.

## Key lines

> A and B began the year with only £1,000 apiece. They borrowed nought; they stole nought. On the next New-Year’s Day they had £60,000 between them. How did they do it?

A and B each started the year with £1,000. They didn't borrow or steal anything. By the next New Year's Day, they had a combined total of £60,000. How did they achieve this?

_The problem is solved by using zeros to transform the numbers, e.g., turning £1,000 into £10,000 or £60,000._

> L makes 5 scarves, while M makes 2: Z makes 4 while L makes 3. Five scarves of Z ’s weigh one of L ’s; 5 of M ’s weigh 3 of Z ’s. One of M ’s is as warm as 4 of Z ’s: and one of L ’s as warm as 3 of M ’s. Which is best, giving equal weight in the result to rapidity of work, lightness, and warmth?

L produces 5 scarves while M produces 2; Z produces 4 while L produces 3. Five of Z's scarves weigh as much as one of L's, and five of M's weigh as much as three of Z's. One of M's scarves is as warm as four of Z's, and one of L's is as warm as three of M's. Determine the best scarf-maker, considering speed, lightness, and warmth equally.

_The solution involves multiplying proportional marks for each quality, resulting in the order M, L, Z._

## Links

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