Hi, and welcome back from the summer to a new series of mathematical riddles! I’ve decided to include only one riddle per post this semester, which will hopefully mean that I’ll be able to keep a more consistent posting schedule. As always, if you have a nice mathematical riddle that you would like to share, then let us know and we’ll see if we can post it. Today’s riddle is a nice puzzle about swimming and monsters; check out the post below to read more!
Imagine that you are at the center of a circular pool of unit radius. At the very edge of the pool, there is a monster who is trying to catch you. The monster cannot swim, so it can only run around the edge of the pool. You know that you can run faster than it while on the ground, so if you can manage to reach any point on the edge of the pool before the monster can get there then you will escape. However, the monster runs four times faster than you can swim. Is it possible for you to escape from the pool and the monster?
In order to clarify the riddle, suppose that the monster instead ran three times faster than you could swim. Then the obvious thing to do would be to swim in a straight line to the edge of the pool directly opposite from the monster’s starting point. To reach this point, the monster would have to travel π times as far as you (i.e., a distance of πr versus r). Since π > 3, you would thus be safe.
However, since the monster runs four times as fast as you, the simple strategy above will result in you getting eaten. Can you think of a more complicated strategy that does work in this case?
If that’s too easy, then can you escape if the monster runs five times faster than you? What is the maximum speed (e.g., five times, six times) that the monster can run such that you can still escape?