Puzzle No. 2 - carnivorous beetles

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