JJ's Mind Challenge Thread

[castorpollux]

I made this thread because ishieymoro is ruining gheb's interview thread. Therefore I made this thread so that curious wofl's can figure out the answer without impeding the spotlight away from the interview thread. I know the answer to this question, and I will tell you if you are correct if you give me the correct explanation. Otherwise I'll play devil's advocate and try and confuse you.

So here is the question:

Barracuda_Drifter hands you two envelopes and says each of them have a single check written to you in them.
He then adds that one check in a random envelope has double the amount as the other check in the other envelope.

You pick an envelope and open it to find a check with X amount of money in it. Barracuda_Drifter then offers you a choice. You can either take the check that has X amount on it, or you can you pay him 10% of the amount on that check in order to switch envelopes.

Should you switch?

 

[Seagull Joe]

I'll mind challenge you!

DO: Compute the partition function (Z=Z¬elZtr), internal energy (U-Uo), Entropy (S), Helmholtz free energy (A-Ao), Gibbs free energy (G-Go) and Enthalpy (H-Ho) for 1 mole of atomic oxygen (O(g)) at 298 K and 1 atm. The degeneracy of the ground electronic state is 3 (we say it is a ground-state triplet) and the first electronically excited state (a singlet, hence degeneracy of 1) has an energy of 15867 cm-1. See the equation sheet for closed-form partition functions and thermodynamic state functions. Check your answer with those listed in thermodynamic tables.

 

[castorpollux]

that's a chemistry/physics problem that uses chem/physics terminology. that isn't a mind challenge because only people who have a background in those subjects can do that problem. that's just trying to make yourself seem smart by using jargon most people don't understand O_O



If i had a background in physics/chemistry, it'd probably be a really simple plug and chug problem. I just don't know the formulas

 

[Seagull Joe]

that's a chemistry problem that uses chem terminology. that isn't a mind trick. that's just trying to make yourself seem smart by using jargon most people don't understand O_O

If i had a background in chemistry, it's probably a really simple problem. I just don't know the formulas

True true. Your problem confuses me.

 

[castorpollux]

True true. Your problem confuses me.

which part are you confused by?

 

[Seagull Joe]

Everything.

 

[castorpollux]

Everything.

okay basically there are 2 envelopes with money inside of it. You are told that 1 envelope has double the amount of money than the other envelope

you get to choose 1 of the envelopes



you open the envelope to find 100 dollars in it.





then barracuda drifter offers you a choice. You can pay him 10 dollars to get the money inside the OTHER envelope, or you can keep the 100 dollars that's in the one you opened.


should you switch?

 

[Seagull Joe]

No, I shouldn't switch.

 

[castorpollux]

No, I shouldn't switch.

why not?

the other envelope can either have 200 dollars or 50 dollars

you can either win 100 dollars or lose 50 dollars.


you can win more than you lose... so shouldn't you switch?

 

[Ishiey]

Why are you always so mean to me ;_; lol

Two ways of looking at this, or at least that I've seen explained so far - your way, and my way

Your way, you pick x. If you switch, the envelope contains either 2x or .5x. You pay .1x to switch, so that means you have a 50-50 chance between 1.9x or .4x if you switch. Average of those is 1.15x, which is greater than x, so switching looks good.

My way looks like this and involves just x and 2x as the two initial packages:
Pick x, stick - x
Pick 2x, stick - 2x
Average from sticking - 1.5x
Pick x, switch - 1.9x
Pick 2x, switch - .8x
Average from switching - 1.35x
Since sticking average > switching average, sticking looks like the better option.

 

[KRDsonic]

^That's why I would stay.


This question does remind me of a slightly similar question someone asked me in high school, but the question dealt with 3 things instead of 2, and it was a bit different... and stuff.

 

[castorpollux]

Why are you always so mean to me ;_; lol

Two ways of looking at this, or at least that I've seen explained so far - your way, and my way

Your way, you pick x. If you switch, the envelope contains either 2x or .5x. You pay .1x to switch, so that means you have a 50-50 chance between 1.9x or .4x if you switch. Average of those is 1.15x, which is greater than x, so switching looks good.

My way looks like this and involves just x and 2x as the two initial packages:
Pick x, stick - x
Pick 2x, stick - 2x
Average from sticking - 1.5x
Pick x, switch - 1.9x
Pick 2x, switch - .8x
Average from switching - 1.35x
Since sticking average > switching average, sticking looks like the better option.

first says switching will make you more money in the long run
second says switching will make you lose more money in the long run

Both can't be correct because they clearly contradict each other. Which one is incorrect and why?



Also arda, lets say you pick an envelope and there is a 100 dollars in it. You aren't sure which "package" it is. It could be the (50, 100) package or the (100, 200) package


Do you really think you still shouldn't switch? Caz i'm sure if you kept picking 100 dollars over and over again, you would def. make more money by switching everytime

^That's why I would stay.


This question does remind me of a slightly similar question someone asked me in high school, but the question dealt with 3 things instead of 2, and it was a bit different... and stuff.

That problem is called the monty hall problem. the solution to that is to always switch

 

[Ishiey]

I know that both can't be correct, and I spent a minute trying to find out why one wasn't correct but I can't find a reason :< Like, I know you're right lol, but I don't understand why and can't prove it off the top of my head.

Let's start with this: can you tell me why my way is wrong?

EDIT: Wait. Your way assumes that you're always paying $10 to switch, but mine can be either $10 or $20 (.1x or .1(2x)). Like, the reward system in yours is skewed, if that makes sense, or maybe mine is, idk how to really explain it any better in words but yeah :x

 

[Choice]

you're never losing anything since you start with nothing, i figure just switch, but that's just me. my mentality is that irregardless i'm gaining more than what i've begun with so a risk to gain even more is always appealing so long theres no chance at losing everything.

 

[castorpollux]

I know that both can't be correct, and I spent a minute trying to find out why one wasn't correct but I can't find a reason :< Like, I know you're right lol, but I don't understand why and can't prove it off the top of my head.

Let's start with this: can you tell me why my way is wrong?

EDIT: Wait. Your way assumes that you're always paying $10 to switch, but mine can be either $10 or $20 (.1x or .1(2x)). Like, the reward system in yours is skewed, if that makes sense, or maybe mine is, idk how to really explain it any better in words but yeah :x

i already know the correct answer and which explanation is wrong. If I told you, I'd be giving you the answer

 

[castorpollux]

you're never losing anything since you start with nothing, i figure just switch, but that's just me. my mentality is that irregardless i'm gaining more than what i've begun with so a risk to gain even more is always appealing so long theres no chance at losing everything.

why should you switch every time?


If that's the case, why not make a "mental" switch before hand since you know you are going to switch everytime. That way you save yourself the 10%.


In other words, since you know there will be an amount "x" when you choose an envelope, and you know there will be a 1.25x expected value by switching, why not just switch before opening the first envelope?

This will then create an infinite loop of switching.


ALWAYS SWITCHING CAN'T BE RIGHT CAN IT?!!?!?

 

[Ishiey]

i already know the correct answer and which explanation is wrong. If I told you, I'd be giving you the answer

Or just being a good teacher and letting me know the error of my ways

 

[castorpollux]

Or just being a good teacher and letting me know the error of my ways

nope. there's no fun in me spoonfeeding the answer.


it took me weeks to figure this out

 

[Ishiey]

-_________-

Fine, I have finals now, but I'll try to prove it one way or another when I get out... after the other million tasks I have to get done once school is out, that is

 

[castorpollux]

-_________-

Fine, I have finals now, but I'll try to prove it one way or another when I get out... after the other million tasks I have to get done once school is out, that is

we both know you don't study for finals. such a bad excuse

 

[Ishiey]

It's true Spent all of yesterday sleeping and playing Yoshi's Island, because mechanics statics is for *****es... No regrets.

Take note of where most engineering classes lie :3

 

[castorpollux]

It's true Spent all of yesterday sleeping and playing Yoshi's Island, because mechanics statics is for *****es... No regrets.

Take note of where most engineering classes lie :3

http://www.geekosystem.com/engineering-professor-meme/2/

 

[Choice]

hahaha, they're so true its saddening =/

 

[Ishiey]

Yeah, basically why I regret paying for any of my classes this semester :/

 

[Zync]

Dang people in Math Majors, how do they work?!?!?!

 

[.AC.]

is it subjective?

 

[castorpollux]

is it subjective?

is what subjective?


if you're talking about this question, then no. There is a clear definite answer and explanation to it.

 

[.AC.]

i am not sure how to google this
my best guess would be that it is not recommendable to change since the risk is higher than the reward, kinda like trying to fsmash falco when you are at 0%. But i think somebody already said it

 

[Choice]

you're putting the test case too early. you can avoid the infinite loop

 

[Ishiey]

Elaborate?...

 

[Choice]

i mean in reference to jj's rebuttal to my solution. he said why not just switch before opening the first envelope?

the question given doesn't begin til after you open the first envelope though, so how could you even run into this issue?

 

[castorpollux]

i mean in reference to jj's rebuttal to my solution. he said why not just switch before opening the first envelope?

the question given doesn't begin til after you open the first envelope though, so how could you even run into this issue?

before you open the envelope, you know that it will be some amount 'X'. You know that regardless of what that amount 'X' is, you will have an expected value of 1.25X after you switch. In order to avoid the 10% payment to switch, shouldn't you make a "mental switch" instead? because switching will make you a 25% profit in the long run.




@AC

Since you can win more than you can lose, isn't the risk less than the reward?

 

[Choice]

i see what you're saying. yes, i guess so?

 

[castorpollux]

i see what you're saying. yes, i guess so?

so basically before you open the envelope, you go into an infinite loop of switching?

THAT CAN'T BE RIGHT

 

[.AC.]

so then switching is worth it since the reward is higher than the risk right? assuming you do it multiple times you are more likely to end up with a higher winning than a loss (bad explanation :/)