> > "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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> 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.

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.

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.

Dar "The cat/rat ratio man" ien