If 3 cats eat 3 mice in 3 minutes; how many cats for 100 mice in 100 minutes?

[Horror Business]

i know this seems simple, and perhaps it's a trick, but I'm confused! is the answer 100?

 

[Math Is Hard]

well, let's see, it seems it takes each cat three minutes to eat a mouse...

must be a trick, my cat can't finish a mouse in less than 5 minutes...

 

[Gokul43201]

i know this seems simple, and perhaps it's a trick, but I'm confused! is the answer 100?

No it's not. The cats are all eating at the same time, aren't they ? Just picture a row of cats eating mice. They all start at the same time, and finish at the same time. How much time has elapsed ?

 

[Physics_wiz]

i know this seems simple, and perhaps it's a trick, but I'm confused! is the answer 100?

3 minutes.

 

[tribdog]

how many mice can one cat eat in 100 minutes? 1 cat eats 100/3 mice. 100mice/(100/3micepercat)=3cats

 

[Moonbear]

how many mice can one cat eat in 100 minutes? 1 cat eats 100/3 mice. 100mice/(100/3micepercat)=3cats

Well, that depends on if it still counts if a cat vomits up previous mice and continues eating, or if you have to factor in cat stomach volume, or how much time is lost to vomiting up previously eaten mice.

 

[tribdog]

I didn't think of the cat vomiting.
I know I could eat you all day and have no problem whatsoever.

 

[Moonbear]

I didn't think of the cat vomiting.

I doubt the author of the original question considered it either. It's a good proof of how out of touch mathematicians are with reality. They think just because 3 cats can eat 3 mice in 3 minutes, those same cats can just keep eating at the same rate and finish off 100 mice in 100 minutes. But, that's 33 1/3 mice per cat in 100 minutes, so it raises a lot of problems in reality. 33 1/3 mice is a lot of mice for a cat. You'll definitely be finding lots of vomited mouse bits on the carpet if the cat tries to eat that many mice. And, how do they work out that 1/3 mouse each? If they are fighting over the last mouse, it might take a long longer to eat that one. Plus, once the cat is full, they probably won't be very fast at chasing mice, they will go take a nap for a hour or so, during which time the mice could be running across their tails and they still wouldn't get up and chase them. And even if they kept eating (more typical of a dog than a cat though), they'd get slower and slower as they got fuller, playing with their food more before eating it. You need to factor in the changing rate of eating with fullness. See, this is an amazingly complex problem in reality, but I'm sure some math teaching writing the question wasn't aware of that

(This is why I used to score really horribly on multiple choice exams. )

 

[vikasj007]

i think the problem was more focussed on finding out whether a person can spot the mathematical answer for it, and not if it is applicable in real life or not.

anycase, if u try to apply it in reality, then u will have to specify,
the cat,
the exact volume of its stomach,
the no. of days for which it was starving to prepare for such an event,
the amount of body fat stored in the cat,
general inclinatio0n of the cat towards eating, and mice particularly.
apart from that, the general conditions of temprature, humidity, and other factors, which will play a role in the cat getting tired while eating, and thus affecting its speed.

and a very important thing which mised out, is the mice, u will have to specify the mice which are being eaten by the cats, the smaller the mice, the faster and more in no. can be eaten by the cats.

after considering all this, i came up with an equation, but it was way too complicated for me to understand, forget about explaining it to you all.
[ just kidding :) ]


but still i think that it possible for three extremely large cats,( maybe, lions) to eat 33 1/3 mice without vomiting.

so, it was not such an unrealistic problem after all.

 

[Moonbear]

but still i think that it possible for three extremely large cats,( maybe, lions) to eat 33 1/3 mice without vomiting.

so, it was not such an unrealistic problem after all.

Ah, you've beat me at my own game...but of course, cat is a very generic term and I was foolishly assuming a house cat. 33 1/3 mice in 100 minutes would be no problem at all for a large cat like a lion or tiger, at least assuming they aren't ob/ob mice (those are the ones with a genetic mutation that allows them to get VERY fat).

 

[Dual Op Amp]

The question is How many cats?

 

[theCandyman]

Highlight:
It takes a cat three minutes to eat one mouse, 100 mice is equivlent to 300 minutes. So, we must divide 300 by a number to get 100 minutes, that number is three. Three cats.

 

[vikasj007]

well, if you are trying to solve this problem in purely mathematical terms, then the answer is simply 3 cats.

although i don't think that this problem can be easily applied to real life situations as they would involve far too many parameters.

 

[z4955]

33.333... cats

 

[RandallB]

Four or more Cats
3 cats would eat 99 mice in 99 minutes.
Only one cat would be able to get the the last one and would not be able to eat it within the remaining one minute.

So it would take 4 or more cats to eat 100 mice "in" (within) 100 minutes.

RB

 

[NeutronStar]

Based on the data it appears that it takes a single cat 3 minutes to eat a mouse

At that rate a single cat could eat 33.333… mice in 100 minutes

So 3 cats could eat 3 times as much as one cat or 100 mice in 100 minutes.

So I don't see why the answer wouldn't be just 3 cats.

This assumes they can eat continuously at that rate and share at least one mouse as a meal. It also assumes that the don't spend any time hunting for, or playing with, their food. Very unrealistic.

The brain teaser is from the way the question is worded. If it takes 3 cats 3 minutes to eat 3 mice, the first instinct is to say that it will take 100 cats 100 minutes to eat 100 mice. This brain teaser is probably meant to be told in a bar as a joke around drunkards.

 

[shmoe]

Hmm, I have 3 cats handy. Does anyone have 100 mice I can 'borrow'? My cats are rather incompetent mousers though, I may have to tie up the mice (blindfold them as well for humane reasons).

 

[Rogerio]

Four or more Cats
3 cats would eat 99 mice in 99 minutes.
Only one cat would be able to get the the last one and would not be able to eat it within the remaining one minute.

So it would take 4 or more cats to eat 100 mice "in" (within) 100 minutes.

RB

Well, after 99 mice, the cats won't be so hungry, and will peacefully share the last one.
So, its going to take only 3 cats to do the job :-)

 

[Gokul43201]

And it helps if the last mouse is already cut into thirds.

 

[RandallB]

Well, after 99 mice, the cats won't be so hungry, and will peacefully share the last one.
So, its going to take only 3 cats to do the job :-)

Well I figure it will take 3 cats about 5 minutes just to agree to share and even more time to agree on making a fair split. So the best chance is if the big cat get the last mouse. And after 33 mice they will all be large kittys. And even with there best chance it will still take 102 minutes to do the job.
So with a 100 minute dead line I'd need 4 cats.

But I agree using 4 cats to do the job in 75 minutes - that would be "within" 100 minutes - but not really "IN" 100 minutes. ... What to DO to solve??

---- Let's review ---
In our special or general relativity view of the problem 3 cats would do.
BUT down on the quantum level where Cats only come in whole cats
And mice are eaten only in whole mice.
We only see a statistical probability of how many Mice are eaten at a given defined time. Or a statistical probability of the time when exactly 100 mice will be eaten.

So far sending cats around a Cat Accelerator into a Cat Collider has not generated any ¾ Cat or 1/4 Cat sized elements. And even if it did - they probable would not BE cats and may not be able to eat mice.

Just a part of the problem and conflict between GR and Quantum Theory.

There is only one thing to do - we need we need higher level math here.
Any body know some people on String Theory (String preferred over M).
They may be able to help us towards a unified theory and solution.!

Ya Think.

RB

 

[phreak]

This probably isn't correct, but it's worth a shot:

I simple solved this equation:

3/3/3 = x/100/100

.333 = x/10000

And I simple got 3334 (it would, of course, round up) ^_^

 

[RandallB]

And I simple got 3334

I missed your units there - is that in Cat Strings or Cat Tails?
Are you using String theory -- Or M Theory

 

[Gokul43201]

Or are those Schrodinger's cats ?

 

[Ba]

Or are those Schrodinger's cats ?

I hope alive they don't eat so well when they're dead.

 

[kennive]

easy. 3 minutes

 

[Jimmy Snyder]

If a chicken and a half can lay an egg and a half in a day and a half, then how long will it take a cockroach to kick all of the seeds out of a cucumber?

 

[mgb_phys]

Are you using String theory

String theory doesn't really work with cats - they just run around in circles playing with any bits of string they find, a complete waste of time without producing any productive result.

On second thoughts ...

 

[Office_Shredder]

All your highfalutin math is nice, but it's obvious nonna you've been in the field. You give me two cats, a half pound o' catnip, a blender, a vacuum with a reverse setting and a six foot to a side cube, and those cats'll polish off the mice in a half hour tops.

 

[mgb_phys]

but it's obvious nonna you've been in the field. You give me two cats, a half pound o' catnip, a blender, a vacuum with a reverse setting and a six foot to a side cube, and those cats'll polish off the mice in a half hour tops.

You're thinking of rabbits

 

[mjysci]

According to the question,we can infer that 3 cats eat 1 mice in 1 minutes

so,3 cats eat 100 mice in 100 minutes

the answer is 3 cats.

 

[ikos9lives]

It would depend on if the 3 cats each 3 mice total in 3 minutes, or eat 3 mice each in 3 minutes.

1 mice per minute: 100 mice in 100 minutes.-3 cats

3 mice per minute: 100 mice in 33.3 minutes-1 cat.

 

[The legend]

who cares about how many... just open a pet shop!

 

[M Grandin]

3 cats 3 mice 3 min --- ? cats 100 mice 100 min

The task may also be solved in two independent steps:

1) To increase 3 mice to 100, the number of cats multiplied by 100/3 :

3 x (100/3) cats 100 mice 3 min

2) To increase 3 min to 100 the number of cats multiplied by 3/100 :

3 x (100/3) x (3/100) = 3 cats 100 mice 100 min

 

[notsosmartman]

im guessing it takes 1 cat to eat 1 mouse in 1 minute... give the same 3 cats 100 minutes they will eat 100 mice ?

 

[I like Serena]

You're all reading the question wrong.
3 cats eat 3 mice in 3 minutes, so each cat eats 1 mouse in 1 minute.
The answer is that 1 cat eats 100 mice in 100 minutes.
This must be the proper answer, because the other interpretation leaves us with a 1/3 mouse that gives ambiguity in the answer and a solution should not be ambiguous.

 

[dextercioby]

They're supposed to eat at the same time. :D

 

[JaredJames]

You're all reading the question wrong.
3 cats eat 3 mice in 3 minutes, so each cat eats 1 mouse in 1 minute.
The answer is that 1 cat eats 100 mice in 100 minutes.
This must be the proper answer, because the other interpretation leaves us with a 1/3 mouse that gives ambiguity in the answer and a solution should not be ambiguous.

No, if three cats take three minutes to eat three mice that means it takes each cat three minutes to eat one mouse.

So it can't be 100 mice in 100 minutes.

 

[I like Serena]

They're supposed to eat at the same time. :D

I thought each cat had 3 mice to eat, making a total of 9 mice.
The wording of the question does not seem to prohibit that.
That is: 3 cats eat 3 mice (each) in 3 minutes.

 

[JaredJames]

I thought each cat had 3 mice to eat, making a total of 9 mice.
The wording of the question does not seem to prohibit that.
That is: 3 cats eat 3 mice (each) in 3 minutes.

No, if it meant each it would have said each. That completely changes the question.

 

[Dale]

So it is 3 cat-minutes per mouse, which means 300 cat-minutes for 100 mice. To accomplish 300 cat-minutes of work in 100 minutes requires 3 cats working in principle. However, this is not taking into account the overhead required for team meetings, paperwork, and management, so you need a manager, an extra worker, and a secretary cat for a total of 6 cats. Of course, while one of these expert cats may eat one mouse in 3 minutes for very little reward eating 2 mice in 6 minutes requires more incentives and 3 mice in 9 minutes even more. What is more is that the incentives become much more expensive as the number of mice in a single shift increases. The company had to hire a financial cat to determine the best allocation of resources, and he determined that after 4 mice the incentives become too expensive, so about 25 cats are needed. Now, in principle 25 cats could accomplish the job in about 12 minutes, leaving each cat 88 minutes to spare. So the original manager cat was promoted to upper management decided to recruit "working managers" from within the pool of worker cats and have the worker cats take on most of the additional paperwork requirements that such a large workforce generates. So the final tally is 28 cats.

 

[JaredJames]

So it is 3 cat-minutes per mouse, which means 300 cat-minutes for 100 mice. To accomplish 300 cat-minutes of work in 100 minutes requires 3 cats working in principle. However, this is not taking into account the overhead required for team meetings, paperwork, and management, so you need a manager, an extra worker, and a secretary cat for a total of 6 cats. Of course, while one of these expert cats may eat one mouse in 3 minutes for very little reward eating 2 mice in 6 minutes requires more incentives and 3 mice in 9 minutes even more. What is more is that the incentives become much more expensive as the number of mice in a single shift increases. The company had to hire a financial cat to determine the best allocation of resources, and he determined that after 4 mice the incentives become too expensive, so about 25 cats are needed. Now, in principle 25 cats could accomplish the job in about 12 minutes, leaving each cat 88 minutes to spare. So the original manager cat was promoted to upper management decided to recruit "working managers" from within the pool of worker cats and have the worker cats take on most of the additional paperwork requirements that such a large workforce generates. So the final tally is 28 cats.

If these are British cats then with an expansion of such magnitude you'd be looking at having at least one health and safety executive on top of that. Wouldn't want to get sued for violating safe working practices now would you.

 

[Dale]

If these are British cats then with an expansion of such magnitude you'd be looking at having at least one HSE executive on top of that. Wouldn't want to get sued for violating safe working practices now would you.

Good point, I figured that cats wouldn't have a union, being cats, but I didn't consider lobbies and regulations.

 

[dextercioby]

So it is 3 cat-minutes per mouse, which means 300 cat-minutes for 100 mice. To accomplish 300 cat-minutes of work in 100 minutes requires 3 cats working in principle. However, this is not taking into account the overhead required for team meetings, paperwork, and management, so you need a manager, an extra worker, and a secretary cat for a total of 6 cats. Of course, while one of these expert cats may eat one mouse in 3 minutes for very little reward eating 2 mice in 6 minutes requires more incentives and 3 mice in 9 minutes even more. What is more is that the incentives become much more expensive as the number of mice in a single shift increases. The company had to hire a financial cat to determine the best allocation of resources, and he determined that after 4 mice the incentives become too expensive, so about 25 cats are needed. Now, in principle 25 cats could accomplish the job in about 12 minutes, leaving each cat 88 minutes to spare. So the original manager cat was promoted to upper management decided to recruit "working managers" from within the pool of worker cats and have the worker cats take on most of the additional paperwork requirements that such a large workforce generates. So the final tally is 28 cats.

I like this, 3 normal cats in the hypothesis vs 28 corporate cats )) I will add it to my FB profile, if you don't mind.

 

[I like Serena]

No, if it meant each it would have said each. That completely changes the question.

How do you know?

If the question had been stated properly, it would read either:
A. 3 cats eat a total of 3 mice in 3 minutes, ...
B. 3 cats eat 3 mice each in 3 minutes, ...

As it is, I believe the semantics allow for either interpretation.

 

[BobG]

So it is 3 cat-minutes per mouse, which means 300 cat-minutes for 100 mice. To accomplish 300 cat-minutes of work in 100 minutes requires 3 cats working in principle. However, this is not taking into account the overhead required for team meetings, paperwork, and management, so you need a manager, an extra worker, and a secretary cat for a total of 6 cats. Of course, while one of these expert cats may eat one mouse in 3 minutes for very little reward eating 2 mice in 6 minutes requires more incentives and 3 mice in 9 minutes even more. What is more is that the incentives become much more expensive as the number of mice in a single shift increases. The company had to hire a financial cat to determine the best allocation of resources, and he determined that after 4 mice the incentives become too expensive, so about 25 cats are needed. Now, in principle 25 cats could accomplish the job in about 12 minutes, leaving each cat 88 minutes to spare. So the original manager cat was promoted to upper management decided to recruit "working managers" from within the pool of worker cats and have the worker cats take on most of the additional paperwork requirements that such a large workforce generates. So the final tally is 28 cats.

How do you know?

If the question had been stated properly, it would read either:
A. 3 cats eat a total of 3 mice in 3 minutes, ...
B. 3 cats eat 3 mice each in 3 minutes, ...

As it is, I believe the semantics allow for either interpretation.

Better add a team of lawyer cats to interpret the wording the contract. Counting the HSE, I think you're up to 35 cats.

 

[Dale]

Fat cat lawyers. We humans seem to have a surplus.

 

[Physics-Learner]

i know this seems simple, and perhaps it's a trick, but I'm confused! is the answer 100?

boy, you guys can sure drag a thread out. however, i don't think there is room for semantics, if you want to be serious.

and there is no need for sharing of mice. the point is that the rate is the same, so it takes the same number of cats.

the answer, of course, is 3.

the "trick" is that most people will say 100, if they don't give it much thought. 3-3-3 and x-100-100.

it is easy to fill in the x with 100.

 

[ashishsinghal]

the answer is easy. it just depends on the time taken to eat one mouse.

 

[Sybren]

Dimensional analysis has helped me here.
It takes 3 cats 3 minutes to eat 3 mice, so the eating rate is (introducing the useful unit catminute=cat * minute):
3 mice/ 3 cats / 3 minutes = 1/3 mouse cat^-1 minute^-1 = 1/3 mouse per catminute.

100 mice / x cats / 100 minutes = 1/x mouse per catminute

If the eating rate is determined at 1/3 mouse per catminute, then clearly

3 cats will eat 100 mice in 100 minutes!
[/color]

 

[Darken-Sol]

1 unless it belongs to schroedinger, then it may or it may not.