# Critical Thought Experiments



## Heisenberg (Sep 4, 2012)

You don't know me. I send you a letter stating that I am a precognitive psychic. To prove this I tell you I am going to make one specific prediction per week for the next 6 months. I then proceed to send you 26 letters, each with some sort of successful prediction. Some predict the outcome of elections. Some predict the winners of sports events of all types and regions. I predict trophy winners of various races and contests. Some predict the rising and falling of various unrelated stocks. I successfully predict the next president, the next to be fired on The Apprentice, the outcome of a popular murder trial, and so on and so on. My last prediction was even personal, that you would have a car accident sometime in the next week damaging your left fender. Each prediction is well in advance and is never wrong. The variety is such that I can not have inside information about all areas, and the volume is such that it can not be pure chance. At the end of the 6 months do you believe I am a psychic? If I am not physic and it wasn't left to chance, how did I do it?


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## mindphuk (Sep 4, 2012)

Stock market tip scam


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## sworth (Sep 4, 2012)

"...when you have eliminated the impossible, whatever remains, however improbable, must be the truth..."

Being psychic is impossible


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## cannabineer (Sep 4, 2012)

Heisenberg said:


> You don't know me. I send you a letter stating that I am a precognitive psychic. To prove this I tell you I am going to make one specific prediction per week for the next 6 months. I then proceed to send you 26 letters, each with some sort of successful prediction. Some predict the outcome of elections. Some predict the winners of sports events of all types and regions. I predict trophy winners of various races from horse to human to car. Some predict the rising and falling of various unrelated stocks. I successfully predict the next president, the next to be fired on The Apprentice, and so on and so on. My last prediction was even personal, that you would have a car accident sometime in the next week. Each prediction is well in advance and is never wrong. The variety is such that I can not have inside information about all areas, and the volume is such that it can not be pure chance. At the end of the 6 months do you believe I am a psychic? If not, why?


OK I'll take a nibble. It is very improbable but still possible that Mr. Psychic threw the dice 26 times and won every time. So while I would be quite impressed, and would need to allow that Mr. Psychic is probably onto something big here, I can't countenance that as proof. 

Verdict: inconclusive. cn


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## tyler.durden (Sep 4, 2012)

I agree with MP. Let's say you send out one million letters. Of those letters, half say the stock will go up and half say the stock will go down. You'd be correct for 500,000 people. you do this again and this time is correct for 250,000 people. By the fifth letter you have been correct 100% of the time for 30,000 people. A lot of those 30,000 will buy what you are selling. 
I did this kind of thing as a teenager: I got a letter with a 2 cent stamp and the seller said he would teach me the secret of mailing any letter for 2 cents (I was into direct marketing at the time, and this would've saved me a fortune). I sent in the $20 and never received anything, keep in mind this was before the internet. I then realized that if you stick a 2 cent stamp on a shitload of letters, some were bound to slip through the cracks. I ran the scam myself and received a few hundred dollars in profit. Then, one day someone rang my apartment buzzer early in the morning. It was a post office executive! I let him up and he handed me about 500 of my most recent mailed letters with the 2 cent stamp. He explained that if I do this again, I'm going to jail. I think he was surprised to see an 18 year old was running this scam, and I bet he's told the story and laughed his ass off dozens of times throughout the years. I certainly would have


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## Heisenberg (Sep 4, 2012)

cannabineer said:


> OK I'll take a nibble. It is very improbable but still possible that Mr. Psychic threw the dice 26 times and won every time. So while I would be quite impressed, and would need to allow that Mr. Psychic is probably onto something big here, I can't countenance that as proof.
> 
> Verdict: inconclusive. cn


You are on the right track thinking about odds, but the 26th prediction was not simply 1/6 chance.


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## Heisenberg (Sep 4, 2012)

tyler.durden said:


> I agree with MP. Let's say you send out one million letters. Of those letters, half say the stock will go up and half say the stock will go down. You'd be correct for 500,000 people. you do this again and this time is correct for 250,000 people. By the fifth letter you have been correct 100% of the time for 30,000 people. A lot of those 30,000 will buy what you are selling.
> I did this kind of thing as a teenager: I got a letter with a 2 cent stamp and the seller said he would teach me the secret of mailing any letter for 2 cents (I was into direct marketing at the time, and this would've saved me a fortune). I sent in the $20 and never received anything, keep in mind this was before the internet. I then realized that if you stick a 2 cent stamp on a shitload of letters, some were bound to slip through the cracks. I ran the scam myself and received a few hundred dollars in profit. Then, one day someone rang my apartment buzzer early in the morning. It was a post office executive! I let him up and he handed me about 500 of my most recent mailed letters with the 2 cent stamp. He explained that if I do this again, I'm going to jail. I think he was surprised to see an 18 year old was running this scam, and I bet he's told the story and laughed his ass off dozens of times throughout the years. I certainly would have



Very good!! and the car accident? Bonus question, assuming each situation had a 50/50 chance, how many letters did I send out?


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## cannabineer (Sep 4, 2012)

Heisenberg said:


> You are on the right track thinking about odds, but the 26th prediction was not simply 1/6 chance.


Did I imply that? I'm not seeing how ... I'm discarding the last one because it could be made to happen. I'm assuming here that the remaining 25 were not obtained by cheating ... considering the sorts of events being predicted, it would have to be a sophisticated sort of cheat using maneuvers not covered in your "situation setup" description. So getting those 25 right by sheer luck remains improbable but possible. cn


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## cannabineer (Sep 4, 2012)

Heisenberg said:


> Very good!! and the car accident? Bonus question, how many letters did I send out?


Twenty-six. it was in the opener. Introducing other players wasn't. cn


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## Heisenberg (Sep 4, 2012)

cannabineer said:


> Did I imply that? I'm not seeing how ... I'm discarding the last one because it could be made to happen. I'm assuming here that the remaining 25 were not obtained by cheating ... considering the sorts of events being predicted, it would have to be a sophisticated sort of cheat using maneuvers not covered in your "situation setup" description. So getting those 25 right by sheer luck remains improbable but possible. cn


That was my way of saying, hypothetically, that luck wasn't involved. I accept that it could have been, but for fun I was saying it wasn't.


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## cannabineer (Sep 4, 2012)

Heisenberg said:


> That was my way of saying, hypothetically, that luck wasn't involved. I accept that it could have been, but for fun I was saying it wasn't.


I did notice a sentence in the opener about "the volume being such that it cannot be pure chance". I am unable to derive this as being so from what I understand of the rest of the setup. Volume of what, in any case? Tyler's solution relies on what i consider a cheat: saying that the recipient was not the only one. I can find no indication of other players in the opener. Having to presume them without information supplied would be ... inelegant. cn


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## chrishydro (Sep 4, 2012)

I will bite but what does a physic have to gain by doing this, if he or she is one she knows it and has nothing to prove to anyone. Instead of a random person why not use their skills to stop a murder or solve a crime that would happen over if not stopped. Why not win the lottery and give the money to the needy. Why send letters to a perfect stranger?


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## Corso312 (Sep 4, 2012)

You may laugh but I am serious..there is an extremely small % of people who are psychic ....99.99% of the so called psychics are con artists..I would never give one a dime to even find out..but there are a handful of people who have predicted things and solved cases for the police that can be explained no other way.


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## Heisenberg (Sep 4, 2012)

chrishydro said:


> I will bite but what does a physic have to gain by doing this, if he or she is one she knows it and has nothing to prove to anyone. Instead of a random person why not use their skills to stop a murder or solve a crime that would happen over if not stopped. Why not win the lottery and give the money to the needy. Why send letters to a perfect stranger?


Those are all excellent reasons to doubt, but don't explain how I did it.

Ok I guess I should not have ended a puzzle with an opinion based answer. I was looking for an explanation of how it could be done without being psychic, ruling out coincidence. I shouldn't have worded it as "if you dont believe why not".


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## Heisenberg (Sep 4, 2012)

cannabineer said:


> I did notice a sentence in the opener about "the volume being such that it cannot be pure chance". I am unable to derive this as being so from what I understand of the rest of the setup. Volume of what, in any case? Tyler's solution relies on what i consider a cheat: saying that the recipient was not the only one. I can find no indication of other players in the opener. Having to presume them without information supplied would be ... inelegant. cn


Well the mistake was mine for being ambiguous about what I was looking for. I wouldn't waste your time on a puzzle whos answer was chance, but you were totally correct in listing that as a reason not to believe.


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## mindphuk (Sep 4, 2012)

Traveler from the future...


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## cannabineer (Sep 4, 2012)

Heisenberg said:


> Well the mistake was mine for being ambiguous about what I was looking for. I wouldn't waste your time on a puzzle whos answer was chance, but you were totally correct in listing that as a reason not to believe.


But one thing that was not ambiguous is Critical Thinking Puzzle. If I take the "was not chance" sentence and use that as a fulcrum, i deduce that the letters were part of a scam, mooting the question of the letter-writer's psychic ability. But that would then reduce this to a riddle, not a thought puzzle. I cannot believe that you would misrepresent a (insert favorite pejorative here) riddle as a thought-puzzle. So I reject that as an ugly, cheating way of "solving" this one.

Which leaves me stumped, since I am not finding the place to apply the logic-lever. cn


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## cannabineer (Sep 4, 2012)

mindphuk said:


> Traveler from the future...


... runs afoul of Niven's Law. I'd rather restrict myself to the possible. cn


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## mindphuk (Sep 4, 2012)

cannabineer said:


> ... runs afoul of Niven's Law. I'd rather restrict myself to the possible. cn


More probable than psychic powers IMHO.


BTW, I see no real practical difference between the terms riddle and thought puzzle.


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## cannabineer (Sep 4, 2012)

mindphuk said:


> More probable than psychic powers IMHO.
> 
> 
> BTW, I see no real practical difference between the terms riddle and thought puzzle.


One can be derived from the premises by an application of logic. The other hinges on a sly twist of semantics. Example:
How far can someone go into the forest?
Halfway. After that, one is headed out.

That is a riddle, not approachable by logic and hinging on cuteness. Riddles are nothing without the twist. Logic puzzles are nothing with it. Jmo. cn


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## Heisenberg (Sep 4, 2012)

cannabineer said:


> Then I am stumped. I see no way (shy of cheating, which would ruin this as a puzzle of critical thinking and reduces it to a mere riddle, and riddles have always mightily annoyed me by their sly ways of cheating language) that the outcomes could have been fixed. Please tell me if this is indeed a logic puzzle and not a riddle ... I was going on that basic premise since I have not once seen Heisenberg stoop to sophistry.
> But if it is a logic puzzle, i am hung on what appears to be an internal contradiction.
> 
> I could use the "no chance it was chance" as my starting point, decide that means "the whole thing was rigged", which would moot the question of the sender's psychic prowess. But that would be ugly and inelegant and unsatisfying, an answer worthy of a riddle but not a puzzle, which isn't Heis' way. So I reject that. cn



I did call this thread 'logic puzzles' for about 10 seconds and changed it, because I realized it involved critical thinking. I apologize if you saw the original title and was lead astray.

I suppose I would have to call it a riddle that stresses critical thinking principals. It is not a logic puzzle, as in your were supplied all the information and need only to reason your way through. You must make assumptions, which is where critical thinking comes in. I was actually going to use this as an example for the Chief, but realized it would be wasted on him. I thought it would be fun for us instead, and we might learn something. Just as when I did the 'name that logical fallacy" thread, it teaches me as much as anyone else.

Fist let me explain how it was done, then I will explain how I think it relates to critical thinking.

I choose only situations where there is a 50/50 outcome. In sports, a team either wins or it doesn't. Stocks either rise or fall. I choose races with no more than 6 contestants and which give prizes for 1st 2nd and 3rd place, so the chance of winning a prize is still 50/50. (unrealistic to find races which award half the contestants perhaps) I wait till the apprentice is down to 2 people, choose elections with only two candidates, ect. Knowing my outcome will be either-or with each prediction, I start out with millions of letters and send half the either and half the or. After the event I predicted, I drop the half that missed from my mailing list, and send the next prediction to only the hits. I do this for 6 months until 1 person remains on the list, and then I hit them with my car.

The first thing I think this suggests is that we should always search for and consider alternate explanations. This seems elementary to most of us, but obviously not to all who participate here. It is in fact a basic principal of critical thinking, not to favor any explanation at the total exclusion of others, or because we lack of a better one. We must always consider that the information we have is limited, and that there could be more to the picture than what has been supplied. This is especially true when we seem to reach a logical impasse or extreme improbability, such as the one I attempted to present here.

This also demonstrates the usefulness of parsimony and Occam's razor. People often confuse Occam's razor as saying the simplest explanation is most likely to be correct. Here, the explanation of psychic seems to be much less complex than the convoluted explanation I have provided. Yet, proper application of the razor favors the convoluted in this case. That is because Occam's Razor is about parsimony, and not simplicity. It's true that each new assumption offers room for error, but what is more important is the size of the assumption. Although my explanation is complicated, it's still working within the known laws of the universe. The psychic route may offer less assumptions, but the ones it does offer are huge paradigm breaking leaps.

So my intention was not to fool or deceive, it was to demonstrate and inform. Perhaps riddles aren't the best vehicle for what I wanted.


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## mindphuk (Sep 4, 2012)

So my answer was correct, a variation on the stock tip scam. I actually posted that as a clue rather than an answer since I wasn't sure how many people would know what I was talking about. Tyler obviously caught on. My only concern was how was the scammer supposed to hit so many people with their car, especially if they were already convinced and became so paranoid after your 'prediction,' they kept their car in the garage.


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## CC Dobbs (Sep 4, 2012)

Hey man wear s the puzzle


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## Corso312 (Sep 4, 2012)

It would be virtually impossible to predict a a car wreck and front fender damage to a specific area..even if tens of thousands of letters were sent out.


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## mindphuk (Sep 4, 2012)

Corso312 said:


> It would be virtually impossible to predict a a car wreck and front fender damage to a specific area..even if tens of thousands of letters were sent out.


If I predict you will have a house fire this week, then I come over and start a fire in your garage, my prediction came true.


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## Heisenberg (Sep 4, 2012)

mindphuk said:


> So my answer was correct, a variation on the stock tip scam. I actually posted that as a clue rather than an answer since I wasn't sure how many people would know what I was talking about. Tyler obviously caught on. My only concern was how was the scammer supposed to hit so many people with their car, especially if they were already convinced and became so paranoid after your 'prediction,' they kept their car in the garage.


I suspected maybe you had restrained explaining yourself for the sake of other's fun. This is indeed my attempt to adapt the stock tip scam to demonstrating critical thinking. I also didn't want to make it so similar to the stock tip scam that people could simply look it up.

I suppose we have to confine our first millions of people to only those with cars, but great point that they may be so fooled by the scam as to take measures to protect their car. In fact, if the scam is going as well as intended, they probably should be that convinced. Guess we would have to change it to something more likely to be in our favor. Something that is personal and seems accidental. Something we would seemingly have no control over. Where's a mentalist when you need one. 


What do you guys think would be an ironclad clincher for the final prediction? Something that would seem totally random, but leave nothing to chance.


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## cannabineer (Sep 4, 2012)

Heisenberg said:


> I did call this thread 'logic puzzles' for about 10 seconds and changed it, because I realized it involved critical thinking. I apologize if you saw the original title and was lead astray.
> 
> I suppose I would have to call it a riddle that stresses critical thinking principals. It is not a logic puzzle, as in your were supplied all the information and need only to reason your way through. You must make assumptions, which is where critical thinking comes in. I was actually going to use this as an example for the Chief, but realized it would be wasted on him. I thought it would be fun for us instead, and we might learn something. Just as when I did the 'name that logical fallacy" thread, it taught me as much as anyone else.
> 
> ...


I must say that that smacks to me of "oh I forgot to mention". I see nothing in the OP that compels a binary outcome. Example: court cases. These are not binary but quaternary: acquit, convict (or hold liable), dismiss, declare mistrial.
But a proper puzzle or riddle won't have such concealed premises. I see sophistry (unfairly declaring things like trophy races even odds. Neither the America's nor the Stanley Cup starts with a pool of two contending teams) in this, and it damages something that could have been fun. I am a rabid solver of puzzles, but generally deeply dislike riddles, because they _cheat _in just such a manner. 



> Knowing my outcome will be either-or with each prediction, I start out with millions of letters and send half the either and half the or. After the event I predicted, I drop the half that missed from my mailing list, and send the next prediction to only the hits. I do this for 6 months until 1 person remains on the list, and then I hit them with my car.
> 
> The first thing I think this suggests is that we should always search for and consider alternate explanations. This seems elementary to most of us, but obviously not to all who participate here. It is in fact a basic principal of critical thinking, not to favor any explanation at the total exclusion of others, or because we lack of a better one. We must always consider that the information we have is limited, and that there could be more to the picture than what has been supplied. This is especially true when we seem to reach a logical impasse or extreme improbability, such as the one I attempted to present here.
> 
> This also demonstrates the usefulness of parsimony and Occam's razor. People often confuse Occam's razor as saying the simplest explanation is most likely to be correct. Here, the explanation of psychic seems to be much less complex than the convoluted explanation I have provided. Yet, proper application of the razor favors the convoluted in this case. That is because Occam's Razor is about parsimony, and not simplicity. It's true that each new assumption offers room for error, but what is more important is the size of the assumption. Although my explanation is complicated, it's still working within the known laws of the universe. The psychic route may offer less assumptions, but the ones it does offer are huge paradigm breaking leaps.


If we allow for a moment that i haven't shattered the binary-outcome hidden premise, I still can't see the fake psychic paying twenty million in postage (2E25 outcomes means 2E26 minus one letters sent at avg. 28¢ per mailing) for a much smaller prize. Overcritical thinking on my part? cn


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## tyler.durden (Sep 4, 2012)

mindphuk said:


> Traveler from the future...


I was considering this possibility before I decided to side with your first guess


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## tyler.durden (Sep 4, 2012)

cannabineer said:


> I did notice a sentence in the opener about "the volume being such that it cannot be pure chance". I am unable to derive this as being so from what I understand of the rest of the setup. Volume of what, in any case? Tyler's solution relies on what i consider a cheat: saying that the recipient was not the only one. I can find no indication of other players in the opener. Having to presume them without information supplied would be ... inelegant. cn


Then call me inelegant, wouldn't be the first time I've heard it  I did assume that if I'm getting a letter from someone I don't know with an improbable pitch, I can't be the only one. Where would be the money in that?


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## Heisenberg (Sep 4, 2012)

cannabineer said:


> I must say that that smacks to me of "oh I forgot to mention". I see nothing in the OP that compels a binary outcome. Example: court cases. These are not binary but quaternary: acquit, convict (or hold liable), dismiss, declare mistrial.
> But a proper puzzle or riddle won't have such concealed premises. I see sophistry (unfairly declaring things like trophy races even odds. Neither the America's nor the Stanley Cup starts with a pool of two contending teams) in this, and it damages something that could have been fun. I am a rabid solver of puzzles, but generally deeply dislike riddles, because they _cheat _in just such a manner.


Please note my edit you may have missed.



> So my intention was not to fool or deceive, it was to demonstrate and inform. Perhaps riddles aren't the best vehicle for what I wanted.


I must say that critical thinking is not confined to proper puzzles, and the way I presented it, although perhaps not as articulate as I would have liked, is a realistic representation of how the human mind often presents it. The reason we need critical thinking is that life's situations are often duplicitous and misleading. At the end of six months, your brain is likely to forget details and be overwhelmed by the facade. Critical reflection of each case might reveal a binary pattern, but general recollection simply says, it's a lot of hits. This is the very mechanism of psychic cold readings and easy to exploit, as any magician will confirm. I thought figuring out the 50/50 pattern should be part of the riddle, since disguising the pattern is part of the scam.



> If we allow for a moment that i haven't shattered the binary-outcome hidden premise, I still can't see the fake psychic paying twenty million in postage (2E25 outcomes means 2E26 minus one letters sent at avg. 28¢ per mailing) for a much smaller prize. Overcritical thinking on my part? cn


This is why the scenario was presented hypothetically. I only need to add on that the psychic is an insane billionaire. We don't ask why some people only speak in lies, and others only speak in truth in logic puzzles, it's irrelevant. I suppose I unconsciously geared this toward uncritical thinkers learning yet presented it as if it was for critical thinkers to flex their skills. I would love to include puzzles like that as well.


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## eye exaggerate (Sep 4, 2012)

...algorithmics? (sound like the eurythmics if al gore were singer  )


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## cannabineer (Sep 4, 2012)

Sorry guys. I have had the sort of day which left me in sort of a mood. I came, found critical thinking puzzle, and practically salivated. I'm always doing found crosswords etc. (as i don't subscribe to the rural rag of a paper). I guess I remain unclear on just what disbelief to suspend in order to make this one sing. In any case, I've been a grouch. I'll stop. cn


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## cannabineer (Sep 4, 2012)

eye exaggerate said:


> ...algorithmics? (sound like the eurythmics if al gore were singer  )


And I always thought Algorithm was a sort of political contraception. It worked once ... cn


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## mindphuk (Sep 4, 2012)

Heisenberg said:


> I suspected maybe you had restrained explaining yourself for the sake of other's fun.


Yep, since I was the first, I didn't want to be so specific that if you had never heard of the stock tip scam, you wouldn't be able to make the connection to your scenario, but those that are familiar, would probably already have seen the connection. 


> Where's a mentalist when you need one.


I'm here, what can I help you with today? Hell, my audiences are impressed with choices that are 50:50. It's all on how you present them.

Take a look at how a master can make even a 50:50 proposition into a miracle. 
[video=youtube;ei-Pw5KgE7k]https://www.youtube.com/watch?v=ei-Pw5KgE7k[/video]


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## tyler.durden (Sep 4, 2012)

Heisenberg said:


> Very good!! and the car accident? Bonus question, assuming each situation had a 50/50 chance, how many letters did I send out?


Ha! I thought the car accident was just a final layer, dropping the number of people to which the scam could apply close to single digits...


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## cannabineer (Sep 4, 2012)

If we accept that the final accident is a unity-chance event, we have 2E25 binaries. So 2E25 letters were sent out as a first cut. Half each successive time, with only one recipient getting the final letter detailing the accident. he also received the final letter at the end of a convergent series, 2E25 plus 2E24 plus ... equals 2E26 minus one. Add the final letter, and I arrive at a (minimum) total of 2E26 letters sent, or 67,108,864. cn


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## Heisenberg (Sep 5, 2012)

cannabineer said:


> If we accept that the final accident is a unity-chance event, we have 2E25 binaries. So 2E25 letters were sent out as a first cut. Half each successive time, with only one recipient getting the final letter detailing the accident. he also received the final letter at the end of a convergent series, 2E25 plus 2E24 plus ... equals 2E26 minus one. Add the final letter, and I arrive at a (minimum) total of 2E26 letters sent, or 67,108,864. cn


Exactly right. If I send out one letter this week, 2 next week, 4 the week after, ect, I am sending 67,108,864 letters on week 26. So I had to start by sending out this many.


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## Heisenberg (Sep 5, 2012)

cannabineer said:


> Sorry guys. I have had the sort of day which left me in sort of a mood. I came, found critical thinking puzzle, and practically salivated. I'm always doing found crosswords etc. (as i don't subscribe to the rural rag of a paper). I guess I remain unclear on just what disbelief to suspend in order to make this one sing. In any case, I've been a grouch. I'll stop. cn


Not a problem at all. If I ever present this to a class or even just friends, I do not want them to feel the same feelings you had. I need to better construct the premise to hint at the 50/50 pattern so people have more of a chance to figure it out, and do not feel at the end they were duped from the start. Yet I still want to keep a representation of the muddled way in which the brain would reflect on the situation, the picture it constructs at the end of the 26 weeks.

I'll work on it.


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## Doer (Sep 5, 2012)

I have been in dire need this last few years. I thew myself into puzzles. Stacking Children's Block by color was was a step up from picking only the dead leaves off a big bush for hours (only the dead ones). 

Not kidding. Interferon therapy is mind boggling. TV or any type of entertainment, music, reading, etc, is gone. Cognition slowly and surely slips away, until only a minimal, fragile, confused survival stance is left. What to do? 

Think about it....if you could not be interested or engaged with anything. Eat Ganga. It really helps.

IAC, I kept up with more and more complex puzzles, until I could get it together to, at least, hold my bass guitar. Then stand up. Then work on scales again.

Now, after 4 long years, I am still working Defense Grid on Xbox. And I get cognition gain every week. I'd say I'm actually better now, than when this first started close to 20 years ago. 

Video Games, help the brain.


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## cannabineer (Sep 5, 2012)

Doer said:


> I have been in dire need this last few years. I thew myself into puzzles. Stacking Children's Block by color was was a step up from picking only the dead leaves off a big bush for hours (only the dead ones).
> 
> Not kidding. Interferon therapy is mind boggling. TV or any type of entertainment, music, reading, etc, is gone. Cognition slowly and surely slips away, until only a minimal, fragile, confused survival stance is left. What to do?
> 
> ...


My anodyne is a book of Sudoku, with a familiar movie playing in the background. cn


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## missnu (Sep 5, 2012)

I would start watching my moves more carefully thinking that some weirdo is following me messing up my car hoping I will believe they are psychic. Lol.


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## cannabineer (Sep 5, 2012)

missnu said:


> I would start watching my moves more carefully thinking that some weirdo is following me messing up my car hoping I will believe they are psychic. Lol.


You could always reverse the game. When Mr. X runs into you, kidnap him. I mean, here is a guy who just spent millions on postage. A creative investigator with skills of persuasion could end up quite rich. cn


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## Doer (Sep 5, 2012)

Sudoku is my wife's favorite. I have it on XBox, but Defense Grid has flashing lights and explosions! 

Very similar to Sudoku in that very little of what you think at first, will work out in the end, though it seems it will. I've never been good with numbers.


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## cannabineer (Sep 5, 2012)

Doer said:


> Sudoku is my wife's favorite. I have it on XBox, but Defense Grid has flashing lights and explosions!
> 
> Very similar to Sudoku in that very little of what you think at first, will work out in the end, though it seems it will. I've never been good with numbers.


I'm old school. Paper and pencil, a folded Sudoku book in bed, reruns running re'ly, a snootful of Widow and a stem glass of oloroso sherry. ~happy sigh~ cn


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## Doer (Sep 5, 2012)

Sadly, I can only get 9 and some of the numbers, then I'm lost.


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## Heisenberg (Sep 5, 2012)

*Storms moved through my area a few weeks ago, knocking out all power. None of the street lights or signals had any power. Just then, I observed a dark truck driving down the street without it's headlights on. An old woman wearing all black with no reflectors stepped onto the street and into the path of the truck. The moon was not shining, the woman had no flashlight or candle, and no generators were used, yet the driver stopped to let her pass. How was the driver of the truck able to see the woman?*

Hint: Examine your assumptions...


"The least questioned assumptions are often the most questionable." - Paul Broca


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## mindphuk (Sep 5, 2012)

Heisenberg said:


> *Storms moved through my area a few weeks ago, knocking out all power. Just then, I observed a dark truck driving down the street without it's headlights on. An old woman wearing all black with no reflectors stepped onto the street and into the path of the truck. The moon was not out, the woman had no flashlight or candle, and no generators were used, yet the driver stopped to let her pass. How was the driver of the truck able to see the woman?*
> 
> Hint: Examine your assumptions...
> 
> ...


Spoiler -- Too easy. The sun was out, it was daytime.


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## cannabineer (Sep 5, 2012)

Heisenberg said:


> *Storms moved through my area a few weeks ago, knocking out all power. Just then, I observed a dark truck driving down the street without it's headlights on. An old woman wearing all black with no reflectors stepped onto the street and into the path of the truck. The moon was not out, the woman had no flashlight or candle, and no generators were used, yet the driver stopped to let her pass. How was the driver of the truck able to see the woman?*
> 
> Hint: Examine your assumptions...
> 
> ...


Ooo! I know this one. Not giving it away. cn


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## Hepheastus420 (Sep 5, 2012)

cannabineer said:


> OK I'll take a nibble. It is very improbable but still possible that Mr. Psychic threw the dice 26 times and won every time. So while I would be quite impressed, and would need to allow that Mr. Psychic is probably onto something big here, I can't countenance that as proof.
> 
> Verdict: inconclusive. cn


No doubt your mind would be blown though.

I know I should think logically about this, but honestly, if he said a stock would fail, I'd listen to him. If he told me that a walmart would blow up on a certain day, I'd avoid it. That's just me though.


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## Hepheastus420 (Sep 5, 2012)

Heisenberg said:


> *Storms moved through my area a few weeks ago, knocking out all power. Just then, I observed a dark truck driving down the street without it's headlights on. An old woman wearing all black with no reflectors stepped onto the street and into the path of the truck. The moon was not out, the woman had no flashlight or candle, and no generators were used, yet the driver stopped to let her pass. How was the driver of the truck able to see the woman?*
> 
> Hint: Examine your assumptions...
> 
> ...


I wanna be the kid that screams out the answer..


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## dashcues (Sep 5, 2012)

Can I play? Although,like MP said, you gave away the answer.Or,at least,the logic to find it.


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## Heisenberg (Sep 5, 2012)

Anyone can answer who hasn't heard it before. Sounds like most have it figured out.


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## Hepheastus420 (Sep 5, 2012)

He could see because there was daylight out?


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## Heisenberg (Sep 5, 2012)

Hepheastus420 said:


> He could see because there was daylight out?



Absolutely! Good Job.

Sometimes even if all the information we are given is true, we can still be mislead. That is because our brain likes to make assumptions and infer from them. It wouldn't get far in the world if it didn't. Assumptions are something we can't live without, but they can be easily exploited. Our assumptions effect what we infer about the world, and sometimes what we infer can effect assumptions. If you infer from my stress of darkness that the man shouldn't have seen the woman, you assume the sun wasn't out. Of course, when you think about it critically for a minute it becomes apparent.

So if I can use inferences to effect an assumption, then that assumption will effect other inferences. Assuming that the sun was not out (thinking you know) leads to inferring all sorts of silly stuff, like the woman had a glow-stick or a helicopter spotlighted her. These aren't unreasonable explinations, but they are wrong because of an assumption.

The integrity of an assumption directly relates to the quality of the inferences we can make from it.


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## cannabineer (Sep 5, 2012)

Here's one I heard forty years ago and "got" at once. I'm amazed that there sre still folks who don't get this one quickly ... it's all about popular but logically porous assumptions. cn

*A father and son have a car accident and are both badly hurt. They are both taken to separate hospitals. When the boy is taken in for an operation, the surgeon says 'I can not do the surgery because this is my son'. How is this possible?*


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## Heisenberg (Sep 5, 2012)

cannabineer said:


> Here's one I heard forty years ago and "got" at once. I'm amazed that there sre still folks who don't get this one quickly ... it's all about popular but logically porous assumptions. cn
> 
> *A father and son have a car accident and are both badly hurt. They are both taken to separate hospitals. When the boy is taken in for an operation, the surgeon says 'I can not do the surgery because this is my son'. How is this possible?*


Good one. I was robbed at the chance to figure this one out. The person who told me followed with the answer almost immediately.


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## mindphuk (Sep 5, 2012)

Heisenberg said:


> Good one. I was robbed at the chance to figure this one out. The person who told me followed with the answer almost immediately.


What do you call a black man that flies a plane?


Answer - A pilot you fucking racist!

You can uncover the answer like in my previous post by merely selecting it.


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## Heisenberg (Sep 5, 2012)

mindphuk said:


> What do you call a black man that flies a plane?
> 
> 
> Answer - A pilot you fucking racist!
> ...



Heh, I heard the question before, but being from a redneck state they were looking for a different answer.


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## dashcues (Sep 5, 2012)

cannabineer said:


> Here's one I heard forty years ago and "got" at once. I'm amazed that there sre still folks who don't get this one quickly ... it's all about popular but logically porous assumptions. cn
> 
> *A father and son have a car accident and are both badly hurt. They are both taken to separate hospitals. When the boy is taken in for an operation, the surgeon says 'I can not do the surgery because this is my son'. How is this possible?*


What is-didn't say the father in the accident was the father of the son in the car accident.Surgeon was the father of the son in the accident.Father in the accident could be anybody's father.Doesn't say.
Correct?
Pornography for $200 Alex


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## Heisenberg (Sep 5, 2012)

dashcues said:


> What is-didn't say the father in the accident was the father of the son in the car accident.Surgeon was the father of the son in the accident.Father in the accident could be anybody's father.Doesn't say.
> Correct?
> Pornography for $200 Alex


This is true neer, your wording left it open. Such sophistry!


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## dashcues (Sep 5, 2012)

Heisenberg said:


> Heh, I heard the question before, but being from a redneck state they were looking for a different answer.


I had to cheat.I should've paid more attention to your hint.


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## cannabineer (Sep 5, 2012)

I found one that bothered me ... imo there is a flaw in the answer, which I had to look up. cn

Alexander is stranded on an island covered in forest.

One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.

There are cliffs around the island, so he cannot jump off.

How can the Alexander survive the fire? (There are no buckets or any other means to put out the fire)


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## cannabineer (Sep 5, 2012)

dashcues said:


> What is-didn't say the father in the accident was the father of the son in the car accident.Surgeon was the father of the son in the accident.Father in the accident could be anybody's father.Doesn't say.
> Correct?
> Pornography for $200 Alex


Oh my. My mistake for not more carefully vetting a c&p. Oops. 
However when "father&son" is mentioned, it conforms to a common phrase that remains in use for direct relatives. But I applaud "getting your lawyer on". cn


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## PeyoteReligion (Sep 5, 2012)

cannabineer said:


> I found one that bothered me ... imo there is a flaw in the answer, which I had to look up. cn
> 
> Alexander is stranded on an island covered in forest.
> 
> ...


I think he should set fire to the center of the island, and follow the burned area west. The original fire will be unable to follow as it has already been burned up.


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## Heisenberg (Sep 5, 2012)

cannabineer said:


> I found one that bothered me ... imo there is a flaw in the answer, which I had to look up. cn
> 
> Alexander is stranded on an island covered in forest.
> 
> ...



Would depend on how big the island is. At first I thought he could dig a hole, but he probably doesn't have time and he might suffocate. Then I thought maybe he dug a hole the day before complete with vent chamber. But what if the fire lingers over the hole... better to clear out brush and trees from around the hole. But if he is going to clear out flammable stuff from around the hole, he really doesn't need it anymore. If the clearing is big enough the fire wont touch him. In fact, he could create a clear space across half the island down the middle so the fire would burn out before it reached him, but the only way he could do that quickly is burn it. With the wind coming in from the west he would only accelerate his death if he attempted a burn line. He can not put out the fire he started any more than he can the original fire.

Hrmm


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## Heisenberg (Sep 5, 2012)

PeyoteReligion said:


> I think he should set fire to the center of the island, and follow the burned area west. The original fire will be unable to follow as it has already been burned up.


I think this is right, start a new burn and follow it. It would be one way at least.


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## dashcues (Sep 5, 2012)

cannabineer said:


> I found one that bothered me ... imo there is a flaw in the answer, which I had to look up. cn
> 
> Alexander is stranded on an island covered in forest.
> 
> ...


might depend on where Alexander is on the island.He may be farther west than the lightning strike hit?If so he should stay where he's at.


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## dashcues (Sep 5, 2012)

dashcues said:


> might depend on where Alexander is on the island.He may be farther west than the lightning strike hit?If so he should stay where he's at.


Scratch that..."the fire will burn the whole island" .


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## PeyoteReligion (Sep 5, 2012)

Heisenberg said:


> I think this is right, start a new burn and follow it. It would be one way at least.


This is a wildfire survival technique, so I'm for sure going with it.


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## cannabineer (Sep 5, 2012)

Heisenberg said:


> I think this is right, start a new burn and follow it. It would be one way at least.


This was essentially the given answer. I approached this as a problem in topology and could find no way to cross the fireline. The given answer involves stealing a firebrand from the blaze's edge, retreating to the windward side of the island, and setting a counterfire.
In real life this would work since one can control a small fire and step into the burnt area. But as a topology puzzle it dissatisfied, since a fire would spread from a point, recognizing only the island's edges and the burnt areas as boundaries. There's no getting "behind" a closed circle of fire that was necessarily started from outside the circle. 

One of the comments cracked me up: " ... only to die days later from exposure and starvation." cn


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## Heisenberg (Sep 5, 2012)

*One day you are running through a forest and meet a leprechaun. He says he will give you his pot of gold if you can find it. He presents three boxes and tells you the gold is under one of them, and the other two are empty. You point to a box, but rather than reveal what's under it, he picks up the box beside it and shows you that one was empty. He then says that you can change your pick if you want, or stay with your original. If you want to give yourself a statistical advanage which choice would you make, or does it not matter?*


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## PeyoteReligion (Sep 5, 2012)

cannabineer said:


> This was essentially the given answer. I approached this as a problem in topology and could find no way to cross the fireline. The given answer involves stealing a firebrand from the blaze's edge, retreating to the windward side of the island, and setting a counterfire.
> In real life this would work since one can control a small fire and step into the burnt area. But as a topology puzzle it dissatisfied, since a fire would spread from a point, recognizing only the island's edges and the burnt areas as boundaries. There's no getting "behind" a closed circle of fire that was necessarily started from outside the circle.
> 
> One of the comments cracked me up: " ... only to die days later from exposure and starvation." cn


I approached it like a real life situation, and the solution was pretty easy. This has come close to happening to me while hiking near Cle Elum in eastern Washington. Except the island part, but being in the woods just the same.


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## cannabineer (Sep 5, 2012)

Heisenberg said:


> *One day you are running through a forest and meet a leprechaun. He says he will give you his pot of gold if you can find it. He presents three boxes and tells you the gold is under one of them, and the other two are empty. You point to a box, but rather than reveal what's under it, he picks up the box beside it and shows you that one was empty. He then says that you can change your pick if you want, or stay with your original. If you want to give yourself a statistical advanage which choice would you make, or does it not matter?*


Not sure if my analysis is valid, but I would change my pick every time. cn


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## PeyoteReligion (Sep 5, 2012)

Heisenberg said:


> *One day you are running through a forest and meet a leprechaun. He says he will give you his pot of gold if you can find it. He presents three boxes and tells you the gold is under one of them, and the other two are empty. You point to a box, but rather than reveal what's under it, he picks up the box beside it and shows you that one was empty. He then says that you can change your pick if you want, or stay with your original. If you want to give yourself a statistical advanage which choice would you make, or does it not matter?*


Statistically it shouldn't matter. Your choice does not affect which box the gold will be under. Stick with my first guess.


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## cannabineer (Sep 5, 2012)

PeyoteReligion said:


> Statistically it shouldn't matter. Your choice does not affect which box the gold will be under. Stick with my first guess.


Iirc it turns out that this is a case where a quirk of statistics turns up.

I would change every time.
If I stay with my first choice, I have a one in three chance of hitting. But if I always change, my chances improve to one out of two. 
The trick is: the leprechaun engages in a maneuver that changes the odds; he always selects an empty box. If I stay, I'll have chosen before he discards a blank. If I always change, I'll have chosen after he discards the blank. I want to use that advantage. cn


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## PeyoteReligion (Sep 5, 2012)

cannabineer said:


> Iirc it turns out that this is a case where a quirk of statistics turns up.
> 
> I would change every time.
> If I stay with my first choice, I have a one in three chance of hitting. But if I always change, my chances improve to one out of two.
> The trick is: the leprechaun engages in a maneuver that changes the odds; he always selects an empty box. If I stay, I'll have chosen before he discards a blank. If I always change, I'll have chosen after he discards the blank. I want to use that advantage. cn


At this point we are assuming that we get to continually choose and get shown an empty box. Op never specified if the leprechaun would be so generous or if at that point we need to make a 50/50 shot between your original pick and the other box not yet revealed. I'm pretty high right now, but how do your odds get any better than that? I bet that fucking leprechaun has all sorts of tricky maneuvers to not give the answer away. Btw, is t he already supposed to fork over the gold once you cantch him anyways?


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## tyler.durden (Sep 5, 2012)

Heisenberg said:


> *One day you are running through a forest and meet a leprechaun. He says he will give you his pot of gold if you can find it. He presents three boxes and tells you the gold is under one of them, and the other two are empty. You point to a box, but rather than reveal what's under it, he picks up the box beside it and shows you that one was empty. He then says that you can change your pick if you want, or stay with your original. If you want to give yourself a statistical advanage which choice would you make, or does it not matter?*


I would say the statistics would be the same if there wasn't more to it, but it's best to stick with your first choice: I assume the lad wouldn't want me to take his gold, so if my original pick didn't have the gold under it, he likely would have picked up the box and I'd lose right then. Why give me another shot if my choice was wrong?


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## cannabineer (Sep 5, 2012)

PeyoteReligion said:


> At this point we are assuming that we get to continually choose and get shown an empty box. Op never specified if the leprechaun would be so generous or if at that point we need to make a 50/50 shot between your original pick and the other box not yet revealed. I'm pretty high right now, but how do your odds get any better than that? I bet that fucking leprechaun has all sorts of tricky maneuvers to not give the answer away. Btw, is t he already supposed to fork over the gold once you cantch him anyways?


No; we get to choose twice, but the leprechaun only gets to make the one maneuver. We make an initial choice; the leprechaun acts; we make a second choice (stay or switch). 
Actually I believe I understated the benefit of switching.

Let's say you pick a door and hold. Your chances of winning are one in three, and the leprechaun's discard doesn't help or hurt those chances.

Let's say you pick a door and switch. The chances that your original pick was good is one in three. This means the chances of the gold being in the two other boxes are *two out of three*. The leprechaun will assuredly discard an empty box, leaving you with one choice that has a 2/3 chance of hitting.
Always switch. cn


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## mindphuk (Sep 5, 2012)

tyler.durden said:


> I would say the statistics would be the same if there wasn't more to it, but it's best to stick with your first choice: I assume the lad wouldn't want me to take his gold, so if my original pick didn't have the gold under it, he likely would have picked up the box and I'd lose right then. Why give me another shot if my choice was wrong?


Nope, 'neer is right. This is a rewording of the Monty Hall problem that fools a lot of mathematicians. It is always correct to change. It works out to 1/3 of the time you lose, 2/3 you win.


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## tyler.durden (Sep 5, 2012)

cannabineer said:


> No; we get to choose twice, but the leprechaun only gets to make the one maneuver. We make an initial choice; the leprechaun acts; we make a second choice (stay or switch).
> Actually I believe I understated the benefit of switching.
> 
> Let's say you pick a door and hold. Your chances of winning are one in three, and the leprechaun's discard doesn't help or hurt those chances.
> ...


I don't get this: when the leprechaun discards one, the probability of your original pick instantly changes to 2 out of 3, the same as if you switch, no? Am I missing something?


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## tyler.durden (Sep 5, 2012)

mindphuk said:


> Nope, 'neer is right. This is a rewording of the Monty Hall problem that fools a lot of mathematicians. It is always correct to change. It works out to 1/3 of the time you lose, 2/3 you win.


Wow, I'll bet you're right, but I still can't see how it works. Can someone explain it to me like I'm six?


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## cannabineer (Sep 5, 2012)

tyler.durden said:


> Wow, I'll bet you're right, but I still can't see how it works. Can someone tell explain it to me like I'm six?


This one is conceptually very tough, because it violates a deep-seated bit of common sense that muddles our ability to correctly assign probabilities in a perturbed system. The hinge of it is, if you hold, you're gaining nothing from the discard. If you switch, you gain something. The discard is not random and is perturbing the outcome.

If you switch:
your first choice has one chance in three if being the winner. 
If it is, you'll lose.

If however your first pick is a loser (chances two out of three), the remaining two boxes are one good, one dry. The leprechaun WILL discard the dry one. That's the kicker. 
If your initial choice was dry, and you switch, you have a unity chance of getting the prize. 
Thus, switching as a matter of routine raises your win chances to 2 out of 3.

The Wikipedia entry is informative imo. cn

https://en.wikipedia.org/wiki/Monty_Hall_problem


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## PeyoteReligion (Sep 5, 2012)

Ah fuck, i was thinking along the same longs as tyler. It makes enough sense. Because i made my choice when three options were available, and sticking with that choice even though one was removed still leaves me with the same odds.

But like I said, that fucker is supposed to pay up just for catching him.


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## tyler.durden (Sep 5, 2012)

cannabineer said:


> This one is conceptually very tough, because it violates a deep-seated bit of common sense that muddles our ability to correctly assign probabilities in a perturbed system. The hinge of it is, if you hold, you're gaining nothing from the discard. If you switch, you gain something. The discard is not random and is perturbing the outcome.
> 
> If you switch:
> your first choice has one chance in three if being the winner.
> ...


Thank you, gentlemen, my mind is blown! This is the graph from your link, Neer, that finally simplified it enough for me to comprehend:


behind Door 1behind Door 2behind Door 3result if staying at door #1result if switching to the door offered*Car*GoatGoat*Car*GoatGoat*Car*GoatGoat*Car*GoatGoat*Car*Goat*Car
*
It's amazing that thousand of Ph.Ds could not see this. I guess I was in somewhat good company. Good, stupid company


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## cannabineer (Sep 5, 2012)

tyler.durden said:


> Thank you, gentlemen, my mind is blown! This is the graph from your link, Neer, that finally simplified it enough for me to comprehend:
> 
> 
> behind Door 1behind Door 2behind Door 3result if staying at door #1result if switching to the door offered*Car*GoatGoat*Car*GoatGoat*Car*GoatGoat*Car*GoatGoat*Car*Goat*Car
> ...


Not stupid. I think this is a brilliant puzzle (and I'd +rep Heis for it if I could, but I need to suck off a few more unicorns first ... horny bastards) because it "catches" on a glitch in our ability to think probabilistically. cn


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## tyler.durden (Sep 5, 2012)

cannabineer said:


> Not stupid. I think this is a brilliant puzzle (and I'd +rep Heis for it if I could, but I need to suck off a few more unicorns first ... horny bastards) because it "catches" on a glitch in our ability to think probabilistically. cn


Yeah, I can't rep the guy anymore, either. I haven't been this challenged in years, thanks for the lesson. I love this sub-forum...


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## PeyoteReligion (Sep 5, 2012)

It's just counter intuitive. Damn preconceived notions! You guys would love this YouTube guy, his channels is called Veritasium. He covers tons of misconceptions that people have about all sorts of things, like where trees get most of their mass from. This guy wrote his phd on how to educate people with videos. He found that just telling someone "trees get most of their mass from air" they just to oh yeah I knew that, and the misconception strengthens. Instead he asks them, and most everyone forgets that plants inhale co2. Good videos if anyone is interested.
http://m.youtube.com/watch?v=RQaW2bFieo8


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## Heisenberg (Sep 6, 2012)

Neer not only gave the right answer, he also saw the lesson behind it. Humans are great at pattern recognition, and terrible at probability assessment. The problem is, because of intuition, we feel we are skilled at judging probability. I am glad this sparked some conversation. It's nice to see people handle disagreement without taking it personally or feeling insulted.

I have not viewed the wiki page, but this is how my mind breaks it down.

When you pick the first box your chances are 1/3. The leprechaun takes one choice away. At this point we are more or less given a new choice, it's a new game. If you stay, you still have 1/3 chance because you are still playing the old game. If you switch, your new choice is governed by 1/2 odds. If during my new choice I pick the same box (essentially stay with my original) I am also staying with the 1/3 odds.

Another way to see it is, the leprechaun is essentially giving you a choice between a single box or a pair. He is saying you can have box 1 (1/3 chance) or you can have box 2 AND box 3. (2/3 chance) The fact that he showed one of the pair is empty offers no new information, you already knew that.


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## Heisenberg (Sep 6, 2012)

*Lets see if you learned anything. You meet an old high school friend on the bus. You ask if He has any children, and he says he has two. You ask if he has any daughters, and he says yes. You now know that he has two children and one is female. What are the chances that he has two daughters?*

I expect not all will agree on this one.


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## PeyoteReligion (Sep 6, 2012)

Heisenberg said:


> *Lets see if you learned anything. You meet an old high school friend on the bus. You ask if He has any children, and he says he has two. You ask if he has any daughters, and he says yes. You now know that he has two children and one is female. What are the chances that he has two daughters?*
> 
> I expect not all will agree on this one.


Fuck you got me again. Intuition tells me 50/50 boy girl. But clearly that didn't work before for me. 

The only thing that makes me think he has TWO females is that you said "has any daughters, and he said yes." Daughters implies more than one, so that means 100% two girls?


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## UncleBuck (Sep 6, 2012)

Heisenberg said:


> *The variety is such that I can not have inside information about all areas, and the volume is such that it can not be pure chance*. At the end of the 6 months do you believe I am a psychic? If I am not physic and it wasn't left to chance, how did I do it?


the part in bold seems to try to semantically preclude the next two parts.

but you could have a variety that seems to dabble in inside information from all areas, and the volume can be limited enough to preclude pure chance.

you are trying to assert an 'a priori' that can be explained by 'a posteriori'.

take that bullshit and go elsewhere.

i said good day sir.

I SAID GOOD DAY!


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## Heisenberg (Sep 6, 2012)

PeyoteReligion said:


> Fuck you got me again. Intuition tells me 50/50 boy girl. But clearly that didn't work before for me.
> 
> The only thing that makes me think he has TWO females is that you said "has any daughters, and he said yes." Daughters implies more than one, so that means 100% two girls?


You are right, the question is ambiguous, and it's meant to be. I am attempting show that numbers have their own internal logical consistency which sometimes conflicts with our logic. He may have meant daughters plural, but easily could have meant single. Say your life depended on it, would you think it's safer to assume he meant daughters plural, or forgo that assumption in favor of odds based on what you can know for sure?


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## PeyoteReligion (Sep 6, 2012)

Ok help me with this guys. I told cannabineers situation to a friend, the island that catches on fire one that I solved. After I tell her that I start another fire on the island and take cover behind the new burn line, she points out that the size of the island was never specified and she assumed that it was small and thus not large enough to do such a task. I tell her the island size was not specified and that if you limited the size of the island to the point where setting a backfire is not safe, then you fail the puzzle. 

Is this correct, or was she safe in assuming that the island was too small for that task? I think she failed because she assumed the size of the island. This is where over thinking comes into play, and I'm sure that's what stopped her from solving the problem.


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## UncleBuck (Sep 6, 2012)

Heisenberg said:


> You are on the right track thinking about odds, but the 26th prediction was not simply 1/6 chance.


that possibility is not ruled out a priori.

you have not given me a four sided triangle or a woman taller than herself yet.


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## PeyoteReligion (Sep 6, 2012)

Heisenberg said:


> You are right, the question is ambiguous, and it's meant to be. I am attempting show that numbers have their own internal logical consistency which sometimes conflicts with our logic. He may have meant daughters plural, but easily could have meant single. Say your life depended on it, would you think it's safer to assume he meant daughters plural, or forgo that assumption in favor of odds based on what you can know for sure?


I assume that he would say daughters if he had two. But we all know what assumptions make...
Also I'm making this assumption off very little evidence, so it is risky anyways.


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## Heisenberg (Sep 6, 2012)

PeyoteReligion said:


> Ok help me with this guys. I told cannabineers situation to a friend, the island that catches on fire one that I solved. After I tell her that I start another fire on the island and take cover behind the new burn line, she points out that the size of the island was never specified and she assumed that it was small and thus not large enough to do such a task. I tell her the island size was not specified and that if you limited the size of the island to the point where setting a backfire is not safe, then you fail the puzzle.
> 
> Is this correct, or was she safe in assuming that the island was too small for that task? I think she failed because she assumed the size of the island. This is where over thinking comes into play, and I'm sure that's what stopped her from solving the problem.


I had the same thoughts. The size of the island does seem to come into play. At some point it would be too small for a burn line to work, but then we wouldn't need to ask the question. The problem is, we the listener do not know that a small island moots the question.


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## UncleBuck (Sep 6, 2012)

Heisenberg said:


> I choose only situations where there is a 50/50 outcome. In sports, a team either wins or it doesn't. Stocks either rise or fall. I choose races with no more than 6 contestants and which give prizes for 1st 2nd and 3rd place, so the chance of winning a prize is still 50/50. (unrealistic to find races which award half the contestants perhaps) I wait till the apprentice is down to 2 people, choose elections with only two candidates, ect. Knowing my outcome will be either-or with each prediction, I start out with millions of letters and send half the either and half the or. After the event I predicted, I drop the half that missed from my mailing list, and send the next prediction to only the hits. I do this for 6 months until 1 person remains on the list, and then I hit them with my car.


i was right. this scenario, however unlikely, is not ruled out a priori.

just semantical fapping.

your puzzle was bad and you should feel bad.

just kidding, i still love you.


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## Heisenberg (Sep 6, 2012)

PeyoteReligion said:


> I assume that he would say daughters if he had two. But we all know what assumptions make...
> Also I'm making this assumption off very little evidence, so it is risky anyways.


Well he just answered 'yes'. The question was, do you have _any_ daughters. The only thing you can safely assume from that is he has at least one. You could infer he has two, and the chances of you being right would be...


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## PeyoteReligion (Sep 6, 2012)

Heisenberg said:


> I had the same thoughts. The size of the island does seem to come into play. At some point it would be too small for a burn line to work, but then we wouldn't need to ask the question. The problem is, we the listener do not know that a small island moots the question.


I think you nailed it, I was unable to point it out. If the island was too small it's a baited question. So we must assume its large enough for any situation. That's why I said she failed; because she failed to take into account that the island me be large. Seems she forgot Australia is an island/continant.


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## PeyoteReligion (Sep 6, 2012)

Heisenberg said:


> Well he just answered 'yes'. The question was, do you have _any_ daughters. The only thing you can safely infer from that is he has at least one. You could infer he has two, and the chances of you being right would be...


Always 50/50. Unless he wears a fur cod peice that raises his average testicle temperature, making him more likely to have females.


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## dashcues (Sep 6, 2012)

I'm stumped?!?
Think I've talked myself into guessing.I'll go with Peyote's answer ...50/50?


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## cannabineer (Sep 6, 2012)

PeyoteReligion said:


> I think you nailed it, I was unable to point it out. If the island was too small it's a baited question. So we must assume its large enough for any situation. That's why I said she failed; because she failed to take into account that the island me be large. Seems she forgot Australia is an island/continant.


I think we can assume that the island is "on a human scale", not much less or much more than two miles long. (The datum that the fire would consume the island militates against it being as big as, say, Jamaica.) That leaves enough room for maneuver and not too much to cover. I assumed something like this.
To me the problem is that I found it under "logic puzzles" but i see it as a riddle, relying on the peculiar properties of small, managed fires to give an "out" from a topological impossibility. cn


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## cannabineer (Sep 6, 2012)

Imo the "daughters" riddle hinges on the lingual sophistication of the respondent. To me "any daughters" automatically means "one or more", so the construction doesn't have a biasing effect. So I say the chances of him having at least one daughter are unity, and two daughters, nonzero. But I don't know how to assign odds without dabbling in semantic sophistry, which has no value imo. cn


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## Heisenberg (Sep 6, 2012)

cannabineer said:


> Imo the "daughters" riddle hinges on the lingual sophistication of the respondent. To me "any daughters" automatically means "one or more", so the construction doesn't have a biasing effect. So I say the chances of him having at least one daughter are unity, and two daughters, nonzero. But I don't know how to assign odds without dabbling in semantic sophistry, which has no value imo. cn


The question plays on ambiguity, not a trick of semantics. The man doesn't have a son named 'daughter' or an effeminate son he refers to as daughter. The point is it asks for a statistical answer and most will give one of intuition.


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## cannabineer (Sep 6, 2012)

Heisenberg said:


> The question plays on ambiguity, not a trick of semantics. The man doesn't have a son named 'daughter' or an effeminate son he refers to as daughter. The point is it asks for a statistical answer and most will give one of intuition.


So is "definitely has one, could have two" a sufficient answer? 

It reminds me of an anecdote my momma brought back from India. She asked a fellow if he had a family. "Yes", the man said proudly, "two sons and three children." Momma could have strangled him. cn


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## Heisenberg (Sep 6, 2012)

cannabineer said:


> So is "definitely has one, could have two" a sufficient answer?
> 
> It reminds me of an anecdote my momma brought back from India. She asked a fellow if he had a family. "Yes", the man said proudly, "two sons and three children." Momma could have strangled him. cn


Semantic riddles stress creative thinking, so I wont be including those here. Let me ask a different way. If you know a man has tossed a coin twice (two births) and you know one of those events resulted in tails (female), what are the odds that the other event resulted in tails as well?


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## Doer (Sep 6, 2012)

I know baby Harpies have tails....100% female, those Harpies.


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## cannabineer (Sep 6, 2012)

Heisenberg said:


> Semantic riddles stress creative thinking, so I wont be including those here. Let me ask a different way. If you know a man has tossed a coin twice (two births) and you know one of those events resulted in tails (female), what are the odds that the other event resulted in tails as well?


Since non-correlation is a golden principle of the statistics of randomness, I'd say 50%. cn


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## tyler.durden (Sep 6, 2012)

Heisenberg said:


> Semantic riddles stress creative thinking, so I wont be including those here. Let me ask a different way. If you know a man has tossed a coin twice (two births) and you know one of those events resulted in tails (female), what are the odds that the other event resulted in tails as well?


I think 50/50. In flipping a coin I think the odds always reset to 50/50. For daughters, there are more women born than men in the world, so maybe in that case the odds may be slightly bent toward girls...


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## cannabineer (Sep 6, 2012)

tyler.durden said:


> I think 50/50. In flipping a coin I think the odds always reset to 50/50. For daughters, there are more women born than men in the world, so maybe in that case the odds may be slightly bent toward girls...


... as am I. cn


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## PeyoteReligion (Sep 6, 2012)

The second coin toss is no affect by the result of the first toss. So again it's 50/50.


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## cannabineer (Sep 6, 2012)

PeyoteReligion said:


> The second coin toss is no affect by the result of the first toss. So again it's 50/50.


I'd be surprised if Heis tells us otherwise.

I'd like to offer one of my favorite logic puzzles.
*In a room whose door is closed is an electric light of ordinary sort.
Outside the room is a switch plate with three switches. 
One of the switches operates the light.
You are allowed to set the switches any way you want until just before you open the door; then it's hands off.
Figure out which switch operates the light.*
cn


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## mindphuk (Sep 6, 2012)

Here's a problem that completely crushed the post limit of a forum I was on when it was first introduced. The answer was already demonstrated by Mythbusters but if you have never heard of it, try to figure it out.
*
A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"​*​


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## cannabineer (Sep 6, 2012)

No takers at all for mine? Do I smell bad?? cn


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## cannabineer (Sep 6, 2012)

mindphuk said:


> Here's a problem that completely crushed the post limit of a forum I was on when it was first introduced. The answer was already demonstrated by Mythbusters but if you have never heard of it, try to figure it out.
> *A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"​*


A request for disambiguation. Is the plane moving relative to a stationary observer, or only relative to the conveyor apparatus? cn


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## Heisenberg (Sep 6, 2012)

tyler.durden said:


> I think 50/50. In flipping a coin I think the odds always reset to 50/50. For daughters, there are more women born than men in the world, so maybe in that case the odds may be slightly bent toward girls...





PeyoteReligion said:


> The second coin toss is no affect by the result of the first toss. So again it's 50/50.


This is true. One event does not influence the other, yet that is not the issue. We want to know the likelihood that the events match.


Odds are the domain of numbers. The information we are seeking comes from that domain. The odds that any man who has sired two children will have two girls is 25%. If we look at each birth as an event, and each event as having two equally possible outcomes, we have four possible results, one of which gives us double female. It looks like this.


Birth 1Birth 21YYYY2YXYX3XYXY4XXXX

The chance of each birth resulting in female is 1/2. .... 1/2 x 1/2 = 1/4

If we account for the information the man supplied, that at least one child is a female, we can elminate the double male result. That leaves 3 possible outcomes, only one of which gives him two daughters. The chance of this man having two daughters is 1/3.


Intuition inclines people to view the two similar outcomes, male/female, female/male, as the same, since they both give a negative answer which leads to the same assumption. The brain doesn't want to have to take the time to distinguish as it sees no meaningful difference between the two results. This leads people to view the outcome as being 50/50. He either has two or he doesn't. There are many situations in life where making intuitive assumptions can be an advantage, but when we are seeking answers which dwell in the domain of numbers, we must use thier logic, which is sometimes counter-intuitive.


http://gwydir.demon.co.uk/jo/probability/info.htm


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## mindphuk (Sep 6, 2012)

cannabineer said:


> A request for disambiguation. Is the plane moving relative to a stationary observer, or only relative to the conveyor apparatus? cn


Will the plane move?


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## Heisenberg (Sep 6, 2012)

cannabineer said:


> No takers at all for mine? Do I smell bad?? cn


I am pondering it. As I refuse to look it up, I may need a while to think.


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## cannabineer (Sep 6, 2012)

mindphuk said:


> Will the plane move?


I'll have to commit my guess: "the plane moves in one direction" means it is in motion with velocity V relative to a stationary observer. If the conveyor moves at -V, the gear is spinning as if the plane were moving at 2V net. So I would say the plane has no difficulty taking off (assuming a long enough motorized runway for the plane to achieve V sub R!), since the wings and engines are moving air and not ground. Wonder if the tires are rated for the centrifugal force of 2V sub R, though ... cn


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## cannabineer (Sep 6, 2012)

Heisenberg said:


> I am pondering it. As I refuse to look it up, I may need a while to think.


Thank you. I was insufferable for days when I figured it out without peeking. cn


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## PeyoteReligion (Sep 7, 2012)

cannabineer said:


> I'd be surprised if Heis tells us otherwise.
> 
> I'd like to offer one of my favorite logic puzzles.
> *In a room whose door is closed is an electric light of ordinary sort.
> ...


So I'm tryin to turn the light on? Hmmm.this is a tough one. I don't even have an initial gut feeling about any of them. For no reason at all, I wanna say the one closest to the door, which was not specified and probably dosent matter.


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## Heisenberg (Sep 7, 2012)

Eureka!! 

At first I wanted to systematically eliminate switches by opening the door to check. But I figure we only get one shot or else the question is unnecessary. Stumped, I started looking at the wording. 'Ordinary'. This got me to thinking about different bulbs, which made me think of my grow tent. Why do I not use ordinary bulbs... spectrum, cost.. and heat. I sometimes feel the tent without opening it to see if it's too hot. If the lights are off, it's not even warm. So I was thinking we could turn on a switch, feel the door and see if it warms up, but I guess doors don't normally heat up from ordinary light bulbs. But the bulb itself gets hot, which lead to my eureka moment, scaring my cats in the process. We ignore the first switch and turn on the second long enough to warm up the bulb. We then turn off the second switch and turn on the third. When we open the door, if the light is on it's the third switch. If the light is dark but warm it is the second switch, and if the light is dark and cold, it's the first switch. Of course I can't actually tell you which switch is the one unless I am there in person.

How about it?


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## mindphuk (Sep 7, 2012)

cannabineer said:


> I'll have to commit my guess: "the plane moves in one direction" means it is in motion with velocity V relative to a stationary observer. If the conveyor moves at -V, the gear is spinning as if the plane were moving at 2V net. So I would say the plane has no difficulty taking off (assuming a long enough motorized runway for the plane to achieve V sub R!), since the wings and engines are moving air and not ground. Wonder if the tires are rated for the centrifugal force of 2V sub R, though ... cn


You are correct. The problem seems to be that people instinctively think of it as if it were a car or bike where they remain stationary with respect to an outside observer. They have a cognitive block where they just can't get the concept of the thrust acting on the air mass above the treadmill with free spinning wheels in the gear. The speed of the treadmill is irrelevant, the plane can take off at belt speeds higher than take off speed, it will only make the wheels spin faster.


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## Heisenberg (Sep 7, 2012)

Here is another puzzle dealing with probable outcomes, easy one this time. Everyone should get this if they think about it. This requires only logic.*

You are blindfolded and standing in front of a drawer which contains only the following: 10 red socks, 10 green socks, 10 blue socks, 10 black socks and 10 white socks. Since you can not see, what is the minimum number of socks you need to pull out of the drawer to guarantee you have a matching pair?*


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## UncleBuck (Sep 7, 2012)

Heisenberg said:


> Here is another puzzle dealing with probable outcomes, easy one this time. Everyone should get this if they think about it. This requires only logic.*
> 
> You are blindfolded and standing in front of a drawer which contains only the following: 10 red socks, 10 green socks, 10 blue socks, 10 black socks and 10 white socks. Since you can not see, what is the minimum number of socks you need to pull out of the drawer to guarantee you have a matching pair?*


6.

you pull sock 1, of color a.

you pull sock 2, of color b.

you pull sock 3, of color c.

you pull sock 4, of color d.

you pull sock 5, of color e.

when you pull sock 6, it will be either color a, b, c, d, or e, thus giving you a matching pair.

learned that one in fifth grade. new jersey has great public schools.


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## Heisenberg (Sep 7, 2012)

UncleBuck said:


> 6.
> 
> you pull sock 1, of color a.
> 
> ...


Correct, but you left out the obligatory insult I have come to expect from each of your posts.

No points for you.


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## cannabineer (Sep 7, 2012)

Heisenberg said:


> Eureka!!
> 
> At first I wanted to systematically eliminate switches by opening the door to check. But I figure we only get one shot or else the question is unnecessary. Stumped, I started looking at the wording. 'Ordinary'. This got me to thinking about different bulbs, which made me think of my grow tent. Why do I not use ordinary bulbs... spectrum, cost.. and heat. I sometimes feel the tent without opening it to see if it's too hot. If the lights are off, it's not even warm. So I was thinking we could turn on a switch, feel the door and see if it warms up, but I guess doors don't normally heat up from ordinary light bulbs. But the bulb itself gets hot, which lead to my eureka moment, scaring my cats in the process. We ignore the first switch and turn on the second long enough to warm up the bulb. We then turn off the second switch and turn on the third. When we open the door, if the light is on it's the third switch. If the light is dark but warm it is the second switch, and if the light is dark and cold, it's the first switch. Of course I can't actually tell you which switch is the one unless I am there in person.
> 
> How about it?


It's a good moment when you get it, no? 
My protocol would have been a little different but equivalent.
I'd label the switches 1,2 and 3.
I'd leave 1 and 2 on and 3 off.
Just before entering the room, I'd turn off switch 2. So, if the lightbulb was (it was controlled by):

on: switch 1
off, warm: switch 2
off, cold: switch 3
cn


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## UncleBuck (Sep 7, 2012)

Heisenberg said:


> Correct, but you left out the obligatory insult I have come to expect from each of your posts.
> 
> No points for you.


twatbiscuit.


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## tyler.durden (Sep 7, 2012)

UncleBuck said:


> twatbiscuit.


Sounds delicious...


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## Heisenberg (Sep 9, 2012)

tyler.durden said:


> Thank you, gentlemen, my mind is blown! This is the graph from your link, Neer, that finally simplified it enough for me to comprehend:
> 
> 
> behind Door 1behind Door 2behind Door 3result if staying at door #1result if switching to the door offered*Car*GoatGoat*Car*GoatGoat*Car*GoatGoat*Car*GoatGoat*Car*Goat*Car
> ...


My friend actually got up and walked out this morning over this question. Even after showing him the chart and demonstrating the only possible outcomes, which he accepted, he still couldn't reconcile it in his head, and so refused to believe it. He wanted to take the 'agree to disagree' route, but of course there is no arguing with math. This is a person who is passionately for evidence when it comes to creationism, ESP, and the like, yet when presented with something that countered his intuition, he wanted to let his intuition trump real world data. He is always asking me how people can be positive about God with all the doubt there is, and now he has experienced that himself. It's very hard to overcome what _seems_ right in our heads.

Later, what finally convinced him was raising the original choice to one in a billion. With those odds, it's very unlikely the person picks the car first. He was able to agree on that. After we go through the process of eliminating all other boxes but one, I told him he couldn't switch. He had to stay with his original odds. This way, he was able to retain his doubt that the first pick overcame 1/billion odds, and recognized that to take advantage of the 50/50 he needs to switch.

I then asked him the 'daughters' question, and he got it wrong and wanted to argue, even after showing him the outcomes. So even though he learned to overcome his intuition in one case, he didn't learn the value of questioning it. If it is this hard to get a person with a skeptical disposition to accept something as certain as math, imagine the challenge we face in getting people to question their intuition on matters like god, health, or consciousness.


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## Heisenberg (Sep 9, 2012)

*Two Gangsters are driving directly at each other each going 100mph. They enter a bridge 200 miles long from opposite ends. Immediately upon entering the bridge, one gangster fires a bullet at the other car. The bullet is magic, and travels at a constant speed of 1000mph. It travels to the other car and bounces off, travels back to the first car and bounces off, and so on until the cars, never slowing, meet in the middle in a fiery crash. 

What is the total distance the bullet traveled?


*No lesson to this one, just a brain teaser.


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## cannabineer (Sep 9, 2012)

Heisenberg said:


> *Two Gangsters are driving directly at each other each going 100mph. They enter a bridge 200 miles long from opposite ends. Immediately upon entering the bridge, one gangster fires a bullet at the other car. The bullet is magic, and travels at a constant speed of 1000mph. It travels to the other car and bounces off, travels back to the first car and bounces off, and so on until the cars, never slowing, meet in the middle in a fiery crash.
> 
> What is the total distance the bullet traveled?
> 
> ...


Ooo! Took me a moment, but I think I found the handle. (I am not giving it away.) 

As for the daughters question, it really is instructive as to the resistance of our common sense against a certain sort of probability argument. A coupla nights ago, I "solved" the daughters one for myself by imagining a large population of dads with two children. Assuming a 1:1 probability of the children being boys and girls, 25% will have had two boys, 25% will have had two girls and 50% will have had boy girl or girl boy (25% for either of those). 
What the question does is exactly equivalent to the leprechaun or goat problem : _it removes a category_, perturbing previously unremarkable odds. In the daughters case, it disqualified the 2M dads, leaving ponly MF and 2F dads in their 2:1 ratios.
So if faced with situations like these, spotting the category-removal situations becomes a difficultly-acquired skill ... cn

<add> I cannot PM you ...


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## mindphuk (Sep 9, 2012)

I'm gonna go with...1000 miles. It will take exactly an hour for the cars to crash so the bullet has a full hour to perform its journey.


You all should know by now how to uncover my spoiler.


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## cannabineer (Sep 9, 2012)

mindphuk said:


> I'm gonna go with...1000 miles. It will take exactly an hour for the cars to crash so the bullet has a full hour to perform its journey.
> 
> 
> You all should know by now how to uncover my spoiler.


In public, good Sir?? cn


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## cannabineer (Sep 9, 2012)

cannabineer said:


> In public, good Sir?? cn


<edit> Now that I have done some delicate and discreet uncovering ... we both used the same "hook".

<edit!> looks like I replied rather than edit.


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## tyler.durden (Sep 9, 2012)

Heisenberg said:


> My friend actually got up and walked out this morning over this question. Even after showing him the chart and demonstrating the only possible outcomes, which he accepted, he still couldn't reconcile it in his head, and so refused to believe it. He wanted to take the 'agree to disagree' route, but of course there is no arguing with math. This is a person who is passionately for evidence when it comes to creationism, ESP, and the like, yet when presented with something that countered his intuition, he wanted to let his intuition trump real world data. He is always asking me how people can be positive about God with all the doubt there is, and now he has experienced that himself. It's very hard to overcome what _seems_ right in our heads.
> 
> Later, what finally convinced him was raising the original choice to one in a billion. With those odds, it's very unlikely the person picks the car first. He was able to agree on that. After we go through the process of eliminating all other boxes but one, I told him he couldn't switch. He had to stay with his original odds. This way, he was able to retain his doubt that the first pick overcame 1/billion odds, and recognized that to take advantage of the 50/50 he needs to switch.
> 
> I then asked him the 'daughters' question, and he got it wrong and wanted to argue, even after showing him the outcomes. So even though he learned to overcome his intuition in one case, he didn't learn the value of questioning it. If it is this hard to get a person with a skeptical disposition to accept something as certain as math, imagine the challenge we face in getting people to question their intuition on matters like god, health, or consciousness.


I was thinking about what you stated in this post, Heis. The majority of my friends are skeptical stoners, and the main reason I feel they are so willing to question their intuition,memory and perception in general is they are _used_ to forgetting, misplacing, and perceiving things incorrectly because of heavy weed use. When it can take 20 minutes to find keys you left in your other jeans (or in the door from the night before), it's much easier to see how easy it is to be fooled by your own mind...


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## Beefbisquit (Sep 10, 2012)

UncleBuck said:


> twatbiscuit.


Twatbisquit is my second cousin


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## Heisenberg (Sep 10, 2012)

mindphuk said:


> I'm gonna go with...1000 miles. It will take exactly an hour for the cars to crash so the bullet has a full hour to perform its journey.
> 
> 
> You all should know by now how to uncover my spoiler.


 Correct, the bullet traveled for an hour at 1000 mph.


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## guy incognito (Sep 16, 2012)

Heisenberg said:


> *Lets see if you learned anything. You meet an old high school friend on the bus. You ask if He has any children, and he says he has two. You ask if he has any daughters, and he says yes. You now know that he has two children and one is female. What are the chances that he has two daughters?*
> 
> I expect not all will agree on this one.


He either has mm, mf, fm, or ff. Those are the only 4 combinations of children he can have. You already know he has at least one daughter, so he doesn't have mm. So he has a 1/3 chance of having 2 daughters, and 2/3 chance having mf/fm.


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## guy incognito (Sep 16, 2012)

Heisenberg said:


> Exactly right. If I send out one letter this week, 2 next week, 4 the week after, ect, I am sending 67,108,864 letters on week 26. So I had to start by sending out this many.


Wait a minute, you would only be sending 33,554,432 on week 26. You would be sending 67,108,864 on week 27.

2^(w-1) where w is the week number. 

2^(1-1) = 1 for week 1, 
2^(2-1) = 2 for week 2,
...
2^(26-1) = 33,554,432 for week 26.

So reverse that on week 1 you send 2^(26-1) = 33,554,432 letters, the next week you send 2^(25-1) and so on down to week 1 where you only send a single letter. So you end up with 2^25 + 2^24 + ... 2^0 which is (2^26)-1 = 67,108,863 total.



cannabineer said:


> If we accept that the final accident is a unity-chance event, we have 2E25 binaries. So 2E25 letters were sent out as a first cut. Half each successive time, with only one recipient getting the final letter detailing the accident. he also received the final letter at the end of a convergent series, 2E25 plus 2E24 plus ... equals 2E26 minus one. Add the final letter, and I arrive at a (minimum) total of 2E26 letters sent, or 67,108,864. cn


The final letter is already included in the series. it is 2E26-1, not 2E26


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## guy incognito (Sep 16, 2012)

PeyoteReligion said:


> At this point we are assuming that we get to continually choose and get shown an empty box. O*p never specified if the leprechaun would be so generous or if at that point we need to make a 50/50 shot between your original pick and the other box not yet revealed.* I'm pretty high right now, but how do your odds get any better than that? I bet that fucking leprechaun has all sorts of tricky maneuvers to not give the answer away. Btw, is t he already supposed to fork over the gold once you cantch him anyways?


Yes he does. You always get shown an empty box regardless of which box you chose. If you pick an empty box he shows you the other empty box. If you pick the gold, he shows you one of the empty boxes. Your choice influences which box he shows you, but it is always empty. 

You always switch. the 1/3 of the time you picked the right box originally you get fucked. But the 2/3 of the time you picked the wrong box from the start, you end up switching to the only other possible choice which is gold.


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## cannabineer (Sep 17, 2012)

guy incognito said:


> Wait a minute, you would only be sending 33,554,432 on week 26. You would be sending 67,108,864 on week 27.
> 
> 2^(w-1) where w is the week number.
> 
> ...


The converging pyramid of letters for the first 25 weeks meets that criterion, yes. But the accident (unity chance, not part of the pyramid) adds one more letter for the round answer. cn


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## guy incognito (Sep 17, 2012)

cannabineer said:


> The converging pyramid of letters for the first 25 weeks meets that criterion, yes. But the accident (unity chance, not part of the pyramid) adds one more letter for the round answer. cn


No, all 26 weeks count. the 25th week he sends 2 letters out, one is right and one is wrong. The one that is correct gets targeted for an accident filling the final letter in the series.


weekletterstotal letters133,554,43233,554,432216,777,21650,331,64838,388,60858,720,25644,194,30462,914,56052,097,15265,011,71261,048,57666,060,2887524,28866,584,5768262,14466,846,7209131,07266,977,7921065,53667,043,3281132,76867,076,0961216,38467,092,480138,19267,100,672144,09667,104,768152,04867,106,816161,02467,107,8401751267,108,3521825667,108,6081912867,108,736206467,108,800213267,108,832221667,108,84823867,108,85624467,108,86025267,108,862261
67,108,863


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## cannabineer (Sep 17, 2012)

I just reviewed the OP and the mark did indeed receive 26 letters total. I concede the point. cn


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## Heisenberg (Jan 4, 2013)

Here is one I heard recently. I don't expect this to stump anyone, but it's fun to figure out.


*There is a table with three boxes on it, each with an incorrect label. One box is labeled "Buds", another box is labeled "Bongs", and the last box is labeled "Buds & Bongs". You are allowed to pick one box and pull one item from it. How can you label each box correctly?*


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## Zaehet Strife (Jan 4, 2013)

The box with buds and bongs in it must be the biggest box, so i would pick either the bud box, or the bongs box, the other smaller box will be the opposite of the box i picked. 

Or are all the boxes the same size and weight? 

I'm not good at these.


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## Heisenberg (Jan 4, 2013)

hehe

Nothing about the boxes themselves reveals the contents other than the labels.


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## Beefbisquit (Jan 4, 2013)

Heisenberg said:


> Here is one I heard recently. I don't expect this to stump anyone, but it's fun to figure out.
> 
> 
> There is a table with three boxes on it, each with an incorrect label. One box is labeled "Buds", another box is labeled "Bongs", and the last box is labeled "Buds & Bongs". You are allowed to pick one box and pull one item from it. How can you label each box correctly?


If each one is wrong, the one labeled 'bud and bongs' has to either be buds or bongs, not both. So, if you pull the buds out of it, the one labeled buds has to be bongs and the one labeled bongs has to be both buds and bongs. 

Likewise, if you lift the 'buds and bongs' and its bongs, the 'bongs' box has to have buds under it, as the 'buds' box can't have buds under it.


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## Heisenberg (Jan 4, 2013)

Beefbisquit said:


> If each one is wrong the one labeled 'bud and bongs' has to either be buds or bongs, not both. So, if you pull the buds out of it, the one labeled buds has to be bongs and the one labeled bongs has to be both buds and bongs.
> 
> Likewise, if you lift the 'buds and bongs' and its bongs, the 'bongs' box has to have buds under it, as the 'buds' box can't have buds under it.


Correct. If the one labeled "Buds & Bongs" is wrong, then it can only have one or the other. Once you find out which it is and switch the correct label to it, you only have one move left you can do, which is to switch labels on the remaining two boxes.


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## Beefbisquit (Jan 5, 2013)

Heisenberg said:


> Correct. If the one labeled "Buds & Bongs" is wrong, then it can only have one or the other. Once you find out which it is and switch the correct label to it, you only have one move left you can do, which is to switch labels on the remaining two boxes.


Reminded me of Sudoku strategy I use... lol


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## greenswag (Jan 6, 2013)

I'm confused, what if the 'buds and bong's box has bongs like you said. How come that makes the 'bongs' box, have to have buds, and the buds box have both buds and bongs? What if the bongs box has buds and bongs, and the buds box has bongs?

I just did it irl. you have the three [buds and bongs] [buds] [bongs] you looks in buds and bongs, there are buds. You remove the false label now you have -buds and bongs- [ ] [buds] [bongs] The problem is, you don't know which one to switch, who is to say [buds] has both buds and bongs to correctly switch the labels, thus making [bongs] labeled correct. Oh wait, if you know for a fact that they are ALL labeled incorrectly, then that means [bongs] must be false, and because you know the previous [buds and bongs] is actually [buds], you switch labels, making
[buds and bongs] = [buds]
[buds]= [bongs] and
[bongs]= [buds and bongs]
...right?

I was over thinking lol, I do that way too much I especially hated when they made test in school that you're too smart for and you start over analyzing what they say thinking "it can't be that simple" when it really was, would just have to deduce that every other answer was wrong. Still got the correct answer but it took a lot longer than needed -.-


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## cannabineer (Jan 6, 2013)

Someone posted a similar riddle in T&T I think, but the boxes were labeled "apples", "oranges", "apples&oranges". 
The rules were you could pull _one _article out of one box. 
I could not figure it out. cn


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## Heisenberg (Jan 6, 2013)

Glad you guys found it stimulating.  Reminded me a bit of the Monty Hall problem which is my favorite.


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## tyler.durden (Jan 6, 2013)

Heisenberg said:


> Glad you guys found it stimulating.  Reminded me a bit of the Monty Hall problem which is my favorite.


Goddamn Monty Hall problem. It still fucks with me - even though I get the answer intellectually, it doesn't sit right with my gut...


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## Beefbisquit (Jan 7, 2013)

tyler.durden said:


> Goddamn Monty Hall problem. It still fucks with me - even though I get the answer intellectually, it doesn't sit right with my gut...


I follow it. 

It still seems strange that in the second set of decisions, that choosing the same door again wouldn't still constitute a 1/2 choice.


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## SnakeByte (Jan 7, 2013)

sworth said:


> "...when you have eliminated the impossible, whatever remains, however improbable, must be the truth..."
> 
> Being psychic is impossible


And the evidence to support said fact? 
You can disprove false psychics. But not being psychic. Sorry.
Nice try though


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## Heisenberg (Jan 8, 2013)

SnakeByte said:


> And the evidence to support said fact?
> You can disprove false psychics. But not being psychic. Sorry.
> Nice try though


Yes, Psychics currently enjoy the same plausibility and level of evidence as gremlins, unicorns and The Kraken, which also can not be disproved.


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## Heisenberg (Jan 8, 2013)

Beefbisquit said:


> I follow it.
> 
> It still seems strange that in the second set of decisions, that choosing the same door again wouldn't still constitute a 1/2 choice.


It wouldn't. There has to be a switch in order to take advantage of the new odds. Imagine the original odds are 1/100. Monty reveals all doors but the one you chose, and one other. You see all doors that were opened had a goat. The one you chose has the same odds as before he revealed anything because your choice was arbitrary while his choice of which box to leave is not arbitrary. The one he left is either a goat or the real deal. He would only leave a goat IF you picked the car to begin with, so the chances of him leaving a goat are 1/100. If you chose a goat (99/100) he will leave the car. Now, imagine he doesn't give you a chance to change your pick, and just reveals the door he left, forcing you to stay with your original odds. The second thing that would force you to stay with your original odds is if he gives you a choice and you choose the same door; its no different than not having the choice. The door you picked is 1 of 100. The door he offers is 1 of 2. There has to be the action of switching before the odds change.

Lets say it's not doors, but instead he shows you a barrel containing 3 balloons and says one of them has glitter inside. He asks you to pull one out and place it on a table. He then pulls a magic balloon from his pocket and says IF the one you picked has glitter, this one will not. If the one you picked is empty, this one will have glitter. He puts it on the table and tells you to choose one. The magic balloon has the reverse odds of you. The odds you picked glitter are 1/3, making the odds of the magic balloon containing glitter, 2/3. When Monty shows you three doors and by process of elimination shows you that the remaining door's odds are chiral to yours, you have to switch to that door to take advantage of the magic.


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## tyler.durden (Jan 8, 2013)

^^ Still not sure I get it, Heis. Would you post an analogy using strippers?


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## mindphuk (Jan 8, 2013)

Beefbisquit said:


> I follow it.
> 
> It still seems strange that in the second set of decisions, that choosing the same door again wouldn't still constitute a 1/2 choice.


The reason the probability changes is based on one important fact. The person revealing the other door has perfect information, which then gives you new information. IOW, Monty KNOWS which of the other door has the goat or the prize. By revealing the goat, he effectively created a new game.


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## cannabineer (Jan 8, 2013)

tyler.durden said:


> ^^ Still not sure I get it, Heis. Would you post an analogy using strippers?


They won't show you the one who is the Tuckmaster. cn


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## Heisenberg (Feb 3, 2013)

This is going to sound similar to a previous one, but pay attention.

*You meet an old friend on the bus. He tells you he has two children. One is a girl born on a Friday. What are the odds that your friend has two daughters?
*


No trick of words or logic, I just want to know the mathematical chance based on the information given.


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## Beefbisquit (Feb 3, 2013)

Heisenberg said:


> This is going to sound similar to a previous one, but pay attention.
> 
> You meet an old friend on the bus. He tells you he has two children. One is a girl born on a Friday. What are the odds that your friend has two daughters?
> 
> ...


The fact that he has a daughter already doesn't have any bearing on the odds of his second child being a female. 50/50 chance of it being a female.


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## Heisenberg (Feb 3, 2013)

Beefbisquit said:


> The fact that he has a daughter already doesn't have any bearing on the odds of his second child being a female. 50/50 chance of it being a female.


This would be correct if the question was, what are the chances of the second child being a girl. The question is, given what you know, what are the chances he has two daughters.


See this post for a previous similar question and answer.


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## Beefbisquit (Feb 3, 2013)

Heisenberg said:


> This would be correct if the question was, what are the chances of the second child being a girl. The question is, given what you know, what are the chances he has two daughters.
> 
> 
> See this post for a previous similar question and answer.


There's a total of four outcomes for the two pregnancy's. Two outcomes for the first and two for the second. 1/2 x 1/2= 1/4 or .25%


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## Heisenberg (Feb 3, 2013)

Beefbisquit said:


> There's a total of four outcomes for the two pregnancy's. Two outcomes for the first and two for the second. 1/2 x 1/2= 1/4 or .25%


I am inclined to agree with your logic, though you need to take it a step further and eliminate the boy/boy outcome, so 1/3 chance.


But alas that is not the answer this time because it doesn't account for all the information given...


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## mindphuk (Feb 3, 2013)

Heisenberg said:


> I am inclined to agree with your logic, though you need to take it a step further and eliminate the boy/boy outcome, so 1/3 chance.
> 
> 
> But alas that is not the answer this time because it doesn't account for all the information given...


50%
You designated one as 'being born on a Friday.' That makes the other one either a boy or a girl. In the first scenario, you had the situation where child 1 could be a girl or a boy and child 2 a girl or a boy. Here, you have defined child 1 as a girl, leaving the only probability left with child 2. You eliminate one of the b-g combinations from the original 1 in 3 chance.


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## Heisenberg (Feb 4, 2013)

I didn't mean to imply that the first born was a girl, though I see I have inadvertently suggested that in my response to BB. 

We know he has two children, one of the children is female born on a Friday.


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## NietzscheKeen (Feb 4, 2013)

Why am I just now finding this thread!? It will take me a while to catch up on all the posts, but at least it is intriguing.


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## Beefbisquit (Feb 4, 2013)

Heisenberg said:


> I didn't mean to imply that the first born was a girl, though I see I have inadvertently suggested that in my response to BB.
> 
> We know he has two children, one of the children is female born on a Friday.


OoOoooo....


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## mindphuk (Feb 4, 2013)

Heisenberg said:


> I didn't mean to imply that the first born was a girl, though I see I have inadvertently suggested that in my response to BB.
> 
> We know he has two children, one of the children is female born on a Friday.


We don't need to know who was born first, only that a child was specifically identified. We can just call her Friday. Friday has 100% chance of being a girl. The other child has a 50% chance, which is the same as the odds that both are girls. I don't see how 2:3 would work, but if that's the right answer, please detail.


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## cannabineer (Feb 4, 2013)

I'll give this a whack. i am reading the setup to say that the other is not a girl born on a Friday. If the other is a girl, she'd have to be born on one of the remaining days of the week. A boy would be under no such constraint. I am assuming that the chances of a pregnancy being a boy or girl are at 50/50. So I'm calling a ~46% chance (six out of thirteen) chance that he has two daughters. cn


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## mindphuk (Feb 4, 2013)

cannabineer said:


> I'll give this a whack. i am reading the setup to say that the other is not a girl born on a Friday.


I don't see that as a valid assumption. It could have been, "I have one girl, born on a Friday, and the other girl also happened to be born on a Friday." We only have information about one girl, it doesn't eliminate anything about the second child.


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## Heisenberg (Feb 4, 2013)

Well lets back up a bit. The chance that any man who has sired two children will have two daughters is 1/4. Each birth has a 1/2 chance of being female. 1/2 x 1/2 = 1/4. The possibilities are , MM, MF, FM, FF. Since we know at least one event resulted in female, we eliminate the MM, leaving us with 1/3 chance of the man having two daughters.

Now we are given additional information. The female was born on a Friday. Do we need to adjust our calculations to account for this new information, or is it irrelevant? Do the odds change?


I'll give a little more time before I reveal the answer.


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## cannabineer (Feb 4, 2013)

mindphuk said:


> I don't see that as a valid assumption. It could have been, "I have one girl, born on a Friday, and the other girl also happened to be born on a Friday." We only have information about one girl, it doesn't eliminate anything about the second child.


I've been trying to see how this could be a Monty Hall problem but can't. If it were, then the answer (omitting the trickiness about weekdays) would be one out of three, since BB, GB, GG and BG each have equal probability of being a two-child father's family. (And of the four, only BB is disqualified by Dad's reply.) But I just cannot get past unity probability for one girl = 1/2 probability for two. Someone he'p! cn


<edit> lol. If I incorporate the weekday trickiness, then the chance of two girls is 12/20 or 60%.


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## Heisenberg (Feb 4, 2013)

You do have to assume uniformity over gender and days of the week, if that helps.


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## cannabineer (Feb 4, 2013)

Heisenberg said:


> Well lets back up a bit. The chance that any man who has sired two children will have two daughters is 1/4. Each birth has a 1/2 chance of being female. 1/2 x 1/2 = 1/4. The possibilities are , MM, MF, FM, FF. Since we know at least one event resulted in female, we eliminate the MM, leaving us with 1/3 chance of the man having two daughters.
> 
> Now we are given additional information. *The female was born on a Friday. Do we need to adjust our calculations to account for this new information, or is it irrelevant? Do the odds change?
> *
> ...


I would say No. The man volunteered that the girl was born on a Friday, discharging any selection bias for that day. 
These father/child problems make me say Uncle. cn


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## Heisenberg (Feb 4, 2013)

cannabineer said:


> I would say No. The man volunteered that the girl was born on a Friday, discharging any selection bias for that day.
> These father/child problems make me say Uncle. cn



You are on the right track, but as MP said, you can not make any assumptions about the other child. It could be a boy or a girl, and could have been born on any day of the week.


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## cannabineer (Feb 4, 2013)

Heisenberg said:


> You are on the right track, but as MP said, you can not make any assumptions about the other child. It could be a boy or a girl, and could have been born on any day of the week.


If that is so, I'll say two out of three. 

If this is indeed a Monty Hall problem. 
Is there a way to recognize those as a class? cn


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## mindphuk (Feb 4, 2013)

Heisenberg said:


> Well lets back up a bit. The chance that any man who has sired two children will have two daughters is 1/4. Each birth has a 1/2 chance of being female. 1/2 x 1/2 = 1/4. The possibilities are , MM, MF, FM, FF. Since we know at least one event resulted in female, we eliminate the MM, leaving us with 1/3 chance of the man having two daughters.
> 
> Now we are given additional information. The female was born on a Friday. Do we need to adjust our calculations to account for this new information, or is it irrelevant? Do the odds change?
> 
> ...


Okay, let's break down the number of possibilities. For g-b we have 7 distinct possibilities, the girl on a Friday and the boy on one of the 7 days.
For the b-g, we have the same 7 possibilities.
For the g-g, we have only 13, not 14 as we shouldn't count Friday-Friday twice. So we have 27 possibilities and only 13 are two girls making 13/27 or 48.1%
If we take 'neer's belief that one and only one girl is born on a Friday, then we get 12/26 or 6/13 or 46.1%


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## Heisenberg (Feb 4, 2013)

mindphuk said:


> Okay, let's break down the number of possibilities. For g-b we have 7 distinct possibilities, the girl on a Friday and the boy on one of the 7 days.
> For the b-g, we have the same 7 possibilities.
> For the g-g, we have only 13, not 14 as we shouldn't count Friday-Friday twice. So we have 27 possibilities and only 13 are two girls making 13/27 or 48.1%
> If we take 'neer's belief that one and only one girl is born on a Friday, then we get 12/26 or 6/13 or 46.1%


Absolutely correct! The trick lies in not counting the Friday possibilities twice.

By supplying a bit of seemingly irrelevant information the man changed the odds quite a bit from 1/3 to 13/27. The more specific and rare the information provided (weekdays are 1/7), the closer the chance of having two daughters gets to 50%.


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## Heisenberg (Feb 4, 2013)

Here is an official explanation, except this changes the gender to boys and the weekday to Tuesday.




Let's list the equally likely possibilities of children, together with the days of the week they are born in. Let's call a boy born on a Tuesday a BTu. Our possible situations are:


When the first child is a BTu and the second is a girl born on any day of the week: there are seven different possibilities.
When the first child is a girl born on any day of the week and the second is a BTu: again, there are seven different possibilities.
When the first child is a BTu and the second is a boy born on any day of the week: again there are seven different possibilities.
Finally, there is the situation in which the first child is a boy born on any day of the week and the second child is a BTu &#8211; and this is where it gets interesting. There are seven different possibilities here too, but one of them &#8211; when both boys are born on a Tuesday &#8211; has already been counted when we considered the first to be a BTu and the second on any day of the week. So, since we are counting equally likely possibilities, we can only find an extra six possibilities here.


Summing up the totals, there are 7 + 7 + 7 + 6 = 27 different equally likely combinations of children with specified gender and birth day, and 13 of these combinations are two boys. So the answer is 13/27, which is very different from 1/3.


It seems remarkable that the probability of having two boys changes from 1/3 to 13/27 when the birth day of one boy is stated &#8211; yet it does, and it's quite a generous difference at that.

http://www.newscientist.com/article/dn18950-magic-numbers-a-meeting-of-mathemagical-tricksters.html?full=true


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