Add new comment

Puzzle No. 2 - carnivorous beetles

Submitted by plusadmin on 1 May, 1997
May 1997


Four carnivorous beetles awake from a good night's rest feeling agreeably hungry. These beetles are not too particular about their diets and will always move directly towards their prey at a constant speed of 1 cm/sec. It just so happens that this morning the beetle at point A wakes up looking directly at B, who is looking at C, who is looking at D, who is looking at A. The points A, B, C and D are at the corners of a square of sides 4 cms.

Beetles' starting position
Beetles' path

All the beetles wake up at the same instant and start moving towards their prey. Clearly they will follow a curved path because their breakfast is on the move too!

Diagram of problem

Does A catch up with B, and if so:

  1. How long does this take?
  2. How far does A move in this time?
  3. What happens?

We will publish the best solutions in the next issue, along with the answer to the problem itself.

Solution

About text formats

Filtered HTML

  • Web page addresses and email addresses turn into links automatically.
  • Allowed HTML tags: <a href hreflang> <em> <strong> <cite> <code> <ul type> <ol start type> <li> <dl> <dt> <dd>
  • Lines and paragraphs break automatically.
  • 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.