> > > > "If 3 cats can kill 3 rats in 3 minutes, how long will it take 100 cats to kill 100 rats?"
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> > ...
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> we're assuming several things here (no, not massless volumeless cats ;) such as all the cats are equally fast, and all the rats are equally bad at getting away from the cat.

Well, yes. Those assumptions do have to be made in order to generate any meaningful data at all. A random factor can be added, but when one considers the randomness of the random factor, it becomes clear that an equally exact answer can be generated by leaving it out. :-}

> With that aside, the idea of all the cats killing one rat at a time breaks down with numbers over 8.

I understand what you're talking about, but how did you come up with eight?

> That establishes the clear fact that only one cat is needed to kill each rat.

Correct - only one cat is *needed* to kill each rat, but we knew that from the beginning. The question was, would multiple cats per rat be more efficient than a 1:1 ratio? As you said, it is a pretty wimpy cat that can't hold down a rat while it kills it, but if it makles the process faster for another cat or two to hold the rat down while the first kills it, then it might be more efficient that way.

The trouble is, if we assign two cats per rat, then they may be able to kill the rat faster. Assume for the moment that they can. However, that means that only half the rats are killed in that amount of time (equal numbers of cats and rats, two cats attacking each rat, half the rats go free). If the amount of time saved by adding an additional cat to the killing process is greater than the amount of time it takes to kill the rat with two cats, then it is more efficient that way than with one cat per rat.

Of course, this is all assuming that the cats don't fight over the kill. :-}

Dar "How on Earth did we get into this, anyway?" ien