Interesting Logic Problem

Quote:

---

Originally Posted by Nick Pappagiorgio

Please explain. Again, simplify by using less people to start and work your way up.. It works.

---

I understand the 100 days answer and its explanation. It makes some sense in a purely mathematical way. I have a couple problems with it:

I. Lets take the logic/answer given and start to play it out from 1 person's perspective (lets assume they are blue eyed). The single person with green eye color or in fact the fact that any one person must consider the possibility that they have a unique eye color in addition to more than one other option messes it up:

On day one (I think of being on the island, although you assert its after the professor makes his irrelevant comment, no matter) this person sees 1 green eye, 99 blue eyes, 100 browns. According to the schema/answer since they see the green eye person there on day 2 and don't see any others it must mean they have green eyes!!!! In fact EVERYONE else thinks they have green eyes if they use your logic - they "know" they have green eyes (assuming that the DR sees their green eyes and "knows" not to leave on the 1st night), according to your logic. Whereas the truth is the Dr has no partner to signal him by staying as well.

In fact each person must also consider the possibility that they, just like the DR is the only person with eyes of their color, and therefore lacking any true signalling partner(s). That is they may not belong to a group that can signal its eye color to each other mathematically.

II. In addition even if you have just two eye colors someone mentioned game theory and in that context I just simply think its not in any way realistic other than as a purely theoretical construct. If these are people and not simply mathematical variables (N+1) simple understanding of human nature will tell you that they will not act this way. If the question were worded as computers that were not aware of their power light color but aware of the other computer's power light color you could count on this behavior. With humans they'll act both in ways that will defeat the mathematical prediction based on how "perfect logician" is interpreted to mean perfect=identical.

What I called Stampede Theorem is that in addition to considering the schema for "knowing" your eye color all the "perfect logicians" must consider others such as that which I constructed. As perfect logicians I think they too would come to the conclusion that there is a possibility they are the only one with their eye color and if they try the schema answer they could end up days or in fact months later without "knowing" their eye color . Everyone will stampede to the ferry so to speak, coming up with the schema that will tell them for certain in the most rapid time what their eye color is.Therefore they will decide the only way to confirm and to know their eye color is by trying to get off the island with my previous answer:

Quote:

---

Originally Posted by smitchell333

A) each person will count the # of others with blue eyes (ie for those with blue eyes = N). And the # of others with Green, and Brown eyes).

B) once you know these you will logically know that theoretically you have 4 options - you have:

1) Blue eyes, 2) Green eyes, 3) Brown eyes, 4) you have some other eye color and are the only one. There is no way of ever knowing for CERTAIN whether you have any eye color, other than guessing and presenting yourself as knowing you have an eye color and if you get off - you know.

C) Therefore you (assuming you want off the island) logically construct a plan to escape in the shortest possible time:

1) Night one - present yourself as either randomly blue or brown - you have 0 information to suggest either way but you know that statistically brown and blue are best represented and therefore your best guess - so by laws of chance approximately 50 blue and 50 brown will get off.

2) Night two - present yourself as the other option of the blue/brown from what you presented the day before -you have 0 information to suggest either way but you know that statistically brown and blue are best represented and therefore your best guess - so the remaining 50 blue and 50 brown will get off.

3) Night three - Doctor is the only one remaining - he will present himself as randomly chosen color other than blue, brown, green - "I have grey eyes" - the doctor could get off, but only by a lucky guess.

5) Day 4, etc - Dr presents himself as randomly chosen color other than blue, brown, green - "I have grey eyes" - the doctor could get off, but only by a lucky guess - he could be here forever but probably will be off by day 8 or 9 as there are really only a handful of common eye colors to guess.

---

Quote:

---

Originally Posted by smitchell333

I understand the 100 days answer and its explanation. It makes some sense in a purely mathematical way. I have a couple problems with it:

I. Lets take the logic/answer given and start to play it out from 1 person's perspective (lets assume they are blue eyed). The single person with green eye color or in fact the fact that any one person must consider the possibility that they have a unique eye color in addition to more than one other option messes it up:

On day one (I think of being on the island, although you assert its after the professor makes his irrelevant comment, no matter) this person sees 1 green eye, 99 blue eyes, 100 browns. According to the schema/answer since they see the green eye person there on day 2 and don't see any others it must mean they have green eyes!!!! In fact EVERYONE else thinks they have green eyes if they use your logic - they "know" they have green eyes (assuming that the DR sees their green eyes and "knows" not to leave on the 1st night), according to your logic. Whereas the truth is the Dr has no partner to signal him by staying as well.

---

I now understand the importance of the Doctor's statement and value it now and don't regard it as irrelevant and redundant.

Going more on what you say here, this person that you propose to think that he has green eyes on day two will know that he has blue eyes on the 100th day because if he DID have green eyes (or any non-blue-colored-eyes), then the 99 people he sees with blue eyes would have left on the 99th midnight because they each see only 98 others with blue eyes and logic dictates that they can leave with 100% certainty. But should the 99 others with blue eyes remain after the 99th midnight, then each person that sees 99 blue eyes can leave in full confidence. Follow?

Quote:

---

Originally Posted by smitchell333

II. In addition even if you have just two eye colors someone mentioned game theory and in that context I just simply think its not in any way realistic other than as a purely theoretical construct. If these are people and not simply mathematical variables (N+1) simple understanding of human nature will tell you that they will not act this way. If the question were worded as computers that were not aware of their power light color but aware of the other computer's power light color you could count on this behavior. With humans they'll act both in ways that will defeat the mathematical prediction based on how "perfect logician" is interpreted to mean perfect=identical.

---

That's more of a philosophical approach rather than a mathematical one and one where you are introducing "what ifs". If these were humans, then pick any scenario provided from the peanut gallery. I think you answered your qualm.

Quote:

---

Originally Posted by smitchell333

What I called Stampede Theorem is that in addition to considering the schema for "knowing" your eye color all the "perfect logicians" must consider others such as that which I constructed. As perfect logicians I think they too would come to the conclusion that there is a possibility they are the only one with their eye color and if they try the schema answer they could end up days or in fact months later without "knowing" their eye color . Everyone will stampede to the ferry so to speak, coming up with the schema that will tell them for certain in the most rapid time what their eye color is.Therefore they will decide the only way to confirm and to know their eye color is by trying to get off the island with my previous answer:

---

So...are you saying that everyone goes to the ferry on the 1st night without ever knowing their eye color and just hope that they have blue eyes so that they can leave?

Quote:

---

Originally Posted by Nick Pappagiorgio

Doctor's statement is meaningless. I think it's put there to throw people off and get you to think about something you needn't spend time thinking about.

<snip>

---

Sigh. This question is so much intellectual masturbation. Better to chase the Mntlion's NSFW links....

Quote:

---

Originally Posted by Nick Pappagiorgio

Going more on what you say here, this person that you propose to think that he has green eyes on day two will know that he has blue eyes on the 100th day because if he DID have green eyes (or any non-blue-colored-eyes), then the 99 people he sees with blue eyes would have left on the 99th midnight because they each see only 98 others with blue eyes and logic dictates that they can leave with 100&#37; certainty. But should the 99 others with blue eyes remain after the 99th midnight, then each person that sees 99 blue eyes can leave in full confidence. Follow?

---

Well according to the logic you put forth - he (and everyone who can see a green eyed person) MUST "know" he has green eyes on day/night 2. And this does not end up being true. When that happens, then when all 200 non-green eyes show up saying they have green eyes. If this is allowed (that is false "knowing" events), well then my system would have a much higher certainty of getting them off ASAP. I suppose your answer is that they could deduce after day 2 that the doctor was the only one with green eyes and thus was reason they couldn't leave night 2.

But the core of my objection with the whole thing is that we are talking about humans here and the reality is that you cannot count on cipher-like thinking from 99 or 100 people. Its not philosophical - its REALISTIC - this is more the way that PEOPLE act. Philosophical objection would be something more like - there's no real free will here and therefore human spirit will rebel against the ferryman keeping them down and they take over the ferry boat and all get off day 1. I think its realistic to assume that there is a good chance that at least 1 person gets doubts about it and doesn't want to revist the failure/embarrassment that DID happen on night 2 and doesnt show at the ferry on night 100 or finds a way to beat the system - then total collapse.

I agree if you make them computers with no egos, doubts, etc instead of people - simple - yes your logic works as long as the computer doesn't blue screen on the green eyed false "knowing" event.

Quote:

---

Originally Posted by Nick Pappagiorgio

So...are you saying that everyone goes to the ferry on the 1st night without ever knowing their eye color and just hope that they have blue eyes so that they can leave?

---

I'm saying that they would deduce that they highest probability of getting off the island is to play my game - and that rather than hoping they are playing the odds - its approximately 100/201 that they have brown eyes, 99/201 they have blue eyes, and 1/201 they have green eyes.

Now if you re-word the question to limit somehow the people showing up without having a mathematical argument for how they "know" they are X eye color OK that would prohibit potentially them from coming. Although I still think I would show up on night one and say "to my calculations I am most likely to have have brown eyes since that appears to be the best odds as there is a 100/201 chance I do."

Quote:

---

Originally Posted by TacomaLuv

Uncle Crud, since this was so elementary for you, perhaps I could PM you to look over some of my econometrics papers? We're heading into midterms and I could probably use the help :)

---

Well, not to thrash an obviously mangled and rotting corpse, but if you're studying "econometrics," I feel sorry for you. First, because you're paying to study bullshit. Second, because based on your question you're obviously taking it rather seriously even though it's patent bullshit. And third, because "econometrics" is a pretentious fucking name.

But if you found the original question not only logically and coherently worded, but also difficult, that would maybe explain your sincere and serious study of "econometrics." Maybe.

Or maybe it's a sad requisite on the way to receiving your degree in some other bogus field like "business" or "economics" or "statistics"? Sorry, but to me the dearth of rigorous intellectual dissection of academic subjects is a laughingstock and a rather embarrassing feature of post-secondary education.

Sorry, but that's how I see it. Maybe you can get out of jail free on the excuse that you're a poor, dumb and rather gullible college student?

Quote:

---

Originally Posted by doublediamond223

Well, if we want to play with LOGIC problems, how about some symbolic logic?

(> means horseshoe, can't find the font)

1. A≡W
2. ~A v ~W
3. R > A / ~(W v R)


Prove the conclusion using the 18 rules of inference.

---

Come on, no one?

Damn, what a thread; this rich manichaeistic discourse is so much more satisfying than any $350 sushi dinner! How often is it that I am propositioned to carry someone's lovechild in one breath and then subjected to a scathing ad homonym attack in the next? :D

Crud, a few notes: I don't know how you could miss it, but my question to you was obviously kidding, sorry you're not conversant with my pesky plebeian humor.

You're right, I am a Frightening Hell Spawn of too many analytics classes, yet I doubt many people get their MBAs for the "rigorous intellectual dissection," we all know the emperor has no clothes - it is just an expensive job placement service. Myself, I'm just in it to learn how to write algorithms computing the airspeed velocity of an unladen swallow.

Best of luck in your own quixotic quest for knowledge!
TLuv

Quote:

---

Originally Posted by TacomaLuv

Crud, a few notes: I don't know how you could miss it, but my question to you was obviously kidding, sorry you're not conversant with my pesky plebeian humor.

You're right, I am a Frightening Hell Spawn of too many analytics classes, yet I doubt many people get their MBAs for the "rigorous intellectual dissection," we all know the emperor has no clothes - it is just an expensive job placement service. Myself, I'm just in it to learn how to write algorithms computing the airspeed velocity of an unladen swallow.

Best of luck in your own quixotic quest for knowledge!
TLuv

---

Aw c'mon, the high road?? Disappointing. :p

Quote:

---

Originally Posted by TacomaLuv

Myself, I'm just in it to learn how to write algorithms computing the airspeed velocity of an unladen swallow.

---

Is that an African swallow?:fm:

Quote:

---

Originally Posted by TacomaLuv

Best of luck in your own quixotic quest for knowledge!

---

Actually, he's just hoping to get laid some day.

Quote:

---

Originally Posted by uncle crud

Maybe you can get out of jail free on the excuse that you're a poor, dumb and rather gullible college student?

---

S,
I hope you are coming strong with your maybe as this young lady is none of those things.
I know you love your mental gymnastics on the intraweb, but here you are out of your league.

I heart chix who use the word "Swallow."

Quote:

---

Originally Posted by TacomaLuv

The Doctor is allowed to speak once (let's say at midnight), on one day in all their countless years stuck on the island. When he does this, he says the following:

"Blue eyes = no airflow over the wing = you do not take off."

---

I see where this goes.

Quote:

---

Originally Posted by TacomaLuv

Damn, what a thread; this rich manichaeistic discourse is so much more satisfying than any $350 sushi dinner! How often is it that I am propositioned to carry someone's lovechild in one breath and then subjected to a scathing ad homonym attack in the next? :D

Crud, a few notes: I don't know how you could miss it, but my question to you was obviously kidding, sorry you're not conversant with my pesky plebeian humor.

You're right, I am a Frightening Hell Spawn of too many analytics classes, yet I doubt many people get their MBAs for the "rigorous intellectual dissection," we all know the emperor has no clothes - it is just an expensive job placement service. Myself, I'm just in it to learn how to write algorithms computing the airspeed velocity of an unladen swallow.

Best of luck in your own quixotic quest for knowledge!
TLuv

---

Glad we could be entertaining.

Let us know what the Prof says the official answer is - I feeling he has a trick up his sleeve, or in his pants.
:biggrin: :biggrin:

Quote:

---

Originally Posted by uncle crud

Well, not to thrash an obviously mangled and rotting corpse, but if you're studying "econometrics," I feel sorry for you. First, because you're paying to study bullshit. Second, because based on your question you're obviously taking it rather seriously even though it's patent bullshit. And third, because "econometrics" is a pretentious fucking name.

But if you found the original question not only logically and coherently worded, but also difficult, that would maybe explain your sincere and serious study of "econometrics." Maybe.

Or maybe it's a sad requisite on the way to receiving your degree in some other bogus field like "business" or "economics" or "statistics"? Sorry, but to me the dearth of rigorous intellectual dissection of academic subjects is a laughingstock and a rather embarrassing feature of post-secondary education.

Sorry, but that's how I see it. Maybe you can get out of jail free on the excuse that you're a poor, dumb and rather gullible college student?

---

I want to see how Nash, Aumann, Selten, Harsanyi, von Neumann et al react to you calling "economics" a bogus field ...

Also, for anyone who knows how to construct an inductive proof and knows about the difference between common and first-order knowledge, the problem is very simple. The only slightly complicating thing is the additional superfluous wording in the question.

Holy Shit!!

No one else thought of this:

What if one of the blue eyed is colorblind? According to this approx 1 in 76 or 1.30% of people are color blind.
http://www.wrongdiagnosis.com/c/colo...prevalence.htm

Its all fucked up then, right cause they cant count eyes.

Or what if some of them are fucking crazy. Looks like there is a high incidence of mental illness. Shit those people cant be counted on.

http://www.wrongdiagnosis.com/m/ment...prevalence.htm


Or what if you had blue eyes but wanted to make sweet love with that hottie mathematician with the brown eyes - you wouldn't leave that island for nothing.

The problem I have with this is the use of the word 'interesting' in conjunction with this problem.