If three cats catch three rats in three minutes, how many cats will catch 100 rats in 100 minutes?

I will present to you the standard answer to this, which I am sure most of you have come across countless times.

After that, I’d like to offer you an alternate perspective regarding this puzzle.

Once again, this is a good moment to pause the article and give the problem a go yourself. When you’re ready, keep reading for the solution. And if you come up with your own approach, feel free to share it in the comments — I’d love to see how you tackled it.

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Solution

The usual answer to this old riddle is as follows.

If it takes three cats three minutes to catch three rats, then it must take them one minute each to catch one rat.

And if it takes them a minute for each rat, then the same three cats would catch 100 rats in 100 minutes.

Unfortunately, it is not quite that simple because such an answer presupposes something that is certainly not stated in the problem.

It assumes that all three cats concentrate their attention on the same rat until they catch him in one minute, then turn their combined attention towards another cat.

But suppose that instead of doing this, each cat chases a different rat and takes three minutes to catch it.

In this case, three cats would still catch three rats in three minutes. It would take them six minutes to catch six rats, and 99 minutes to catch 99 rats.

A curious difficulty is upon us.

How long will it take those same cats to catch the 100th rat?

If it still takes them the full three minutes to run him down, then it will take three cats 102 minutes to catch 100 rats.

To catch 100 rats in 100 minutes – assuming this is how the cats go about their rat catching – we will certainly need more than three cats and less than four cats.

Of course, it is possible that when the three cats gang up on a single rat, they can corner him in less than three minutes, but there is nothing in the statement of the riddle that tells us exactly how to measure the time for this operation.

The only correct answer to this problem, therefore, is this: The question is ambiguous and cannot be answered with more information about how those cats catch rats.

And that’s our answer. How amazing. Hey, don’t forget to clap👏 the article as a token of appreciation. Thank you 🦁