> "If 3 cats can kill 3 rats in 3 minutes, how long will it take 100 cats to kill 100 rats?"
>
> All these years, I have never understood why the answer to that question was "3 minutes."

Lewis Carroll (the "Alice In Wonderland" Lewis Carroll) did a study of this particular problem and found it to provide insufficient information. The assumption can be made that each cat is killing its corresponding rat on its own, in which case Kelly's analysis holds true. Carroll's quibble is that he doesn't think this is a reasonable assumption, due to the way the question is phrased. Wouldn't it be quicker for three cats to kill three rats by teaming up and picking them off one by one? If three cats kill one rat at a time, they can surround it and close in. If they can do that in a minute, they can take care of three in three minutes. But one cat trying to catch on rat on its own might take significantly longer, and the statement of the question doesn't promise us it won't. So three cats attacking three rats independently of each other could take longer than three minutes. 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.

Now doesn't that clear things up for you?