A Tangled Tale · Chapter
Answers to Knot III explained
This chapter presents the solution to a railway meeting problem involving two travellers going opposite ways around a circular railway, with trains starting every 15 minutes in each direction.
What happens
This chapter presents the solution to a railway meeting problem involving two travellers going opposite ways around a circular railway, with trains starting every 15 minutes in each direction. The answer for the first part is 19 trains met by each traveller; for the second part, the easterly traveller meets 12 and the westerly 8. The solution uses a least common multiple of 360 units to divide the railway and calculate meeting points. The chapter also reviews 45 submitted answers, categorizing them as right, wrong, or half-right, and includes a class list of successful solvers.
Themes in this chapter
Mathematical Reasoning
The chapter provides a detailed solution to a train meeting problem using least common multiples, unit division, and rate calculations.
Competition and Achievement
The review of 45 answers and the class list of successful solvers highlight a competitive, achievement-oriented context.
Humor and Absurdity
The commentary on incorrect answers, such as Seagull thinking the easterly train stood still for 3 hours, adds a playful, humorous tone.
Characters to notice
- Clara
Mentioned as a point of confusion: some solvers incorrectly assumed Clara travelled in the easterly train, though the data does not settle this.
- Matthew Matticks
Listed among those who gave no working and are wrong.
- Cheeky Bob
Gave the right answers but would have received no marks in a competition.
- Bo-Peep
Submitted a wrong answer, making errors in counting trains met at the start and end.
- Tom-Quad
Omitted part (1) and made an error in part (2) by counting the train met on arrival.
- Algernon Bray
Listed among the 'classic Ten' who solved the whole problem correctly.
Key passages
“Two travellers, starting at the same time, went opposite ways round a circular railway. Trains start each way every 15 minutes, the easterly ones going round in 3 hours, the westerly in 2. How many trains did each meet on the way, not counting trains met at the terminus itself?”
Two people begin at the same point and travel in opposite directions around a circular track. Trains depart in each direction every 15 minutes; eastbound trains take 3 hours to complete a circuit, westbound take 2 hours. How many trains does each traveller encounter, excluding those met at the starting station?
This is the problem statement for the first part of Knot III.
“They went round, as before, each traveller counting as 'one' the train containing the other traveller. How many did each meet?”
The travellers repeat the journey, but now each counts the train carrying the other traveller as one of the trains they meet. How many trains does each meet under this new rule?
This is the problem statement for the second part of Knot III.