Clue to puzzle question #13: Circular Field, Hungry Dog

13. You are standing at the centre of a circular field of radius R. The field has a low wire fence around it. Attached to the wire fence (and restricted to running around the perimeter) is a large, sharp-fanged, hungry dog. You can run at speed v, while the dog can run four times as fast. What is your running strategy to escape the field?

I have to say this is one of my favourite puzzles, the answer just works so well.

The obvious answer of standing in the middle and running away from the dog simply doesn't work, this is easily provable.

I think at this point a lot of people think well it must be impossible we can't get any further away than R. But think what would happen if we ran in a very tight circle around the center....

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