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gordonm888
gordonm888
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February 10th, 2019 at 10:40:16 AM permalink
A few thoughts


Consider the end of the chain of purchases. When the purchase price gets down to one penny then that last purchaser will be unable to re-sell the bottle and will be confined to hell for eternity. In principle, no one will buy it under those conditions. Indeed, no one would buy the bottle for two cents, because they should be unable to sell it for one cent. Extending this logic, no one would be able to sell the bottle because at any point in the chain they should be unable to find a subsequent buyer.

That indeed may be the answer that is looked for by the Wizard. The fear of being unable to find a buyer will prevent anyone from selling it.

But perhaps this logical chain can be broken. Because there will always be buyers, just as there will always be gamblers who will play 6:5 blackjack.

Buyers who might be willing to be the last person to buy the bottle for one penny, or for a few pennies, would be:

1. People who are going to Hell anyway. Mass murderers. Or Donald Trump and Hillary Clinton. (uh-oh. A hijack?)
2. People who do not believe in Hell. Atheists and non-Christians.
3. People who are not logicians. The Kardashians, for example.
4. Hedonists who opt for short-term pleasure (their grant of a wish by the genie) despite long-term consequences. Drug addicts and alcoholics. Men with a hard-on. Women with a credit card. Et cetera. (ooh, descending into sexism here, not a pretty thing.)
5. People who are willing to martyr themselves for something they love. Example: A parent with a child who is dying a slow painful death.

There might also be tactics for breaking the logical chain. Something involving time reversal (which was not specifically ruled out in the problem statement.) Wishing that any subsequent buyer will immediately die before they can can re-sell the bottle. Wishing for eternal life for all buyers of the bottle, including yourself.


However, none of these possible solutions seem to result in a "least amount you should pay." So I assume the Wizard envisions a different solution to this problem.

P.S. Wow, young Barbara Eden was really hot, wasn't she?
unJon
unJon
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February 10th, 2019 at 11:01:33 AM permalink
Quote: gordonm888

A few thoughts


Consider the end of the chain of purchases. When the purchase price gets down to one penny then that last purchaser will be unable to re-sell the bottle and will be confined to hell for eternity. In principle, no one will buy it under those conditions. Indeed, no one would buy the bottle for two cents, because they should be unable to sell it for one cent. Extending this logic, no one would be able to sell the bottle because at any point in the chain they should be unable to find a subsequent buyer.

That indeed may be the answer that is looked for by the Wizard. The fear of being unable to find a buyer will prevent anyone from selling it.

But perhaps this logical chain can be broken. Because there will always be buyers, just as there will always be gamblers who will play 6:5 blackjack.

Buyers who might be willing to be the last person to buy the bottle for one penny, or for a few pennies, would be:

1. People who are going to Hell anyway. Mass murderers. Or Donald Trump and Hillary Clinton. (uh-oh. A hijack?)
2. People who do not believe in Hell. Atheists and non-Christians.
3. People who are not logicians. The Kardashians, for example.
4. Hedonists who opt for short-term pleasure (their grant of a wish by the genie) despite long-term consequences. Drug addicts and alcoholics. Men with a hard-on. Women with a credit card. Et cetera. (ooh, descending into sexism here, not a pretty thing.)
5. People who are willing to martyr themselves for something they love. Example: A parent with a child who is dying a slow painful death.

There might also be tactics for breaking the logical chain. Something involving time reversal (which was not specifically ruled out in the problem statement.) Wishing that any subsequent buyer will immediately die before they can can re-sell the bottle. Wishing for eternal life for all buyers of the bottle, including yourself.


However, none of these possible solutions seem to result in a "least amount you should pay." So I assume the Wizard envisions a different solution to this problem.

P.S. Wow, young Barbara Eden was really hot, wasn't she?

This is why I wanted to know if I could make a compound wish:

Buy for two cents then wish for the thing you want delivered to you by an atheist logician
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
Wizard
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Wizard
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February 10th, 2019 at 12:08:55 PM permalink
Quote: unJon

A few questions:

1) Can you sell it for negative amounts (ie, pay someone to take it)?

2) Can you make compound wishes (ie, I wish I had A and B)?

3) Is there such a thing as an uncountable infinite amount of U.S. currency in this hypothetical world of real genies and hell?

4) Can the same person own the genie more than once?

This reminds me of that Twighlight Zone episode where a man brings a box with a red button and tells the couple that if they push the red button someone they donít know will be killed and the couple will receive a million dollars.



1. No
2. No -- that would be like asking for "more wishes."
3. No, but I don't think that plays into it.
4. I don't see why not, but you can't sell it to yourself. However, I will say that collusion is not allowed.
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard
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Wizard
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February 10th, 2019 at 12:10:53 PM permalink
Quote: Dalex64

I would pay a penny.

I would pre-arrange a buyer, take him to the sale, take his money and add my penny and buy the bottle, make my wish and hand over the bottle to my buyer.



Given that the pre-arranged buyer must be a logician, I think he would want to know what he will have to pay. In other words, you need to be more specific.
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard
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Wizard
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February 10th, 2019 at 12:17:15 PM permalink
I think it's safe to unhide your portion about the possible buyers. First, let me remind you of part of the original question -- "You have no reason to doubt the stranger's offer. You believe in hell and expect to not otherwise go there. What is the least amount you should pay? "

Quote: gordonm888

Buyers who might be willing to be the last person to buy the bottle for one penny, or for a few pennies, would be:

1. People who are going to Hell anyway. Mass murderers. Or Donald Trump and Hillary Clinton. (uh-oh. A hijack?)
2. People who do not believe in Hell. Atheists and non-Christians.
3. People who are not logicians. The Kardashians, for example.
4. Hedonists who opt for short-term pleasure (their grant of a wish by the genie) despite long-term consequences. Drug addicts and alcoholics. Men with a hard-on. Women with a credit card. Et cetera. (ooh, descending into sexism here, not a pretty thing.)
5. People who are willing to martyr themselves for something they love. Example: A parent with a child who is dying a slow painful death.



1. Maybe I should have been more clear, but all logicians would be in the same shoes you are, in particular believing in hell and also believing they would not otherwise go there.
2. See #1
3. I said you had to sell it to a logician.
4. I would argue such people can't be logicians, as their life choices are not very logical.
5. That's probably your strongest point. However, again, we're trying to keep this simple and pertinent information like that was not left out.
It's not whether you win or lose; it's whether or not you had a good bet.
gordonm888
gordonm888
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February 10th, 2019 at 1:08:47 PM permalink
Quote: Wizard


1. Maybe I should have been more clear, but all logicians would be in the same shoes you are, in particular believing in hell and also believing they would not otherwise go there.
2. See #1
3. I said you had to sell it to a logician.
4. I would argue such people can't be logicians, as their life choices are not very logical.
5. That's probably your strongest point. However, again, we're trying to keep this simple and pertinent information like that was not left out.



These answers are fair enough. The point that was really not clear to me (and still may not have been stated as explicitly as you intended) is that the genie's bottle can only be sold to logicians -not only by you but by anyone else who sells the bottle.

In actuality, I wonder how many people would qualify as logicians. I think the 'problem statement' intends us to assume an essentially infinite supply of logicians and money -that our solution to the problem should not exploit the fact that there are only 300 logicians in the US, or that some of them are broke and can't afford a genie bottle. :) This is a logic problem that is dressed up as a dilemma involving human beings.
ChesterDog
ChesterDog
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February 10th, 2019 at 1:35:21 PM permalink
Quote: Wizard

A stranger offers to sell you a bottle containing a genie. The genie will grant her owner, and any subsequent new owner, one wish. As usual, with genie puzzles, you can't ask for more wishes or anything that would negate the deal to buy the bottle. That said, the only rule is within a year of buying the bottle, you must sell it to another logician for less that what you paid. The rules to the new owner will be the same as for you and you must be truthful about them. The transaction must be in U.S. currency and in amounts evenly divisible by a penny. If you do not find such a buyer, you will spend eternity in hell. You have no reason to doubt the stranger's offer. You believe in hell and expect to not otherwise go there. What is the least amount you should pay?...



Assume there is a minimum price you, a logician, would pay. All logicians would have the same minimum price since they all use the same correct reasoning. But any new selling price would be at least one cent lower than the previous selling price, which contradicts the fact that all logicians would have the same minimum. Therefore, the original assumption is wrong, and there is no answer.
Wizard
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Wizard
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February 10th, 2019 at 1:55:16 PM permalink
Quote: ChesterDog

Assume there is a minimum price you, a logician, would pay. All logicians would have the same minimum price since they all use the same correct reasoning. But any new selling price would be at least one cent lower than the previous selling price, which contradicts the fact that all logicians would have the same minimum. Therefore, the original assumption is wrong, and there is no answer.



To that, I would say that not all logicians think exactly alike. To a point Gordon made, nor do they all have exactly the same amount of money. However, we can assume for the problem that there are plenty of logicians.
It's not whether you win or lose; it's whether or not you had a good bet.
CrystalMath
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February 10th, 2019 at 1:57:30 PM permalink
You could wish to be Satan, then hell wonít seem so bad.
I heart Crystal Math.
SOOPOO
SOOPOO
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February 10th, 2019 at 2:04:20 PM permalink
Quote: Wizard

Quote: ChesterDog

Assume there is a minimum price you, a logician, would pay. All logicians would have the same minimum price since they all use the same correct reasoning. But any new selling price would be at least one cent lower than the previous selling price, which contradicts the fact that all logicians would have the same minimum. Therefore, the original assumption is wrong, and there is no answer.



To that, I would say that not all logicians think exactly alike. To a point Gordon made, nor do they all have exactly the same amount of money. However, we can assume for the problem that there are plenty of logicians.



I like Chester's answer far more than your response to Chester. I believe for the purpose of a puzzle like this all logicians should think exactly alike. And how much money someone has is clearly a red herring in a puzzle like this. Should be no factor. Someone deciding on whether they will spend eternity in hell should be bankroll independent.

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