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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 wrote:
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.

• 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

• 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 wrote:

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

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

Interesting.....

illiniPride wrote:
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 wrote:
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 wrote:
illiniPride wrote:
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 wrote:
manbearpig wrote:
illiniPride wrote:
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 wrote:
manbearpig wrote:
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 wrote:
worst answer ever.. better go edit it and make accounts to give yourself bananas..

manbearpig wrote:
manbearpig wrote:
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 wrote:
Dimethyltryptamine wrote:
worst answer ever.. better go edit it and make accounts to give yourself bananas..

manbearpig wrote:
manbearpig wrote:
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 wrote:
illiniPride wrote:
manbearpig wrote:
illiniPride wrote:
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 wrote:
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 wrote:
Dimethyltryptamine wrote:
worst answer ever.. better go edit it and make accounts to give yourself bananas..

manbearpig wrote:
manbearpig wrote:
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 wrote:
I'm not sure if you are trolling?

Not trolling =)

Dimethyltryptamine wrote:

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 wrote:

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 wrote:

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 wrote:

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 wrote:

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 wrote:

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 wrote:
Dimethyltryptamine wrote:
I'm not sure if you are trolling?

Not trolling =)

Dimethyltryptamine wrote:

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 wrote:

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 wrote:

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 wrote:

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 wrote:

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 wrote:

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 wrote:

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 wrote:

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 wrote:
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 wrote:
Dimethyltryptamine wrote:

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 wrote:

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

manbearpig wrote:
manbearpig wrote:
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 wrote:
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 wrote:
manbearpig wrote:
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 wrote:
Dimethyltryptamine wrote:
worst answer ever.. better go edit it and make accounts to give yourself bananas..

manbearpig wrote:
manbearpig wrote:
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 wrote:
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 wrote:
Dimethyltryptamine wrote:
worst answer ever.. better go edit it and make accounts to give yourself bananas..

manbearpig wrote:
manbearpig wrote:
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 wrote:
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.

• 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 wrote:
sayandarula wrote:
manbearpig wrote:
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 wrote:

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 wrote:
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 wrote:
manbearpig wrote:
sayandarula wrote:
manbearpig wrote:
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.

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 wrote:
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 wrote:
prospie wrote:
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 wrote:
illiniPride wrote:
prospie wrote:
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 wrote:
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 wrote:
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 wrote:
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 wrote:
manbearpig wrote:
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.