Answer To Puzzle

Since no one solved Jimmy Carter's killer rabbit puzzle, I offer my solution.

The rabbit can escape. How?

Let's recall the situation. The rabbit is at the center of a circular pond, trying to escape capture by a secret service agent. If the rabbit can reach the shore without the agent being there, it can hop away. But the agent covers ground four times faster than the rabbit can swim.

The only formula you need is circumference=2(pi)r.

Let r=1 unit of length, so the circumference of the pond is 2(pi) or approximately 6.28. To get to the farthest side of the pond, the agent must run half the circumference, or pi. If the rabbit makes a direct move for the shore 180 degrees from the agent, it'll swim 1 unit while the agent runs 3.14 units--less than four times the distance so the rabbit will be caught.

Ask yourself how far out can the rabbit swim while staying as far from the agent as possible? Another way to put it, at what point can the rabbit swim in a circle with 1/4 the circumference of the pond (since at that point they can both move in a circle and stay even with each other). The answer is 1/4 the radius. (Plug the number in if you're not sure.)

So the rabbit can spiral outwards from the center to the 1/4 radius point, making sure to always remain at the farthest point possible from the agent. (As long as the rabbit is inside the 1/4 circle, it can swim, effectively, faster than the agent can run.)

So now the rabbit is 1/4 from the center of the pond, and therefore 3/4 from the shore, and a straight line from the rabbit to the agent will go through the center of the pond.

The rabbit now swims directly to the point on shore that's 180 degrees from the agent. The agent has to run 3.14 units. Let's assume, for ease of calculation, that takes 3.14 seconds. The rabbit, going four times slower, has to swim .75 units. Multiply .75 times four and we see the rabbit gets to the shore in 3 seconds, giving it enough time to hop away to safety.