A Tangled Tale · Chapter
§3: The Sons' Ages explained
This chapter presents a mathematical problem about three sons' ages, where the relationships between their ages at two different times lead to a solution.
What happens
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 submitted by readers, praising only a few for their logical rigor. The chapter concludes with a farewell from the author, reflecting on the end of the series.
Themes in this chapter
Mathematical Reasoning
The chapter centers on solving an algebraic age problem, emphasizing logical deduction and critique of flawed reasoning.
Humor and Absurdity
The narrator uses playful, sarcastic commentary to mock incorrect solutions, comparing solvers to animals like Old Hen and Old Cat.
Social Critique
The critique of solvers' methods reflects on intellectual rigor and the pitfalls of assumption-based reasoning.
Characters to notice
- Jane E.
Submitted an incomplete solution, calculating present ages but leaving the second occasion unnoticed.
- Dinah Mite
Correctly determined the relationship between ages at first but made a tentative assumption, resulting in a merely 'honourable' classification.
- Algernon Bray
Solved the problem correctly but noted that fractional ages would lead to infinite answers, earning highest honours.
- Simple Susan
Used a partly tentative method to find five possible sets of ages and eliminated four, classified as 'Clumsily Right'.
- White Sugar
Detected an oversight in the problem regarding the son's exact age on the day of coming of age, providing a second solution.
Key passages
“At first, two of the ages are together equal to the third. A few years afterwards, two of them are together double of the third. When the number of years since the first occasion is two-thirds of the sum of the ages on that occasion, one age is 21. What are the other two?”
Initially, the sum of two ages equals the third. Later, the sum of two ages is twice the third. The time elapsed since the first occasion is two-thirds of the total ages at that time, and one son is now 21. Find the other two ages.
This is the core problem statement of the chapter.
“I take this opportunity of thanking those who have sent, along with their answers to the Tenth Knot, regrets that there are no more Knots to come, or petitions that I should recall my resolution to bring them to an end.”
The author thanks readers who expressed sadness that the series is ending or asked him to continue.
This reflects the author's farewell and the end of the puzzle series.