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