A Tangled Tale · Chapter
Answers to Knot VIII explained
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 speed and distance cal
What happens
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 speed and distance calculations. The chapter includes commentary on incorrect answers from correspondents.
Themes in this chapter
Mathematical Reasoning
The chapter presents mathematical solutions to puzzles, including relative speed and distance calculations.
Logic and Paradox
The Pigs Problem involves a logical condition that seems to defy straightforward mathematical solution, and the Grurmstipths Problem touches on Zeno-like paradoxes.
Characters to notice
- Balbus
Balbus comments on the Pigs Problem, stating it cannot be solved mathematically or by verbal quibble.
- Nolens Volens
Nolens Volens attempts to solve the Pigs Problem by changing the direction of travel and adding a condition about carrying pigs. Also attempts the Grurmstipths Problem using an Achilles-and-Tortoise-like method.
- Dinah Mite
Dinah Mite provides a partially correct answer to the Grurmstipths Problem but errs in concluding the overtaking time.
- Delta
Delta is listed in the class list for the Grurmstipths Problem.
Key passages
“Place twenty-four pigs in four sties so that, as you go round and round, you may always find the number in each sty nearer to ten than the number in the last.”
Arrange 24 pigs across 4 pens so that, when you circle around, each pen's count is closer to 10 than the previous pen's count.
This is the statement of the Pigs Problem.
“Since the omnibus met is due at the starting-point in 2½ minutes, it goes in that time as far as the traveller walks in 12½; i.e. it goes 5 times as fast.”
Because the oncoming bus will reach the start in 2.5 minutes, it covers in that time the same distance the traveler walks in 12.5 minutes, meaning the bus is five times faster.
This explains the speed ratio used in the Grurmstipths solution.