> > > "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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> > So assuming that three cats need to team up to kill three rats in three minutes, a hundred cats attacking a hundred rats should be *quicker* than three minutes.
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> Quicker? I would think it would take longer than three minutes done that way... it seems to me that, since the rats won't just be lined up waiting for the kill, the time spent chasing down one hundred rats each individually (and one after the other) would take much more than three minutes all by itself. In this case, if each cat hunted his own rat, and they all did it seperately, then they could all catch and kill their rats in a reasonably short amount of time. A hundred cats all teaming up on each individual rat, however, would probably take longer just because of the sheer number of rats and the time it will take to catch them all.
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> Of course, a hundred cats per rat is wasteful, anyway - they won't all have a useful function. So what we really have to do is optimise the cat/rat ratio - figure out how many cats per rat is the most efficient use. To do this, just keep adding another cat and refiguring the time it takes the mass of cats to kill the rat until you reach the point of diminishing returns - that will give you your most efficient cat usage (offhand, I don't think the number will be significantly higher than two, but I don't raeally know). Then compare the amount of time it takes however many groups of that many cats you can take out of the hundred to kill a hundred rats, and compare that to all of them doing it individually.
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> Dar "The cat/rat ratio man" ien


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.

That's fine.

We have to know how the cat is killing the rat. I saw a cat kill a rat once, and I'll go on the assumption that (when the cats aren't toying with the rat) they all kill it that way, which is to bite it's neck, severing the spinal cord.

With that aside, the idea of all the cats killing one rat at a time breaks down with numbers over 8. 8 cats is the largest number of cats that can be attacking the rat at the same time. Add another cat, and in order for the cat to get to the rat, he'll have to nudge another cat out of the way. Now we could say that the cats will form a large circle around the rat consisting of 30 cats or so, then tighten the circle by subtracting cats, but these are cats we're talking about. .they're not THAT smart.

Assuming 8 cats are sitting around the rat getting ready to kill it, we still have only one cat that can deliver the fatal bite because all 8 cats can't bite the same place at the same time. This means the other 7 cats are useless and don't need to be there. You could make the argument that at least one more cat needs to be there to hold the rat down so the first cat can bite it, but if the first cat can't hold his own rat down and bite it at the same time, he's a pretty wimpy cat.

That establishes the clear fact that only one cat is needed to kill each rat. Therefore, if the cats and rats are the same in number, and the cats go along with our assumptions listed above and with the assumption that one cat won't see the rat another cat is catching, and want to catch that rat more than the rat he's currently chasing (and in real life, all cats want what the other cat has more than what they have) then we know that, by the original question, each cat takes 3 minutes to kill it's rat. Therefore the answer is truly 3 minutes, and there is plenty of information in the original question assuming the reader has been indoctrinated with the concept of conveniently forgetting basic laws of nature. Any physics course should supply this indoctrination in abundance.