Classic Cat Caper: Newsletter Challenge (June 2020)

One cat...

Supposed the same efficiency for the three cats, then one cat.

Supposed different efficiency for every cat; maybe some of them are really bad hunters, then at least four cats.

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

3 cats catch 3 rats in 3 minutes

3 cats catch 99 rats in 99 minutes

You need another cat because each cat needs 3 minutes per rat.

So the answer is 4.

I think it is 3 minutes per rat per cat...that would only be 99 rats in 100 min...therefore you would need 4 cats to meet the goal...even though the 4th cat would only have to catch 1 rat in the 100 minutes...

Ok ok, I'll go quietly, don't shoot...

I was having this awful dream...

Sounds like someone has a rat problem.

If each cat took one minutes to catch a rat, then three cats would take three minutes, So, if there are 100 rats and 100 minutes, then each cat, taking one minute to catch a rat, would result in 100 cats catching 100 rats in 100 minutes. the 100 minutes being a collective time estimate, not a fixed time period?

That's crazy eyed cat lady reasoning....

Better next time?

One, Two, Many, Eat, Snooze (feline logic)

It takes at least thirty-four(34) cats to catch 100 rats in 100 minutes. Cats can count up to two. Once a cat has caught three rats, its conclusion is that it has caught "many" rats so it starts playing with rat DB trophies and eating the rats it has caught. After eating three rats, a cat will develop an intense postprandial torpor which will result in "mostly sleeping" for three days. During those three days no additional rats will be targeted. Since three days is greater than 100 minutes, a cat which has caught three rats is "spent" and cannot be expected to catch any more rats within the allotted time.

So, the calculation is ceil(100/3)=ceil(33 and 1/3)= 34

Before being too judgemental regarding feline counting skills, realize that early humans had a similar mathematical insufficiency but in most human populations "many" was seven. Once hunter-gatherer humans developed symbolic representation of one finger per one object, "many" became ten. Wow, match that you stupid cats. One, two, three, four, five, six, seven, eight, nine, many prunes, eat the prunes, snooze. Uh oh!

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thewildotter

Never give a job to a cat, that a dog can do better....

1

To avoid meddling with roundups, lets talk with integers only: Three cat will catch 99 mice in 99 days. After that, there will be one rat left to be caught in one day. Say we wake up the morning of that day, fully unaware that the 3 cats already cought those 99 rats in the previous 99 days. What makes us belive that the same three cats cannot catch that last rat within that day? Does anything change in the cats capability to catch rats? If not then "three" IS the answer.

Unless there is some probabilistic twist in the problem: What is the probability that the 3 cats will catch the remaining rat in one day? Or to generalize, what is the probability of 3 cats of the given rat-catching capability, to catch 100 rats in 100 days? And is it meant to be EXACTLY 100 days (in which the probability is EXACTLY zero)? Is it AT MOST 100 days? I doubt the problem is intended to be probabilistic, though, because there could be no definite answer.

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

My three day cat torpor period must have distracted you from the units specified in the original post. ROTFL I still stand by my answer. Specifically, I stand by the sleepy(and short attention span) cats result I reached after a lifetime of futile cat-"roundups"(herding cats is frustrating work and it annoys the cats) and missing some cat or other for days because they were just off hidden somewhere sawing Z's.

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thewildotter

Far be it from me to presume that I might contribute to the discussion of “gurus”. However, I do know that cats sleep 80% of the time. From the given information, the average time for one cat to catch one rat is 3 minutes. In 100 minutes, it would be expected that a cat will sleep 80 minutes; this leaves only 20 minutes for hunting rats. In 20 minutes, based on the given information, and assuming it is a consistent average, one cat will catch only 6 rats in 100 minutes. In order to catch 100 rats, it will then take 17 cats.

In my view there are two approaches (at least):

1. Math approach - 3 cats catch 3 rats in 3 minutes, so 1 cat catches 1 rat in 3 minute. The 3 minutes period cannot be divided, it represent the average time of a hunting session of a cat to catch a rat. Having 100 rats we need 100 hunting sessions. This can happen having 100 cats performing 1 hunting session each, so that after just 3 minutes all rats are caught, or by minimum 4 cats performing 25 hunting session each for a total time of 75 minutes (note: 3 cats are not sufficient because they would complete only 99 hunting sessions in 100 minutes).

2. Nature approach - after a cat has caught a rat, it will spend the rest of time to play with that rat, finally to eat it, then satisfied to relax a bit and maybe sleep. So most probably 100 cats will be necessary to catch 100 rats in 100 minutes.

In summary, the nature approach result (100 cats) is not in contrast with the math approach result (4 to 100 cats) and even the challenge is not strictly asking for the minimum number of cats (just "how many cats"), so I think 100 cats could be the right answer.

OK, if you assumed that 3 cats collectively caught 3 rats in 3 minutes, then 3 rats / 3 minutes / 3 cats = 0.33 rats per minute per cat. The task is 100 rats / 100 minutes = 1 rat per minute. That would lead to an answer of 1/0.33 = 3 cats. But that is not supposed to be the answer. However if the question really means "how many individual cats would catch 100 rats in 100 minutes", then assuming that all cats had identical success rates, the answer would be no cats be able to do that. To go further, if the question meant that each of 3 cats caught 3 rats in 3 minutes, meaning 1 rat per minute, then assuming that all cats had identical success rates, the answer is that all cats would be able to catch 100 rats in 100 minutes, unless you introduce other factors like fatigue.

Answer for this question is now posted.

Not a trick question. You can't have fractions of cats. The real question is what is meant by the words used. "In 100 minutes"? Balancing theory with real-world practicality, you have to read between the lines. Then, the question becomes, "How many (minimum#) cats would catch 100 rats (with)in 100 minutes?

Only one

Del The Cat