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Crazy Thought Experiment/Logic Problem

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Re: Crazy Thought Experiment/Logic Problem

Postby Gold Bearer » Monday July 4th, 2016 5:39pm

knightkrawler wrote:Both of them seeing each other clears it up.
Prisoner A picks the color he sees on B, prisoner B picks the color he doesn't see on A.
The right guess is green:

situation: A white B white
guesses: A white B blue

situation: A blue B white
guesses: A white B white

situation: A white B blue
guesses: A blue B blue

situation: A blue B blue
guesses: A blue B white
|_P One says they're wearing the same colour hat, one says they're wearing different coloured hats. One must be right.

mitchiemasha wrote:
They can see each other in the courtyard but can't communicate.
Now you never said that. The separately thing confuses this, implies they can't see each other. Other wise it's easy... the 3 hat riddle is better.
Three hat riddle? Let's hear it. :)

Goblin-King wrote:I thought they were in separate rooms. They can see the other prisoner's hat, but not their own, right?
Right. I didn't want to spell out that they could see each other because it would be too much of a give away so I said they're tied up so they couldn't communicate. If they couldn't see each other they'd be no reason for them to be tied up.
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Re: Crazy Thought Experiment/Logic Problem

Postby Big Bene » Tuesday July 5th, 2016 5:19am

Gold Bearer wrote:I know that one. :)

I knew the first one.
It was published by Martin Gardner in Science Fiction Puzzle Tales (normally this means he published it before in Scientific American, and there probably is an even older version as a sort of insider-joke of mathematicans, which he formed into a simple yet intriguing riddle in his usually ingenious way - can't check by now, as I my copy is buried somewhere in a box).
Gardner even cited it as an argument against the omniscience of god (he was a great forethinker of the "sceptic" movement, which he left at an early stage as it became dogmatic and singleminded).
I had - and have - my own thoughts about it, but I don't have the time quite now to read through seven pages of popular epistemology.
Have a look ;)


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Re: Crazy Thought Experiment/Logic Problem

Postby Big Bene » Tuesday July 5th, 2016 5:42am

E) If the heroes search this room, tell them there is an intresting looking book lying on the altar. If a hero wants to investigate, he has to stand next to the altar.
The book reads:
"Behold the prophecy of the unknown god! Two chests shall be revealed, and great fortune is to be found inside, so choose wisely.
The left chest holds 100 coins of pure gold, the right chest may contain 20 coins or may contain 600 coins.
You may open either the left chest only or you may open both chests.
If you are to choose only the left chest, I did put 600 coins into the right one, but if you choose both, I did put only 20 coint into the right one.
The gold is already in there in nothing will change the amount. I already put it in there, for I knew your mind before you made your decision and I looked into your heart before you were concepted. Whatever you do, I did what I did and I will not change it".
After you finished reading, two secret doors open to the left and to the right of teh altar, each revealing a small niche of one square size, containing a treasure chest.
Have a look ;)


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Re: Crazy Thought Experiment/Logic Problem

Postby Big Bene » Tuesday July 5th, 2016 6:04am

And for the spacegoat:
If I really want the car, I would change my choice.
The door I first choose has a car chance of 1/3.
This chance doesn't change, since the host only opens the hint door after I did my choice.
But after he opened it, the last door remaining has a car chance of 1/2, which is a better chance than the 1/3 of the door a choose first.
Have a look ;)


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Re: Crazy Thought Experiment/Logic Problem

Postby Goblin-King » Tuesday July 5th, 2016 8:37am

Big Bene wrote:E) If the heroes search this room, tell them there is an intresting looking book lying on the altar. If a hero wants to investigate, he has to stand next to the altar.
The book reads:
"Behold the prophecy of the unknown god! Two chests shall be revealed, and great fortune is to be found inside, so choose wisely.
The left chest holds 100 coins of pure gold, the right chest may contain 20 coins or may contain 600 coins.
You may open either the left chest only or you may open both chests.
If you are to choose only the left chest, I did put 600 coins into the right one, but if you choose both, I did put only 20 coint into the right one.
The gold is already in there in nothing will change the amount. I already put it in there, for I knew your mind before you made your decision and I looked into your heart before you were concepted. Whatever you do, I did what I did and I will not change it".
After you finished reading, two secret doors open to the left and to the right of teh altar, each revealing a small niche of one square size, containing a treasure chest.

Big Bene wrote:And for the spacegoat:
If I really want the car, I would change my choice.
The door I first choose has a car chance of 1/3.
This chance doesn't change, since the host only opens the hint door after I did my choice.
But after he opened it, the last door remaining has a car chance of 1/2, which is a better chance than the 1/3 of the door a choose first.


Actually this scenario would be fitting for HeroQuest.
Three doors and a goblin "host" presenting either the final reward or even three different routes, two dangerous and one breeze.
Man! This gives me an idea for a quest!

So how about that! An off-topic thread, where everybody participates politely, and it even loops back and becomes HQ related?
Well done friends! Well done! |_P

Other logical puzzles/problems that can be converted to HQ?


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Re: Crazy Thought Experiment/Logic Problem

Postby knightkrawler » Tuesday July 5th, 2016 3:45pm

Big Bene wrote:E) If the heroes search this room, tell them there is an intresting looking book lying on the altar. If a hero wants to investigate, he has to stand next to the altar.
The book reads:
"Behold the prophecy of the unknown god! Two chests shall be revealed, and great fortune is to be found inside, so choose wisely.
The left chest holds 100 coins of pure gold, the right chest may contain 20 coins or may contain 600 coins.
You may open either the left chest only or you may open both chests.
If you are to choose only the left chest, I did put 600 coins into the right one, but if you choose both, I did put only 20 coint into the right one.
The gold is already in there in nothing will change the amount. I already put it in there, for I knew your mind before you made your decision and I looked into your heart before you were concepted. Whatever you do, I did what I did and I will not change it".
After you finished reading, two secret doors open to the left and to the right of teh altar, each revealing a small niche of one square size, containing a treasure chest.


This is actually different than the version GB presented.
Here, the conundrum GB intended for everyone to see is there.

With GB's riddle, the player could pick either the one with the potentially high amount or both. NO QUESTION THAT YOU PICK ONLY B.
Here with BB, the player can pick either the medium amount or both. CONUNDRUM: WHAT TO PICK?

Or did my brains go in a complete twist now?
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Re: Crazy Thought Experiment/Logic Problem

Postby Gold Bearer » Tuesday July 5th, 2016 4:05pm

knightkrawler wrote:
Big Bene wrote:E) If the heroes search this room, tell them there is an intresting looking book lying on the altar. If a hero wants to investigate, he has to stand next to the altar.
The book reads:
"Behold the prophecy of the unknown god! Two chests shall be revealed, and great fortune is to be found inside, so choose wisely.
The left chest holds 100 coins of pure gold, the right chest may contain 20 coins or may contain 600 coins.
You may open either the left chest only or you may open both chests.
If you are to choose only the left chest, I did put 600 coins into the right one, but if you choose both, I did put only 20 coint into the right one.
The gold is already in there in nothing will change the amount. I already put it in there, for I knew your mind before you made your decision and I looked into your heart before you were concepted. Whatever you do, I did what I did and I will not change it".
After you finished reading, two secret doors open to the left and to the right of teh altar, each revealing a small niche of one square size, containing a treasure chest.
This is actually different than the version GB presented.
Here, the conundrum GB intended for everyone to see is there.

With GB's riddle, the player could pick either the one with the potentially high amount or both. NO QUESTION THAT YOU PICK ONLY B.
Here with BB, the player can pick either the medium amount or both. CONUNDRUM: WHAT TO PICK?

Or did my brains go in a complete twist now?
They must have. That version's wrong, you can't get box B without taking both boxes so you wouldn't be able to get the million unless the computer was wrong.

Big Bene wrote:
Gold Bearer wrote:I know that one. :)
I knew the first one.
It was published by Martin Gardner in Science Fiction Puzzle Tales (normally this means he published it before in Scientific American, and there probably is an even older version as a sort of insider-joke of mathematicans, which he formed into a simple yet intriguing riddle in his usually ingenious way - can't check by now, as I my copy is buried somewhere in a box).
Gardner even cited it as an argument against the omniscience of god (he was a great forethinker of the "sceptic" movement, which he left at an early stage as it became dogmatic and singleminded).
I had - and have - my own thoughts about it, but I don't have the time quite now to read through seven pages of popular epistemology.
I did some some digging on it yesterday, it's called Newcomb's Problem, after Willian Newcomb.

"Newcomb's paradox was created by William Newcomb of the University of California's Lawrence Livermore Laboratory. However, it was first analyzed and was published in a philosophy paper spread to the philosophical community by Robert Nozick in 1969, and appeared in Martin Gardner's Scientific American column in 1974. Today it is a much debated problem in the philosophical branch of decision theory but has received little attention from the mathematical side."

"To almost everyone, it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly."
Glad to say I'm definitely not one of the almost everyone, I still can't decide whats best.
Head: Your decision can't affect the outcome of what's in box B so obviously take both.
Heart: Don't you want to win 1,000,000 galactic space credits? You, tummy...
Head: Your being irrational, it's already been decided what's in box B so take both.
"I'll take both." "Okay, you've won 1,100 galactic space credits."
Head: Well at least you got an extra 100.
Heart: No, you just lost 998,900!
Head: You're being irrational again.
Heart: Everyone that's picked both boxes has gotten 1,000. Everyone that picked just box B is now a millionaire. You knew this but you chose to take both. So which one of us is irrational?
And so on.

This is really weird but actually makes sense if you take the logic further and think that in the future an AI will be able to simulate the consciousness of people that have died: http://www.slate.com/articles/technolog ... _time.html

Big Bene wrote:E) If the heroes search this room, tell them there is an intresting looking book lying on the altar. If a hero wants to investigate, he has to stand next to the altar.
The book reads:
"Behold the prophecy of the unknown god! Two chests shall be revealed, and great fortune is to be found inside, so choose wisely.
The left chest holds 100 coins of pure gold, the right chest may contain 20 coins or may contain 600 coins.
You may open either the left chest only or you may open both chests.
If you are to choose only the left chest, I did put 600 coins into the right one, but if you choose both, I did put only 20 coint into the right one.
The gold is already in there in nothing will change the amount. I already put it in there, for I knew your mind before you made your decision and I looked into your heart before you were concepted. Whatever you do, I did what I did and I will not change it".
After you finished reading, two secret doors open to the left and to the right of teh altar, each revealing a small niche of one square size, containing a treasure chest.
"You may open either the left chest only or you may open both chests." You mean either the right chest or both chests.

This wouldn't really work, it needs a super-powerful prediction mechanism or there's just no point in taking one box. What you could do is give them that choice and have it affect a later one. Do it a second time with double the amount of gold. If they chose just the one chest then the variable chest has the higher amount second time and the lower amount if they chose both the first time.

Big Bene wrote:And for the spacegoat:
If I really want the car, I would change my choice.
The door I first choose has a car chance of 1/3.
This chance doesn't change, since the host only opens the hint door after I did my choice.
But after he opened it, the last door remaining has a car chance of 1/2, which is a better chance than the 1/3 of the door a choose first.
The last remaining door after one has been has been eliminated has a 2/3 chance, not 1/2. It has to equal 1. You stand a one in three chance of being right with your first choice so after one has been eliminated you stand a two in three chance if you switch, simply because the one in three chance if you change before a door has been eliminated gets double when the two remaining doors are halved to one other door.

Goblin-King wrote:So how about that! An off-topic thread, where everybody participates politely, and it even loops back and becomes HQ related?
Well done friends! Well done! |_P
And we've mentioned science, recreational drugs and religion, as well as hookers, space goats and space goat hookers for good measure. :)

Goblin-King wrote:Other logical puzzles/problems that can be converted to HQ?
The two hats one could work really well, if it's set up right. One hero gets trapped in a bubble, an NPC is there also trapped inside a blue bubble. A puzzle loving evil magician appears and tells the hero 'insert two hat problem here', that they can't see the colour of they're own bubble because it can only be seen from the outside, that they aren't allowed to ask the NPC what colour their bubble is or to tell the NPC what colour theirs is and that they will be rewarded if they can figure out a way to guarantee that one of them gets it right.

I still want to hear this three hats problem!
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Re: Crazy Thought Experiment/Logic Problem

Postby knightkrawler » Tuesday July 5th, 2016 4:45pm

That threesome yesterday with the spacegoathookers really got my hat too tight.

I misthought and mistyped, but BB's version is still not analogous to yours.
The assessment that there's a real conundrum in his and none in yours still stands because in BB's version, it's the compromise sum/the safe bet that you can pick alone;
in your version, it's the variable sum that you can pick alone.

Your version of the riddle, to me, is still a big honkin' allegory for belief in God playing a role in your life or not.
BB's version is a real logic problem.
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Re: Crazy Thought Experiment/Logic Problem

Postby Gold Bearer » Tuesday July 5th, 2016 5:13pm

If you can take box A or both boxes then the only reason to take both is if you think the computer is wrong. Defeats the object.

Doing it the proper way means that each choice is logically better than the other, depending on how you approach it.
:goblin: 1BP, :orc: 2BP, :fimir: 3BP, :skeleton: 1BP, :zombie: 2BP, :mummy: 3BP, :chaoswarrior: 4BP, :gargoyle: 5BP. US :chaoswarrior: 3BP, US :gargoyle: 4BP.

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Re: Crazy Thought Experiment/Logic Problem

Postby Goblin-King » Tuesday July 5th, 2016 6:30pm

The computer has never guessed wrong. That means it's predictions are very reliable.

If you pick A+B the computer would predict that and you'd get 1,100
If you pick B the computer would have predicted that as well and you'd get 1,000,000

If the computer has guessed correct every time up till now there's no reason it'd suddenly guess wrong now.
There's no "cheating" the computer. How would choosing both ever result in the computer not predicting exactly that?

Is the logic of taking both that you are at least guaranteed 1,000?


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