Hare's Breadth Escape
On the 30th anniversary of the attack, here's something pretty cool--Jimmy Carter's Killer Rabbit Puzzle.
Suppose, the day after attacking President Carter, the rabbit finds itself alone in the middle of the pond, which is perfectly circular. Suppose there is a single Secret Service agent on the edge of the pond, armed with a small net to ensnare the swimming rabbit as it approaches the edge. This net is effective only if the rabbit is still in the water. If the rabbit reaches any point on the edge before the agent does, it can hop away to freedom; if the agent gets there first, the rabbit will be captured.
If the agent runs four times as fast as the rabbit swims, can the rabbit escape? If so, how?
I assume some reader will supply the answer. If not, I'll eventually let it out.
PS For the solution, check out this post.
posted by LAGuy @ 12:16 AM
6 Comments:
I'll try (knowing I'll be wrong).
Make for the shore directly opposite the agent. If the rabbit goes straight however he will be caught. The Agent needs to cover 3.14x more distance but is 4X times faster.
My guess, without doing any further math (because I forget how) is that once the agent has committed himself to how he is running around the pond (I'm assuming the rabbit is able to look over his shoulder without losing speed) and the rabbit has reached half way, the rabbit should veer off at a 45 degree angle (Away from the way the agent is coming) to the shore. I picked 45 degrees randomly on the theory that its a rabbit after all and any more complicated maneuvers would be beyond it.
Good pi.
The rabbit and the agent are both perfectly efficient and perfectly rational. Thus the agent won't "commit" himself to any path that is less than the best available.
I'm afraid math is required to solve this problem (though not particularly hard math). And please show your work.
By "commit" I meant "actually took" but no matter.
-Distance from rabbit to shore= r
-Distance Agent must travel to reach exactly opposite point opposite on pond = r* pi (I'll use 3.14) or 3.14 r (circumference is pi * diameter )
Speed of rabbit= x
Speed of Agent= 4x
Assume r = 100 feet
Assume x= 1 foot per second
If Rabbit makes for the opposite shore from the rabbit, he will do it in 100 seconds but agent running around the edge of the pond will be there in 78.5 seconds (314 feet divided by 4 feet per second).
Therefore when Rabbit is half way to shore (50 feet, 50 seconds elapsed) Agent will be 200 feet along the circumference or 114 feet short of the destination (he will have to pick the right or the left way around, that's what I meant by 'commit'). Rabbit should execute a 45 degree adjustment in his swimming at this point away from the direction the agent is coming. At this point I needs sine and cosine to figure out the sides of triangle and what point on the shore the Rabbit will land and I have forgotten how to use them and my CVS calculator doesn't have a button.
My code word is "invivagg" Fitting.
NE Guy
But I'm guessing you wouldn't have posted a puzzle which requires application of formulas from high school calc, so clearly I'm on the wrong track and resign (maybe tomorrow I'll post the one about frictionless ice)
I believe you're wrong. I need to see the math in any case--without it you're just guessing.
You're also making the math more complicated than it needs to be. (And why pick such big numbers? Make the radius 1 unit of length.)
Actually, the problem does requite high school math. But you already know that circumference=2(pi)r so you're fine.
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