Best Response

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

-MBP

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If the panthers do not know the result of eating the goat, the goat will be eaten exactly once.

That's not the question try again

Assuming you don't run out of grass:
Goat never gets eaten.
#1 goal of Panthers is to survive (can do that just by eating grass).
Becoming a Goat decreases survival chances.

Assuming you do run out of grass:
Grass runs out.
Panther closest to starvation eats goat.
Process continues until you are left with one goat.

illiniPride:

Assuming you don't run out of grass:
Goat never gets eaten.
#1 goal of Panthers is to survive (can do that just by eating grass).
Becoming a Goat decreases survival chances.

Assuming you do run out of grass:
Grass runs out.
Panther closest to starvation eats goat.
Process continues until you are left with one goat.

Sounds good to me

Sometimes lies are more dependable than the truth.

Illini and man bear. I like where your heads at. Any one else with a diff answer or thought process

Because "all panthers are smart and perfectly rational", the goat will not be eaten. Why would a panther want to become a goat?

Alternatively, assuming the panthers are cool with becoming goats and assuming the original goat is pregnant and will give birth to a male goat... the goats will continue to mate (incestuously) and produce offspring until there are exactly 120 goats at which point all of the panthers will, at the same time, devour the goats.

Poff:

Alternatively, assuming the panthers are cool with becoming goats and assuming the original goat is pregnant and will give birth to a male goat... the goats will continue to mate (incestuously) and produce offspring until there are exactly 120 goats at which point all of the panthers will, at the same time, devour the goats.

...lol

Sometimes lies are more dependable than the truth.

It is impossible for the goat population to expand beyond one goat. If the goat is not eaten, he will remain until he dies naturally or runs out of grass. If a panther eats the goat, he becomes the goat leaving the population still at one. And the same process will repeat until the whole population is wiped out for the panthers.

The question is - do they know what happens when you eat the goat?

1) They know -> since they are rational and want to survive, they will eat the grass.
2) They do not know, but all of them see when one kills the sheep -> after eating the first goat, they will realize the consequences and since they want to survive, they will eat the grass only.
3)They do not know, and only one/few see when one kills the sheep -> various cases, ending up with someone eating the grass..

=> will goat get eaten? in 2 of 3 times yes

In all cases they end up eating the grass;
New problem - is there unlimited grass?

1) There is -> problem solved.
2) There isnt -> they will kill the goat and each other until there is enough grass for the rest to survive.

=> will the goat be eaten? in 3 of 4 times yes

yes there's unlimited grass. its a big ass island

Buddyfox:

yes there's unlimited grass. its a big ass island

So magic island = "magic grass?" And then panthers start turning into goats?

Interesting.....

illiniPride:

Assuming you don't run out of grass:
Goat never gets eaten.
#1 goal of Panthers is to survive (can do that just by eating grass).
Becoming a Goat decreases survival chances.

Assuming you do run out of grass:
Grass runs out.
Panther closest to starvation eats goat.
Process continues until you are left with one goat.

This is a tangent to the actual question. In brainteasers, you cannot impose your own assumptions on the scenario in question. In this case, there is no specific constraint on the quantity of grass, so you can't use an assumption about a limited supply in your solution to the problem.

-MBP

manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

This is the correct answer to the problem. All other answers are wrong =)

-MBP

manbearpig:
illiniPride:

Assuming you don't run out of grass:
Goat never gets eaten.
#1 goal of Panthers is to survive (can do that just by eating grass).
Becoming a Goat decreases survival chances.

Assuming you do run out of grass:
Grass runs out.
Panther closest to starvation eats goat.
Process continues until you are left with one goat.

This is a tangent to the actual question. In brainteasers, you cannot impose your own assumptions on the scenario in question. In this case, there is no specific constraint on the quantity of grass, so you can't use an assumption about a limited supply in your solution to the problem.

Its more fun to try and break the question. Besides, a good brainteaser shouldn't be ambiguous IMO.

illiniPride:
manbearpig:
illiniPride:

Assuming you don't run out of grass:
Goat never gets eaten.
#1 goal of Panthers is to survive (can do that just by eating grass).
Becoming a Goat decreases survival chances.

Assuming you do run out of grass:
Grass runs out.
Panther closest to starvation eats goat.
Process continues until you are left with one goat.

This is a tangent to the actual question. In brainteasers, you cannot impose your own assumptions on the scenario in question. In this case, there is no specific constraint on the quantity of grass, so you can't use an assumption about a limited supply in your solution to the problem.

Its more fun to try and break the question. Besides, a good brainteaser shouldn't be ambiguous IMO.

That's true. It should be made explicit that the supply of grass isn't limited. It should even be made specific that all panthers have perfect knowledge of what the other panthers are doing even though it's implied by the 'smart and logical' condition.

-MBP

worst answer ever.. better go edit it and make accounts to give yourself bananas..

manbearpig:
manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

This is the correct answer to the problem. All other answers are wrong =)

Dimethyltryptamine:

worst answer ever.. better go edit it and make accounts to give yourself bananas..

manbearpig:
manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

This is the correct answer to the problem. All other answers are wrong =)

...

No need to edit it. It's the correct answer =)

Your solution on the other hand is way off...

-MBP

I like MBP's answer, but why would a panther ever wanna be a goat? Goats suck. Panthers rock.

I hate victims who respect their executioners

I'm not sure if you are trolling?

Induction?
Assumptions regarding the locations of the panthers?

Idea about odd and even number of panthers is nice, but it drives you around and makes you adapt your story to it; it doesn't have to do much with the question.

I've got one assumption here:
you have probably been doing brainteasers in order to be able to give a smart answer here and there, but it resulted in you trying to push the structure of another brainteaser because this example reminded you of the past one which you have seen.

Trying to learn brainteasers (either for fun or to "increase your chances" on some test) should not cost you creativity or limit you to search for the similar answers which you came across before - it should give you different perspectives to keep in mind.

P.S. I was not discussing what I wrote.. and about that, its nothing new, just the first thing which came to my mind.

manbearpig:
Dimethyltryptamine:

worst answer ever.. better go edit it and make accounts to give yourself bananas..

manbearpig:
manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

This is the correct answer to the problem. All other answers are wrong =)

...

No need to edit it. It's the correct answer =)

Your solution on the other hand is way off...

manbearpig:
illiniPride:
manbearpig:
illiniPride:

Assuming you don't run out of grass:
Goat never gets eaten.
#1 goal of Panthers is to survive (can do that just by eating grass).
Becoming a Goat decreases survival chances.

Assuming you do run out of grass:
Grass runs out.
Panther closest to starvation eats goat.
Process continues until you are left with one goat.

This is a tangent to the actual question. In brainteasers, you cannot impose your own assumptions on the scenario in question. In this case, there is no specific constraint on the quantity of grass, so you can't use an assumption about a limited supply in your solution to the problem.

Its more fun to try and break the question. Besides, a good brainteaser shouldn't be ambiguous IMO.

That's true. It should be made explicit that the supply of grass isn't limited. It should even be made specific that all panthers have perfect knowledge of what the other panthers are doing even though it's implied by the 'smart and logical' condition.

The grass is what immediately stood out to me. Knew I could break the question with that so I didn't bother to think it through further.

Pretty sure you have the 'book' answer though.

Dimethyltryptamine:

I'm not sure if you are trolling?

Induction?
Assumptions regarding the locations of the panthers?

Idea about odd and even number of panthers is nice, but it drives you around and makes you adapt your story to it; it doesn't have to do much with the question.

I've got one assumption here:
you have probably been doing brainteasers in order to be able to give a smart answer here and there, but it resulted in you trying to push the structure of another brainteaser because this example reminded you of the past one which you have seen.

Trying to learn brainteasers (either for fun or to "increase your chances" on some test) should not cost you creativity or limit you to search for the similar answers which you came across before - it should give you different perspectives to keep in mind.

P.S. I was not discussing what I wrote.. and about that, its nothing new, just the first thing which came to my mind.

manbearpig:
Dimethyltryptamine:

worst answer ever.. better go edit it and make accounts to give yourself bananas..

manbearpig:
manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

This is the correct answer to the problem. All other answers are wrong =)

...

No need to edit it. It's the correct answer =)

Your solution on the other hand is way off...

His proof is pretty sound. Basic idea is that only an even # of panthers is stable.

Dimethyltryptamine:

I'm not sure if you are trolling?

Not trolling =)

Dimethyltryptamine:

Induction?

Yeah, its a method of proof whereby you show what happens in a base case, and then its implications on subsequent cases. Look it up and educate yourself =)

Dimethyltryptamine:

Assumptions regarding the locations of the panthers?

Not really introducing any new assumptions. Just inheritance from already known constraints and conditions. There exists a panther that will be able to reach the goat the fastest. Since this panther is perfectly rational, it will exercise it's option to reach the goat the fastest when it is rational to do so. (i.e., when there are an odd number of panthers)

Dimethyltryptamine:

Idea about odd and even number of panthers is nice, but it drives you around and makes you adapt your story to it; it doesn't have to do much with the question.

Actually I solved the problem in generality. And the solution to this question is a specific case of the general solution. Namely 120 panthers is an even number of panthers, which is a special case of my solution.

Dimethyltryptamine:

I've got one assumption here:
you have probably been doing brainteasers in order to be able to give a smart answer here and there, but it resulted in you trying to push the structure of another brainteaser because this example reminded you of the past one which you have seen.

No idea what your point is.

Dimethyltryptamine:

Trying to learn brainteasers (either for fun or to "increase your chances" on some test) should not cost you creativity or limit you to search for the similar answers which you came across before - it should give you different perspectives to keep in mind.

Thanks for the lecture =)

Dimethyltryptamine:

P.S. I was not discussing what I wrote.. and about that, its nothing new, just the first thing which came to my mind.

What you wrote is flat out wrong =)

-MBP

Goat wont be eaten. Fuck you goat.

The question boils down to an odd va even number of panthers. An even number will never eat the goat for fear of being eaten. An odd amount will always result in the goat being eaten.

Some good discussion on the thought process here.

1) ok

3) inheritence? and can't wolves stand at an equal distance from the sheep? circle for example?

5) ponder through those words.. and dont be butthurt, I had good intentions

6) you're welcome

7) coud be

Don't use smileys - or at least dont use them to emphasise words like that, it looks...

manbearpig:
Dimethyltryptamine:

I'm not sure if you are trolling?

Not trolling =)

Dimethyltryptamine:

Induction?

Yeah, its a method of proof whereby you show what happens in a base case, and then its implications on subsequent cases. Look it up and educate yourself =)

Dimethyltryptamine:

Assumptions regarding the locations of the panthers?

Not really introducing any new assumptions. Just inheritance from already known constraints and conditions. There exists a panther that will be able to reach the goat the fastest. Since this panther is perfectly rational, it will exercise it's option to reach the goat the fastest when it is rational to do so. (i.e., when there are an odd number of panthers)

Dimethyltryptamine:

Idea about odd and even number of panthers is nice, but it drives you around and makes you adapt your story to it; it doesn't have to do much with the question.

Actually I solved the problem in generality. And the solution to this question is a specific case of the general solution. Namely 120 panthers is an even number of panthers, which is a special case of my solution.

Dimethyltryptamine:

I've got one assumption here:
you have probably been doing brainteasers in order to be able to give a smart answer here and there, but it resulted in you trying to push the structure of another brainteaser because this example reminded you of the past one which you have seen.

No idea what your point is.

Dimethyltryptamine:

Trying to learn brainteasers (either for fun or to "increase your chances" on some test) should not cost you creativity or limit you to search for the similar answers which you came across before - it should give you different perspectives to keep in mind.

Thanks for the lecture =)

Dimethyltryptamine:

P.S. I was not discussing what I wrote.. and about that, its nothing new, just the first thing which came to my mind.

What you wrote is flat out wrong =)

Dimethyltryptamine:

3) inheritence? and can't wolves stand at an equal distance from the sheep? circle for example?

Sure, but some panthers are faster than others. Some have quicker reflexes. Some have better vision. These assumptions are all inherited from our knowledge of panthers (yes, even magical panthers that turn into goats). This is why you can assume that there exists a panther that will reach the goat the fastest. Distance isn't the only variable.

Dimethyltryptamine:

Don't use smileys - or at least dont use them to emphasise words like that, it looks...

The smileys weren't used to emphasize words. They were used to capture condescension =). How do you function when everything keeps going over your head?

-MBP

manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

ManBearPig~

While I'm normally against verbally felating someone on an online forum... I'll make an exception for you. Between this and that stupid post with that grade school math problem where you were the first to point out the question was ambigious, you have proven yourself to be one smart motherfucker. Though I can bet that a lot of it can be attributed to your background in mathematics.

No homo,
Sayandarula

Money Never Sleeps? More like Money Never SUCKS amirite?!?!?!?

1) Nope, you cant say that about the panthers... as far as i am concerned it is 1 panther * 120..
true, they can be different, but you must also assume that they can be equal, and take care of the both assumptions

2) That happens somethimes - I have a few methods, but what I find most important is not to give up.

manbearpig:
Dimethyltryptamine:

3) inheritence? and can't wolves stand at an equal distance from the sheep? circle for example?

Sure, but some panthers are faster than others. Some have quicker reflexes. Some have better vision. These assumptions are all inherited from our knowledge of panthers (yes, even magical panthers that turn into goats). This is why you can assume that there exists a panther that will reach the goat the fastest. Distance isn't the only variable.

Dimethyltryptamine:

Don't use smileys - or at least dont use them to emphasise words like that, it looks...

The smileys weren't used to emphasize words. They were used to capture condescension =). How do you function when everything keeps going over your head?

Dimethyltryptamine:

worst answer ever.. better go edit it and make accounts to give yourself bananas..

manbearpig:
manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

This is the correct answer to the problem. All other answers are wrong =)

Buddyfox:

The question boils down to an odd va even number of panthers. An even number will never eat the goat for fear of being eaten. An odd amount will always result in the goat being eaten.

Dude, hes fucking right. Get over it.

sayandarula:
manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

ManBearPig~

While I'm normally against verbally felating someone on an online forum... I'll make an exception for you. Between this and that stupid post with that grade school math problem where you were the first to point out the question was ambigious, you have proven yourself to be one smart motherfucker. Though I can bet that a lot of it can be attributed to your background in mathematics.

No homo,
Sayandarula

Haha thanks buddy! Never too late to learn. Let me know if you're interested - I can recommend some excellent books to get you started.

-MBP

illiniPride:
Dimethyltryptamine:

worst answer ever.. better go edit it and make accounts to give yourself bananas..

manbearpig:
manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

This is the correct answer to the problem. All other answers are wrong =)

Buddyfox:

The question boils down to an odd va even number of panthers. An even number will never eat the goat for fear of being eaten. An odd amount will always result in the goat being eaten.

Dude, hes fucking right. Get over it.

Lol thanks dude. Although it is fun to keep messing with this guy.

-MBP

the example itself isn't right..

you may like his answer, but it is not correct

i'm out anyway

illiniPride:
Dimethyltryptamine:

worst answer ever.. better go edit it and make accounts to give yourself bananas..

manbearpig:
manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

This is the correct answer to the problem. All other answers are wrong =)

Buddyfox:

The question boils down to an odd va even number of panthers. An even number will never eat the goat for fear of being eaten. An odd amount will always result in the goat being eaten.

Dude, hes fucking right. Get over it.

#### Financial Modeling Training

IB Templates, M&A, LBO, Valuation.

#### Wall St. Interview Secrets Revealed

30,000+ sold & REAL questions.

#### Resume Help from Finance Pros

Land More Interviews.

Realistic Mock Interviews.

Mondays are miserable enough already: when I see one of these and get sucked into the thread, it just makes life more difficult. Am I the only debbie downer who feels this way?

manbearpig:
sayandarula:
manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

ManBearPig~

While I'm normally against verbally felating someone on an online forum... I'll make an exception for you. Between this and that stupid post with that grade school math problem where you were the first to point out the question was ambigious, you have proven yourself to be one smart motherfucker. Though I can bet that a lot of it can be attributed to your background in mathematics.

No homo,
Sayandarula

Haha thanks buddy! Never too late to learn. Let me know if you're interested - I can recommend some excellent books to get you started.

Touche MBP, touche... what books do you suggest?

manbearpig:

Lol thanks dude. Although it is fun to keep messing with this guy.

Agreed. I find it pretty funny he was defending an argument designed to fuck with the OP.

prospie:
Mondays are miserable enough already: when I see one of these and get sucked into the thread, it just makes life more difficult. Am I the only debbie downer who feels this way?

Music makes things better.

No panther tho :(

HFFBALLfan123:
manbearpig:
sayandarula:
manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

ManBearPig~

While I'm normally against verbally felating someone on an online forum... I'll make an exception for you. Between this and that stupid post with that grade school math problem where you were the first to point out the question was ambigious, you have proven yourself to be one smart motherfucker. Though I can bet that a lot of it can be attributed to your background in mathematics.

No homo,
Sayandarula

Haha thanks buddy! Never too late to learn. Let me know if you're interested - I can recommend some excellent books to get you started.

Touche MBP, touche... what books do you suggest?

Sure thing.

1.a. Don't let the title fool you. This is a rigorous course in Analysis. It assumes that everything you learned about calculus is wrong, and starts from the beginning and does it right. Read this alongside the next one.
http://www.amazon.com/Calculus-4th-Michael-Spivak/...

1.b. An excellent primer to Linear Algebra. It doesn't rely on matrices to develop the theory, and starts with properties of general vector spaces.
http://www.amazon.com/Linear-Algebra-Edition-Steph...

2.a. Once you're comfortable with these (I'd give it 6 months if it's been a while since you've done any math, and assuming you can give it 3-4 hours a week). move onto this book. It is very terse, and so it will test your patience and will power a lot. Some people prefer a book that explains things in much more detail, so look to 2.b. as an alternative, or even as a supplement.
http://www.amazon.com/Calculus-On-Manifolds-Approa...

Give yourself another 6 months for this material, and then you're ready for some really interesting stuff. Start with 3.a.

3.a. Topology! Anyone with an interest in pure mathematics will absolutely love this book. It is absolutely fascinating, and particularly when you get to part 2.
http://www.amazon.com/Topology-2nd-Edition-James-M...

3.b. If you have time, do this alongside Topology, otherwise do it right after. It's considerably more challenging, but definitely worth it.
http://www.amazon.com/Abstract-Algebra-Edition-Dav...

Give yourself a year to get through these books.

Now you're ready for some measure theory.

4. This is a classic. I would skip Rudin or Pugh and go straight to this if you're comfortable with all of the books already mentioned.
http://www.amazon.com/Real-Analysis-Edition-Halsey...

If you can handle a really advanced treatment by this stage, use Folland instead. It is much much more challenging.

Just to round out your tool kit, you should also learn a thing or two about complex analysis, so I recommend the Ahlfors book

Now you have the toolbox you need to be able go into much deeper stuff, depending on what interests you. As someone in finance, probability and stochastic calculus is a natural next point. That's the machinery behind derivatives pricing etc.

Good luck!

-MBP

Idk if this has been said already, but since the Panthers are "are smart and perfectly rational and they want to survive" wouldn't they all do their best to eat all the grass they can before one tries to attempt to eat the goat (which would be a last resort).

After all the grass is consumed, one desperate panther will eat the goat, which will cause the the loss of one panther but the goat number still stays constant at 1. This cycle will continue, and at the end of the day, there will be exactly one panther and one goat on the island. Once the panther eats the goat, there will one goat on the island and it will eventually die of starvation since there will no more grass.

Dimethyltryptamine:

the example itself isn't right..

you may like his answer, but it is not correct

i'm out anyway

Woe is me, the only sane being on these illustrious boards! I shall go to a place where my genius is appreciated, where Panthers are not denied their basic impulses but are allowed to feast on that succulent goat.

illiniPride:
prospie:

Mondays are miserable enough already: when I see one of these and get sucked into the thread, it just makes life more difficult. Am I the only debbie downer who feels this way?

Music makes things better.

No panther tho :(

Hell yah Ratatat! I've seen them live 5 times now. Kick ass band.

BTW, Buddy, you never posted a follow-up answer to the Rubik's Cube question.

My name is Nicky, but you can call me Dre.

I would say 120 panthers remain and the single goat remains. Why?

OP states panthers are smart and rational. If a panther eats the goat, he is not behaving rationally, as even though he prefers to eat goats, it will turn him into one thereby decreasing his chances of survival.

OP says nothing about the panthers cannibalizing each other, thus the only way to ensure survival (albeit not as tasty) is to live off of grass and leave the goat alone.

My name is Nicky, but you can call me Dre.

Panthers are hunters and will never eat grass.
So the strongest panther will eat the goat first.
After the last panther turned to a goat,
it will eat grass forever and die peacefully as an old goat.

aempirei:
illiniPride:
prospie:

Mondays are miserable enough already: when I see one of these and get sucked into the thread, it just makes life more difficult. Am I the only debbie downer who feels this way?

Music makes things better.

No panther tho :(

Hell yah Ratatat! I've seen them live 5 times now. Kick ass band.

BTW, Buddy, you never posted a follow-up answer to the Rubik's Cube question.

My bad - updated. I just figured it was too easy as a lot of people seemed to get the correct answer quickly.

I would like to know why my logic is wrong, there is still one goat left at the end of the feeding frenzy.

MrJetSet:

I would like to know why my logic is wrong, there is still one goat left at the end of the feeding frenzy.

Well I guess I didn't think to define the size of the island. Maybe you'd be right if it was a tiny tiny island with little grass. When you think of an island i figured itd be, at elast, the size of Manhatten, where the goats and 120 panthers wouldnt really have to worry about running out of grass.

GRASS IS A WEED AND GORWS VERY QUICKLY. ESPECIALLY ON MAGIC ISLANDS.

MrJetSet:

I would like to know why my logic is wrong, there is still one goat left at the end of the feeding frenzy.

Your solution is only logical if the panthers aren't. And we have infinite grass yo.

The question is how smart and perfectly rational can a Panther be?
I doubt that a Panther can resist his inner urges even more than humans can.

It has nothing to do with being smart and rational.

manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

I think you are close, but wrong as well
suppose there are an even number of panthers, eg 4
first panther eats the goat, but who will volunteer to eat that panther? knowing that whoever eats the panther will get eaten
panther 1 eats goat
panther 2 eats panther 1
panther 3 eats panther 2
panther 4 eats panther 3
panther 4 wins

but of course, all panthers will want to be panther 4, and no panther wants to be 1 or 2 or 3... so even if the number is even, i believe the panther can eat the goat and get away with it as well

you can try this logic with an odd number of panthers as well, every panther wants to be the last man standing, and it works out to a similar result as the even series

of course, the panther could also decide to not eat the goat

bigun:
manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

I think you are close, but wrong as well
suppose there are an even number of panthers, eg 4
first panther eats the goat, but who will volunteer to eat that panther? knowing that whoever eats the panther will get eaten
panther 1 eats goat
panther 2 eats panther 1
panther 3 eats panther 2
panther 4 eats panther 3
panther 4 wins

but of course, all panthers will want to be panther 4, and no panther wants to be 1 or 2 or 3... so even if the number is even, i believe the panther can eat the goat and get away with it as well

you can try this logic with an odd number of panthers as well, every panther wants to be the last man standing, and it works out to a similar result as the even series

of course, the panther could also decide to not eat the goat

All panthers are perfectly logical and no panthers want to die. Therefore no panther dies (assuming infinite grass).

4 Panther example:

Panther: Damn i want to eat that goat
Other Panther: Ya me too
Panther: You eat it
Other Panther: No way bro, if I do ull eats me instantly!
Panther: No I won't; I'd get eaten
Other Panther: Nah dude. If I eat, then you eat, only two kitties are left! Neither of them will eat you, and you still get goat meat!!!
Panther: You got me foo'. Clever Panther.

illiniPride:
bigun:
manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

I think you are close, but wrong as well
suppose there are an even number of panthers, eg 4
first panther eats the goat, but who will volunteer to eat that panther? knowing that whoever eats the panther will get eaten
panther 1 eats goat
panther 2 eats panther 1
panther 3 eats panther 2
panther 4 eats panther 3
panther 4 wins

but of course, all panthers will want to be panther 4, and no panther wants to be 1 or 2 or 3... so even if the number is even, i believe the panther can eat the goat and get away with it as well

you can try this logic with an odd number of panthers as well, every panther wants to be the last man standing, and it works out to a similar result as the even series

of course, the panther could also decide to not eat the goat

All panthers are perfectly logical and no panthers want to die. Therefore no panther dies (assuming infinite grass).

4 Panther example:

Panther: Damn i want to eat that goat
Other Panther: Ya me too
Panther: You eat it
Other Panther: No way bro, if I do ull eats me instantly!
Panther: No I won't; I'd get eaten
Other Panther: Nah dude. If I eat, then you eat, only two kitties are left! Neither of them will eat you, and you still get goat meat!!!
Panther: You got me foo'. Clever Panther.

lol, couldn't have said it better myself. But yeah, bigun you're wrong. The panthers aren't behaving rationally in your example, so it's violating the condition of the brainteaser.

-MBP

If the Panthers all know that no other Panther will eat the goat, then
why not eat the goat and stay alive as a goat?

manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

Yep, this is the correct answer to this age old brainteaser.

"'In summary, people are morons and who cares. Make a shit ton of money. I've never seen a Ferrari paid for by what people think.' - ANT" -rufiolove

mrbeancounter:

If the Panthers all know that no other Panther will eat the goat, then
why not eat the goat and stay alive as a goat?

Dude, think it through...it's been spelled out pretty explicitly already.

Here is the preference.

Staying alive > eating goat > eating grass

1 panther 1 goat - panther eats goat, since it gets to eat goat, which it prefers to eating grass and still gets to stay alive.

2 panthers 1 goat - neither panther will eat the goat because if it does, it will get eaten right after (i.e. the 1 panther 1 goat case)

3 panthers 1 goat - the panther that can get to the goat the fastest will eat the goat. Because once it becomes a goat, you're back to the 2 panther 1 goat case, in which neither panther will eat the goat.

-MBP

mrbeancounter:

If the Panthers all know that no other Panther will eat the goat, then
why not eat the goat and stay alive as a goat?

5 Panther Example:

Panther: Come here Goat! *nom*
Goat/Panther: Go away. If u eats me, u die! (See the 4 Panther scenario)
Other Panther: But grass is sooo bland....
Goat/Panther: Not to goats.
Other Panther: Asshole

Moral of the story: Panthers don't die, but sometimes they turn into goats.

So the solution is two panthers and one goat.

mrbeancounter:

So the solution is two panthers and one goat.

NO!

I'd also say that with a very high uneven number of panthers,
it is also very likely to be eaten even though according
to manbearpig's logic, you shouldn't be eaten.

mrbeancounter:

I'd also say that with a very high uneven number of panthers,
it is also very likely to be eaten even though according
to manbearpig's logic, you shouldn't be eaten.

Panthers are turning into goats and you are worried about their intelligence?

Think of this like the new planet of the apes movie where they get some brain serum or something. These panthers are fucking smart. That is why they are perfectly logical by definition

manbearpig:
illiniPride:
bigun:
manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

I think you are close, but wrong as well
suppose there are an even number of panthers, eg 4
first panther eats the goat, but who will volunteer to eat that panther? knowing that whoever eats the panther will get eaten
panther 1 eats goat
panther 2 eats panther 1
panther 3 eats panther 2
panther 4 eats panther 3
panther 4 wins

but of course, all panthers will want to be panther 4, and no panther wants to be 1 or 2 or 3... so even if the number is even, i believe the panther can eat the goat and get away with it as well

you can try this logic with an odd number of panthers as well, every panther wants to be the last man standing, and it works out to a similar result as the even series

of course, the panther could also decide to not eat the goat

All panthers are perfectly logical and no panthers want to die. Therefore no panther dies (assuming infinite grass).

4 Panther example:

Panther: Damn i want to eat that goat
Other Panther: Ya me too
Panther: You eat it
Other Panther: No way bro, if I do ull eats me instantly!
Panther: No I won't; I'd get eaten
Other Panther: Nah dude. If I eat, then you eat, only two kitties are left! Neither of them will eat you, and you still get goat meat!!!
Panther: You got me foo'. Clever Panther.

lol, couldn't have said it better myself. But yeah, bigun you're wrong. The panthers aren't behaving rationally in your example, so it's violating the condition of the brainteaser.

well what im trying to say is
if theres is 6 panthers, 1 goat, and i am a panther, i will eat the goat first, and whos going to eat me? knowing that if you eat me there is a chance u will be eaten, unless you are the last panther, there is always a risk of being eaten by another panther

*********edit
nvm, i just thought this thru
you are right, lol,

bigun:
manbearpig:
illiniPride:
bigun:
manbearpig:

Let's do this by induction.

Suppose there is one goat and one panther. The panther will eat the goat.

Suppose there are two panthers and one goat. Neither panther will eat the goat. Because the first panther to eat the goat knows that it will get eaten soon after.

Suppose there are three panthers and one goat. The closest panther to the goat will eat the goat, because he'll know that once he becomes a goat, the two remaining panthers will not eat it.

Then, by continuation, if there are an even number of panthers, the goat will be left alone. If there are an odd number of panthers, the first panther will eat the goat. In this case, the goat will be left alone.

I think you are close, but wrong as well
suppose there are an even number of panthers, eg 4
first panther eats the goat, but who will volunteer to eat that panther? knowing that whoever eats the panther will get eaten
panther 1 eats goat
panther 2 eats panther 1
panther 3 eats panther 2
panther 4 eats panther 3
panther 4 wins

but of course, all panthers will want to be panther 4, and no panther wants to be 1 or 2 or 3... so even if the number is even, i believe the panther can eat the goat and get away with it as well

you can try this logic with an odd number of panthers as well, every panther wants to be the last man standing, and it works out to a similar result as the even series

of course, the panther could also decide to not eat the goat

All panthers are perfectly logical and no panthers want to die. Therefore no panther dies (assuming infinite grass).

4 Panther example:

Panther: Damn i want to eat that goat
Other Panther: Ya me too
Panther: You eat it
Other Panther: No way bro, if I do ull eats me instantly!
Panther: No I won't; I'd get eaten
Other Panther: Nah dude. If I eat, then you eat, only two kitties are left! Neither of them will eat you, and you still get goat meat!!!
Panther: You got me foo'. Clever Panther.

lol, couldn't have said it better myself. But yeah, bigun you're wrong. The panthers aren't behaving rationally in your example, so it's violating the condition of the brainteaser.

well what im trying to say is
if theres is 6 panthers, 1 goat, and i am a panther, i will eat the goat first, and whos going to eat me? knowing that if you eat me there is a chance u will be eaten, unless you are the last panther, there is always a risk of being eaten by another panther

I'm not personifying anymore panthers.

But assuming that the "two panther one goat" situation is valid ad infinitum is kind of irrational don't ya think?

mrbeancounter:

But assuming that the "two panther one goat" situation is valid ad infinitum is kind of irrational don't ya think?

NO!

How is it anything other than perfectly rational?

It is irrational because the ratio of goats to panthers is indefinitely smaller.

mrbeancounter:

the ratio of goats to panthers is indefinitely smaller.

So what? Where is the pattern affected by the ratio or absolute # of panthers? What changes?

illiniPride:
mrbeancounter:

the ratio of goats to panthers is indefinitely smaller.

So what? Where is the pattern affected by the ratio or absolute # of panthers? What changes?

Not saying the pattern is affected but it's kind of stupid to make such a simplifying assumption.

mrbeancounter:
illiniPride:
mrbeancounter:

the ratio of goats to panthers is indefinitely smaller.

So what? Where is the pattern affected by the ratio or absolute # of panthers? What changes?

Not saying the pattern is affected but it's kind of stupid to make such a simplifying assumption.

We are already assuming Panthers can shape-shift into goats. Is perfect rationality any more of a stretch?

illiniPride:
mrbeancounter:
illiniPride:
mrbeancounter:

the ratio of goats to panthers is indefinitely smaller.

So what? Where is the pattern affected by the ratio or absolute # of panthers? What changes?

Not saying the pattern is affected but it's kind of stupid to make such a simplifying assumption.

We are already assuming Panthers can shape-shift into goats. Is perfect rationality any more of a stretch?

What I understand as perfectly rational is different from the situation you are describing.

mrbeancounter:
illiniPride:
mrbeancounter:
illiniPride:
mrbeancounter:
the ratio of goats to panthers is indefinitely smaller.

So what? Where is the pattern affected by the ratio or absolute # of panthers? What changes?

Not saying the pattern is affected but it's kind of stupid to make such a simplifying assumption.

We are already assuming Panthers can shape-shift into goats. Is perfect rationality any more of a stretch?

What I understand as perfectly rational is different from the situation you are describing.

So it is stupid to make simplifying assumptions, and MBP's proof fails as a consequence? Yet the assumptions are included in the original problem. And you still haven't provided a valid proof. So....

illiniPride:
mrbeancounter:
illiniPride:
mrbeancounter:
illiniPride:
mrbeancounter:

the ratio of goats to panthers is indefinitely smaller.

So what? Where is the pattern affected by the ratio or absolute # of panthers? What changes?

Not saying the pattern is affected but it's kind of stupid to make such a simplifying assumption.

We are already assuming Panthers can shape-shift into goats. Is perfect rationality any more of a stretch?

What I understand as perfectly rational is different from the situation you are describing.

So it is stupid to make simplifying assumptions, and MBP's proof fails as a consequence? Yet the assumptions are included in the original problem. And you still haven't provided a valid proof. So....

Didn't say that. I said it is stupid to assume this logic is valid in infinity. That's why I said that "two panthers and one goat" is the most likely correct answer in my opinion.

mrbeancounter:

Didn't say that. I said it is stupid to assume this logic is valid in infinity.

Why?

illiniPride:
mrbeancounter:

Didn't say that. I said it is stupid to assume this logic is valid in infinity.

Why?

Because that won't be the case even with perfectly rational beings.

mrbeancounter:

That's why I said that "two panthers and one goat" is the most likely correct answer in my opinion.

There is no "most likely correct" answer.

Buddyfox:

120 panthers and one goat are put on a magic island that only has grass. Panthers can eat grass, but they would rather eat goats. Assume: A. Each time only one panther can eat one goat, and that panther itself will become a goat after it eats the goat. B. All panthers are smart and perfectly rational and they want to survive. So will the goat be eaten?

This is the question

Buddyfox:

The question boils down to an odd va even number of panthers. An even number will never eat the goat for fear of being eaten. An odd amount will always result in the goat being eaten.

mrbeancounter:
illiniPride:
mrbeancounter:

Didn't say that. I said it is stupid to assume this logic is valid in infinity.

Why?

Because that won't be the case even with perfectly rational beings.

Yes it would. MBP provided the proof. Can you find a flaw in it?

illiniPride:
mrbeancounter:

That's why I said that "two panthers and one goat" is the most likely correct answer in my opinion.

There is no "most likely correct" answer.

Buddyfox:

120 panthers and one goat are put on a magic island that only has grass. Panthers can eat grass, but they would rather eat goats. Assume: A. Each time only one panther can eat one goat, and that panther itself will become a goat after it eats the goat. B. All panthers are smart and perfectly rational and they want to survive. So will the goat be eaten?

This is the question

Buddyfox:

The question boils down to an odd va even number of panthers. An even number will never eat the goat for fear of being eaten. An odd amount will always result in the goat being eaten.

I know but I somehow disagree. As long as there is one single other panther on the island, you always risk being eaten when you turn into a goat.

mrbeancounter:

I know but I somehow disagree. As long as there is one single other panther on the island, you always risk being eaten when you turn into a goat.

...if that panther is not perfectly rational. If the panther is perfectly rational (and assumes all other panthers are as well), it will act as MBP predicts. Since the problem defines all panthers as perfectly rational, they will all act as MBP predicts.

illiniPride:
mrbeancounter:

I know but I somehow disagree. As long as there is one single other panther on the island, you always risk being eaten when you turn into a goat.

...if that panther is not perfectly rational. If the panther is perfectly rational (and assumes all other panthers are as well), it will act as MBP predicts. Since the problem defines all panthers as perfectly rational, they will all act as MBP predicts.

i think the issue here is that Mr Bean Counter doesn't understand the definition of "perfectly rational"... nor does he understand that this question is essentially a math problem/game theory question.

look dude, we're not taking into consideration any behavioral flaws of the panthers that would entice them to eat a goat even if it meant getting eaten. this means that whether there are 2 panthers or 2 million panthers, they will not eat the goat because doing so would mean getting eaten by the nearest panther (who would do it because there would be no consequence).

Money Never Sleeps? More like Money Never SUCKS amirite?!?!?!?

One (fun?) point of skepticism for me is this:

Knowing whether to eat the goat/sheep/whatever it was requires not only knowing whether there are an even number of panthers or odd, but also knowing that all other panthers are aware of this information. Must be a huge clusterfuck when 120 panthers are running around trying to count how many other panthers there are and verify that all the other panthers have successfully done their counting correctly. Better safe than sorry..

Furthermore, the number of panthers seems unlikely to be stable. What if a panther is born or a panther dies? An even number of panthers sitting around eating grass seems like a pretty unstable equilibrium. I wouldn't risk it..

juked07:

One (fun?) point of skepticism for me is this:

Knowing whether to eat the goat/sheep/whatever it was requires not only knowing whether there are an even number of panthers or odd, but also knowing that all other panthers are aware of this information. Must be a huge clusterfuck when 120 panthers are running around trying to count how many other panthers there are and verify that all the other panthers have successfully done their counting correctly. Better safe than sorry..

Furthermore, the number of panthers seems unlikely to be stable. What if a panther is born or a panther dies? An even number of panthers sitting around eating grass seems like a pretty unstable equilibrium. I wouldn't risk it..

You are over-thinking it man. We are to answer the question with the information given.

It doesn't matter if the panthers are aware of how many other panthers there are (although I agree with the even/odd outcome). The panthers are rational, and because they are rational, it is in their best interest not to eat the goat.

Survival is more important than eating better tasting food. There is no need to eat the goat other than hedonistic pleasure. While I believe manbearpig is correct regarding the outcome if an odd number of panthers are present, we know there are 120 and therefore no panthers will eat the goat.

My name is Nicky, but you can call me Dre.

juked07:

One (fun?) point of skepticism for me is this:

Knowing whether to eat the goat/sheep/whatever it was requires not only knowing whether there are an even number of panthers or odd, but also knowing that all other panthers are aware of this information. Must be a huge clusterfuck when 120 panthers are running around trying to count how many other panthers there are and verify that all the other panthers have successfully done their counting correctly. Better safe than sorry..

Furthermore, the number of panthers seems unlikely to be stable. What if a panther is born or a panther dies? An even number of panthers sitting around eating grass seems like a pretty unstable equilibrium. I wouldn't risk it..

NO. There was no specific constraint put on how high the Panthers were able to count, so you can't assume that they would have trouble determining the number of other Panthers.

And what's this about panthers dying and being born? If I told you that there were 10 people in a room and another 5 entered, would you have to ask how many people died to tell me the answer was 15?

NOT THAT HARD PEOPLE.

Money Never Sleeps? More like Money Never SUCKS amirite?!?!?!?

sayandarula:
illiniPride:
mrbeancounter:

I know but I somehow disagree. As long as there is one single other panther on the island, you always risk being eaten when you turn into a goat.

...if that panther is not perfectly rational. If the panther is perfectly rational (and assumes all other panthers are as well), it will act as MBP predicts. Since the problem defines all panthers as perfectly rational, they will all act as MBP predicts.

i think the issue here is that Mr Bean Counter doesn't understand the definition of "perfectly rational"... nor does he understand that this question is essentially a math problem/game theory question.

look dude, we're not taking into consideration any behavioral flaws of the panthers that would entice them to eat a goat even if it meant getting eaten. this means that whether there are 2 panthers or 2 million panthers, they will not eat the goat because doing so would mean getting eaten by the nearest panther (who would do it because there would be no consequence).

Right, since they are perfectly rational, they possess super-natural knowledge?
Is that implied by being perfectly rational?

illiniPride:
mrbeancounter:

I know but I somehow disagree. As long as there is one single other panther on the island, you always risk being eaten when you turn into a goat.

...if that panther is not perfectly rational. If the panther is perfectly rational (and assumes all other panthers are as well), it will act as MBP predicts. Since the problem defines all panthers as perfectly rational, they will all act as MBP predicts.

It's perfectly fine for me if you think so, there are also people out there who think option
pricing models with binary trees reflect the reality perfectly.

illiniPride - dude you deserve a medal for the patience you've demonstrated in this thread.

On a side note - how is this 'debate' still going on?

Patrick, can we start having minimum IQ requirements before people are allowed to sign up for WSO? I know it'll reduce traffic, but it will greatly improve quality ( =P only half serious)

-MBP

mrbeancounter:
illiniPride:
mrbeancounter:

I know but I somehow disagree. As long as there is one single other panther on the island, you always risk being eaten when you turn into a goat.

...if that panther is not perfectly rational. If the panther is perfectly rational (and assumes all other panthers are as well), it will act as MBP predicts. Since the problem defines all panthers as perfectly rational, they will all act as MBP predicts.

It's perfectly fine for me if you think so, there are also people out there who think option
pricing models with binary trees reflect the reality perfectly.

Assuming you use the correct risk neutral probabilities in the binomial trees, these are perfectly legitimate for pricing options. The fact that there are far more sophisticated techniques doesn't change that. In any case, no pricing model reflects reality perfectly. They're called models for a reason, after all. Any model that doesn't account for stochastic risk factors (volatility in particular) and relies on the no-arbitrage constraint is not going to model reality perfectly. And that's pretty much all models.

-MBP

illiniPride:
mrbeancounter:

So the solution is two panthers and one goat.

NO!

LOL!!! wow. This made my morning.

-MBP

manbearpig:
mrbeancounter:
illiniPride:
mrbeancounter:

I know but I somehow disagree. As long as there is one single other panther on the island, you always risk being eaten when you turn into a goat.

...if that panther is not perfectly rational. If the panther is perfectly rational (and assumes all other panthers are as well), it will act as MBP predicts. Since the problem defines all panthers as perfectly rational, they will all act as MBP predicts.

It's perfectly fine for me if you think so, there are also people out there who think option
pricing models with binary trees reflect the reality perfectly.

Assuming you use the correct risk neutral probabilities in the binomial trees, these are perfectly legitimate for pricing options. The fact that there are far more sophisticated techniques doesn't change that. In any case, no pricing model reflects reality perfectly. They're called models for a reason, after all. Any model that doesn't account for stochastic risk factors (volatility in particular) and relies on the no-arbitrage constraint is not going to model reality perfectly. And that's pretty much all models.

So you probably think that those risk neutral probabilities are the same in infinity right?

LOL. Get back to making useless powerpoint slides you consultant. (no offense)

manbearpig:
illiniPride:
mrbeancounter:

So the solution is two panthers and one goat.

NO!

LOL!!! wow. This made my morning.

Seems like you don't get the point. But as long as you have fun, who am I to destroy a hard-working consultant's fantasy world.

mrbeancounter:

So you probably think that those risk neutral probabilities are the same in infinity right?

WTF? LOL what are you talking about man? I don't think you know a thing about derivatives pricing. At least it doesn't sound like it. From your username, I take it you're an accountant, which explains a lot.

mrbeancounter:

LOL. Get back to making useless powerpoint slides you consultant. (no offense)

[/quote]

... not even sure how to respond to this.

-MBP

mrbeancounter:
manbearpig:
illiniPride:
mrbeancounter:

So the solution is two panthers and one goat.

NO!

LOL!!! wow. This made my morning.

Seems like you don't get the point. But as long as you have fun, who am I to destroy a hard-working consultant's fantasy world.

The irony is that you not getting the point is what I found amusing in the first place.

-MBP

mrbeancounter:
illiniPride:
mrbeancounter:
illiniPride:
mrbeancounter:
illiniPride:
mrbeancounter:

the ratio of goats to panthers is indefinitely smaller.

So what? Where is the pattern affected by the ratio or absolute # of panthers? What changes?

Not saying the pattern is affected but it's kind of stupid to make such a simplifying assumption.

We are already assuming Panthers can shape-shift into goats. Is perfect rationality any more of a stretch?

What I understand as perfectly rational is different from the situation you are describing.

So it is stupid to make simplifying assumptions, and MBP's proof fails as a consequence? Yet the assumptions are included in the original problem. And you still haven't provided a valid proof. So....

Didn't say that. I said it is stupid to assume this logic is valid in infinity. That's why I said that "two panthers and one goat" is the most likely correct answer in my opinion.

Ad infinitum means 'to infinity', not 'at infinity'. I think the subtlety is lost on you, so let me spell it out a bit more. The logic is not valid in [sic] infinity. It is valid to infinity. In no case in this sequence of cases will the number of panthers be infinite. There is no solution to this problem for an infinite number of panthers.

-MBP

the answer depends on whether the panthers believe in goat jesus. if so, bon appetit.

manbearpig:
mrbeancounter:

So you probably think that those risk neutral probabilities are the same in infinity right?

WTF? LOL what are you talking about man? I don't think you know a thing about derivatives pricing. At least it doesn't sound like it. From your username, I take it you're an accountant, which explains a lot.

mrbeancounter:

LOL. Get back to making useless powerpoint slides you consultant. (no offense)

... not even sure how to respond to this.

Is that how you work as a consultant to increase the number of slides?

Anyway, you have different probabilities at each stage in a binomial tree and don't assume
that it is the same at every point. How stupid to assume so.

I agree w/ IlliniPride's answer. Without further constraints on the grass, no rational panther will give his life to eat, unless there are only three panthers. So:

2 Panthers: no eat
3 panthers: eat
4 panthers to infinity panthers: no eat
120 panthers: no eat

I assume their utility function values life more than eating the goat, and the grass is unlimited.

It is better to be vaguely right than exactly wrong - JMK

Problem is solved, yet shitshow ensues. THIS...IS...WSO!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

"I'd rather die than be a phony." - Patrice O'Neal

I agree w/ IlliniPride's answer. Without further constraints on the grass, no rational panther will give his life to eat, unless there are only three panthers. So:

2 Panthers: no eat
3 panthers: eat
4 panthers to infinity panthers: no eat
120 panthers: no eat

I assume their utility function values life more than eating the goat, and the grass is unlimited.

You also assume law of conservation of panthers (panthers are neither created nor destroyed, only optionally transformed into goats). I am still on the fence about whether this is a fair assumption. It's clear that the question intends to impose this constraint, but it's so well known that animals can procreate/die that it ruins the question for me.

I realize this is nitpicking at second order effects while so many monkeys are still failing to reach the easy conclusion of the straightforward interpretation of the question.. But the solution to the brainteaser without considering possible complications just requires so little thought.

I agree w/ IlliniPride's answer. Without further constraints on the grass, no rational panther will give his life to eat, unless there are only three panthers. So:

2 Panthers: no eat
3 panthers: eat
4 panthers to infinity panthers: no eat
120 panthers: no eat

I assume their utility function values life more than eating the goat, and the grass is unlimited.

edit: woops double post

it would be a more interesting problem if goats were not conserved. it would be even MORE interesting if we had two subcases of the goats obeying fermi or bose statistics. in the first case you have basically LIFO accounting of the marginal goat being consumed but only one goat per time step consumable. in the latter case you have indistinguishable goats all subject to consumption all at once, where the goats consumed is bounded only by the number of panthers.

ok you smart motherfuckers figure it out.

Since the final result is no grass and 1 goat, the goat will die without the grass. Everyone's fucked. They should all try their swimming skills, because that alone will give them the best chance of survival.

P.S. mrbeancounter, you are an idiot.