[sci.math] hunters

mrh@cybvax0.UUCP (Mike Huybensz) (11/03/86)

In article <4416@reed.UUCP> trost@reed.UUCP (Bill Trost) writes:
> I have a problem that is somewhat similar to this problem.  Imagine quantity
> of hunters on a "very large" section of a plane (very large => boundary
> cases are neglibible).  Now, each hunter shoots his nearest neighbor.
> Question:  How many hunters remain living?

It depends on the arrangement of the hunters.  An arbitrarily small fraction
of the hunters would survive if they were arranged in chains with increasing
distances between each hunter and the next in the chain.  Then the first
hunter would shoot the second, and the N=+1th hunter would shoot the Nth,
leaving only one hunter alive.
					   23
If the hunters are arranged like this:    1ab4
					   65
where 1-6 lie on the vertices of a regular hexagon, and a+b are closer than
2+3, then only a+b will be killed, each with four bullets, for a ration of
3/4 survivors.

There may be arrangements resembling fractal dusts which would allow these
sorts of ratios to persist or cycle through indefinite numbers of fratricidal
episodes.
-- 

Mike Huybensz		...decvax!genrad!mit-eddie!cybvax0!mrh