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Epic Mathematics
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Post by
165617
This post was from a user who has deleted their account.
Post by
MyTie
Here's something to ponder on. It's a variation of the notorious logic puzzle where you have 2 doors and 2 people, one always telling the truth, one always lies.
Three gods guard three doors in an unknown order. The three doors lead to Hell, Heaven, and Limbo, respectively; the three gods are Truth, who always tells the truth, False, who always lies, and Random, who answers randomly. The gods understand English (and other languages for that matter), but will only speak a two-word language in which Ja and Da mean 'yes' and 'no,' but you do not know which means which. The Random's mind can be modeled as a fair coin flip for which, if it lands heads, he will say Ja; if tails, Da.
You can ask up to three yes-no questions total, each to one god (though any god can be questioned more than once). Which three questions should you ask to determine which door leads to Heaven (you do not need to determine any other information).
If a god is faced with a question to which either answer is possible or neither answer is possible, he answers randomly.
Taken from
XKCD IRC Puzzles
EDIT
: Come to think of it, that's not exactly math. It's logic. But they go hand by hand, so whatever.
This is possibly the hardest puzzle I've come across. Logically... hmmm.... You have to ask a question that both true and false are going to to answer the same too, which is, a question inside a question. There also will come a point where you are going to have to deal with the random answer, which should be done by assumption.
Let me think more...
Post by
Blitzfire
How does 4+4=10?
Note: I have done this on a calculator.
Post by
104658
This post was from a user who has deleted their account.
Post by
Haxzor
How does 4+4=10?
Note: I have done this on a calculator.
ahahahaha
Post by
ASHelmy
Here's something to ponder on. It's a variation of the notorious logic puzzle where you have 2 doors and 2 people, one always telling the truth, one always lies.
Three gods guard three doors in an unknown order. The three doors lead to Hell, Heaven, and Limbo, respectively; the three gods are Truth, who always tells the truth, False, who always lies, and Random, who answers randomly. The gods understand English (and other languages for that matter), but will only speak a two-word language in which Ja and Da mean 'yes' and 'no,' but you do not know which means which. The Random's mind can be modeled as a fair coin flip for which, if it lands heads, he will say Ja; if tails, Da.
You can ask up to three yes-no questions total, each to one god (though any god can be questioned more than once). Which three questions should you ask to determine which door leads to Heaven (you do not need to determine any other information).
If a god is faced with a question to which either answer is possible or neither answer is possible, he answers randomly.
Taken from
XKCD IRC Puzzles
EDIT
: Come to think of it, that's not exactly math. It's logic. But they go hand by hand, so whatever.
This is possibly the hardest puzzle I've come across. Logically... hmmm.... You have to ask a question that both true and false are going to to answer the same too, which is, a question inside a question. There also will come a point where you are going to have to deal with the random answer, which should be done by assumption.
Let me think more...
We ask Truth if he is guarding the door to heaven, he will say ja (for example). We then ask False if he he is guarding the door to heaven, he will say either ja, or da. Assume that ja means yes, there is one possible answer, ja from truth and ja from false (which would mean that Truth guards the door to heaven). Now, if ja means no, then there will be two possible answers. Ja from truth, and ja from False (which would mean that False guards the door), or ja from truth and da from false (which would mean that random guards the door). We then ask truth if ja means yes, that should solves it.
I probably messed up somewhere, or misunderstood the question; I usually suck at this sort of thing.
Post by
Haxzor
Do we know which one is which?
Post by
ASHelmy
I have no idea, also, my solution needs tweaking, since we wouldn't know if ja means yes even when we ask, I have to think about this :D.
Edit: how about if we ask him if ja means ja? the answer will have to mean yes...
Post by
Haxzor
maybe if you ask them, will the answer to his question be the same as the answer to this question.
hmmmm
Post by
MyTie
We ask Truth if he is guarding the door to heaven, he will say ja (for example). We then ask False if he he is guarding the door to heaven, he will say either ja, or da. Assume that ja means yes, there is one possible answer, ja from truth and ja from false (which would mean that Truth guards the door to heaven). Now, if ja means no, then there will be two possible answers. Ja from truth, and ja from False (which would mean that False guards the door), or ja from truth and da from false (which would mean that random guards the door). We then ask truth if ja means yes, that should solves it.
I probably messed up somewhere, or misunderstood the question; I usually suck at this sort of thing.
We have to ask what he would answer to a question. I know that much. For instance, pretend you always lie, and you stole my wallet.
Then I ask you that if I asked you if you stole my wallet would you answer 'yes'. You would then answer yes, because you would lie about your answer, which would have been 'no'.
If you tell the truth always, and I ask if you stole my wallet, would you answer 'yes', you would say yes, or course. So either lieing or telling the truth you can get the defendant to answer correctly.
Since there are three, you could ask one of them, assume they are telling the truth to rule out something about the one of the others, and assume they are not random.
I'm still working out what the question would be... and a few little quirks about randomness.
I'm getting there though.
Post by
Interest
I gots a good one (quoted from
the curious incident of the dog in the night-time
page 62, only saying this since it is a work of fiction)
Its the Mony Hall Problem, not sure if this is real or not but Parade mag. had the smartest person in the world IQ wise writing up an article
Here we go:
You are on a game show on television. On this game show the idea is to win a car as a prize. The game show host shows you three doors. He says that there is a car behind one of hte doors and there are goats behind the other two doors. he asks you to pick a door. You pick a door but the door is not opened. Then the game show host opens of the doors you did not pick to show a goat (bcause he knows what is behind the doors). Then he says that you have one final chance to change your mind before the doors are opened and you get a goat or a car. So he asks you if you want to change your mind and pick the other unopened door instead. What should you do?
There is a 2 out of 3 chance that there is a car behind the final door.
Refute or back up and GO!
This is a fun mathematical problem that I always see everywhere.
Do not deny that the probability is 2 out of 3. It's true guys.
Post by
ASHelmy
We ask Truth if he is guarding the door to heaven, he will say ja (for example). We then ask False if he he is guarding the door to heaven, he will say either ja, or da. Assume that ja means yes, there is one possible answer, ja from truth and ja from false (which would mean that Truth guards the door to heaven). Now, if ja means no, then there will be two possible answers. Ja from truth, and ja from False (which would mean that False guards the door), or ja from truth and da from false (which would mean that random guards the door). We then ask truth if ja means yes, that should solves it.
I probably messed up somewhere, or misunderstood the question; I usually suck at this sort of thing.
We have to ask what he would answer to a question. I know that much. For instance, pretend you always lie, and you stole my wallet.
Then I ask you that if I asked you if you stole my wallet would you answer 'yes'. You would then answer yes, because you would lie about your answer, which would have been 'no'.
If you tell the truth always, and I ask if you stole my wallet, would you answer 'yes', you would say yes, or course. So either lieing or telling the truth you can get the defendant to answer correctly.
Since there are three, you could ask one of them, assume they are telling the truth to rule out something about the one of the others, and assume they are not random.
I'm still working out what the question would be... and a few little quirks about randomness.
I'm getting there though.
Back up a bit, so why doesn't my way work, again? :D
Post by
ASHelmy
I gots a good one (quoted from
the curious incident of the dog in the night-time
page 62, only saying this since it is a work of fiction)
Its the Mony Hall Problem, not sure if this is real or not but Parade mag. had the smartest person in the world IQ wise writing up an article
Here we go:
You are on a game show on television. On this game show the idea is to win a car as a prize. The game show host shows you three doors. He says that there is a car behind one of hte doors and there are goats behind the other two doors. he asks you to pick a door. You pick a door but the door is not opened. Then the game show host opens of the doors you did not pick to show a goat (bcause he knows what is behind the doors). Then he says that you have one final chance to change your mind before the doors are opened and you get a goat or a car. So he asks you if you want to change your mind and pick the other unopened door instead. What should you do?
There is a 2 out of 3 chance that there is a car behind the final door.
Refute or back up and GO!
This is a fun mathematical problem that I always see everywhere.
Do not deny that the probability is 2 out of 3. It's true guys.
Wait what? how?
Post by
ArgentSun
Because we don't know which one is Truth, False, and Random. Nor do we know which door is which, not to mention that we have no idea what
ja
and
da
mean (and for a person like me, to whom "da" means "yes" in his native language, and "ja" is well-known as "yes" too...changing mind sets is hard :P )
Post by
Interest
http://en.wikipedia.org/wiki/Monty_Hall_problem
This.
Post by
ArgentSun
You are on a game show on television. On this game show the idea is to win a car as a prize. The game show host shows you three doors. He says that there is a car behind one of hte doors and there are goats behind the other two doors. he asks you to pick a door. You pick a door but the door is not opened. Then the game show host opens of the doors you did not pick to show a goat (bcause he knows what is behind the doors). Then he says that you have one final chance to change your mind before the doors are opened and you get a goat or a car. So he asks you if you want to change your mind and pick the other unopened door instead. What should you do?
There is a 2 out of 3 chance that there is a car behind the final door.
Refute or back up and GO!
You change the door. Change in variables FTW!
Post by
Dralas
You are on a game show on television. On this game show the idea is to win a car as a prize. The game show host shows you three doors. He says that there is a car behind one of hte doors and there are goats behind the other two doors. he asks you to pick a door. You pick a door but the door is not opened. Then the game show host opens of the doors you did not pick to show a goat (bcause he knows what is behind the doors). Then he says that you have one final chance to change your mind before the doors are opened and you get a goat or a car. So he asks you if you want to change your mind and pick the other unopened door instead. What should you do?
There is a 2 out of 3 chance that there is a car behind the final door.
Refute or back up and GO!
You change the door. Change in variables FTW!
Nah, you ask the host "If you could pick a door, which one would you pick?" And pick the one he picks because he'll know which one is correct, but will suspect that you will think that he's picking the wrong door so he picks the correct one in a hope to throw you off and does not think of the possibility that you actually know his plan.
Post by
ArgentSun
I am going to mark a door that has a goat behind it as (G), and the one that has car - (C).
Let's say the doors look like this in the beginning:
(C) (G) (G)
Now, you need to choose a door. You have 3 options - car, goat1, or goat2.
Car
You've chosen door1, the one with the car. Quickly, we reflect that:
(C)
(G) (G)
The host can open either door2 or door3, but both of them have goat behind. So after he opens the door, the situation is either
(C)
(G)
(G)
or
(C)
(G)
(G)
Either way switching your door will give you goat.
Switching door in this case gives you 100% chance of failure.
Goat1
You've chosen door2, a door with a goat behind it.
(C)
(G)
(G)
The host now has to open door3, because it is the only one with a goat behind it:
(C)
(G)
(G)
If you decide to switch your door, you will get a car.
Switching door in this case gives you 100% chance of success.
Goat2
You've chosen door3, a door with a goat behind it.
(C) (G) (G)
The host is not forced to open door2, because it is the only one with a goat behind it:
(C)
(G)
(G)
If you decide to switch your door, you will get a car.
Switching door in this case gives you 100% chance of success.
Each one of those outcomes is equally probable. If you decide to switch the door, you have 2/3 chance of getting the car, and 1/3 if you keep your door.
Under those circumstances
, you should always switch your door, as it has double the chance of winning you a car than if you had kept it.
Post by
346084
This post was from a user who has deleted their account.
Post by
307081
This post was from a user who has deleted their account.
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