NY Times math problem

How should he know? All he said was "Igor, fetch me a brain". Perhaps Igor could answer your question, however. But first you must decide... do you *really* want to know?

I computed the rabbit's fastest escape for various values of v (the agent's maximal speed), assuming the rabbit's maximal speed is 1 and the pond's shore is the unit circle.

We may assume, without loss of generality, that the agent begins at the point (1,0) running counterclockwise, and that, from the agent's point of view, the rabbit never goes left of the center of the pond. (If the rabbit did so, we could construct an equivalent solution in which he did not.) We may also assume that the agent runs at full speed the entire time (the solutions in which he slows down to stop the rabbit from cutting behind him being of little interest).

The fastest escape for the rabbit involves a circle of diameter 1/v whose top is at the pond's center. When the rabbit runs at full speed counterclockwise on this circle, he keeps the pond's center between him and the agent (until the agent gets to (-1,0)). For any given spot on the pond's edge where the rabbit might try to escape, his fastest route there (without going left of the pond's center from the agent's point of view) is to run along this circle until he can run straight to his exit point without crossing through the circle. (The solution for the maximal value v given by Dave is for the rabbit to run a semicircle, then to continue straight (in the positive x direction).) Using paths of this form for arbitrary v, one can solve numerically for the first escape point that allows the rabbit to reach that point at the same time as the agent (tie goes to the rabbit).

Here are some escape times t_e for various values of v:

I don't get the NY times here. Could you transcribe the problem here? (I'm at s.e.design, but crossposting to all of the above.)

Thanks, Rich

SEE

Thanks! :-) Rich

Sounds like you need to switch to decaffeinated!

..a hookah-smoking caterpillar has given you the call

On Sat, 09 May 2009 12:43:03 -0700, Archimedes' Lever wrote his usual brand of drivel:

Archie:

You can win and achieve the adulatrion you so desperately seek. You simply take off at full speed running in a right handed helix until your speed begins to unwind your DNA and you run through your asshole and turn inside out. THEN, girls will talk to you ... maybe.

adulatrion? What's that?

It's the confusion caused by the extra "r" from another post about Archie's mental prowess where I spelled "hemmorhoid" (referencing a potential cause for his frequent headaches) incorrectly. My sincere apologies to the Mensa crew here. I trust no one has become so upset that their solution to the world's problems is put on hold.

Not at all. We have all the time in the world as we plan to force nearly everybody to do our boring puzzles until they kill themselves. World population will decrease, more natural resources etc. If that does not work, we plan on maintaining our master plan of not procreating (a plan forced on us by our proclivities and demeanor with woman) and thus dooming the gene pool to severe regression to the mean. Darwin will then take over with similar results to plan A.

Easily defeated by a form of the Corbomite Maneuver!