Spies Passing in the Night - Solution

Share this page
Submitted by plusadmin on 1 January, 2001
January 2001

Spies Passing in the Night - Solution

The crucial thing needed to solve this problem is the idea that we can map the positions of the two armies, the two spies, and the traveller, against time, and get five straight lines. The slopes of these lines will of course be the various speeds. This is exactly the setup covered by Pappus' Theorem.

Now the result just falls out - it's easier to describe with a diagram than with words. (Thanks to Ashish Bhambhani from Nagpur in India for his correct solution and the diagram below.)

  • Maths in a minute

    Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.

  • Climate change: How can maths help?

    As COP28, the 2023 United Nations Climate Change Conference, kicks off we look at how maths can help understand the climate crisis.

  • The travelling salesman
    map

    How do you create dramatic film out of mathematics? We find out with writer and director Timothy Lanzone.

  • Disease modelling for beginners

    Mathematics plays a central role in understanding how infectious diseases spread. This collection of articles looks at some basic concepts in epidemiology to help you understand this fascinating and important field, and set you up for further study.

  • Maths in a minute: Conditional probability

    Find out why the formula we use to work out conditional probabilities is true!

  • A disappearing number
    scene from play
    We talk about a play that explores the fascinating mathematical collaboration between the mathematicians GH Hardy and Srinivasa Ramanujan.