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On July 23 2007 05:16 Cascade wrote:A solution to devours riddle: (EDIT: just want to brag: the solution was made up on the spot, not something I've read somewhere. This what you get from years and years of university training. ) EDIT2: corrected a flaw. Also redefined n to not write (n-1) al the time. + Show Spoiler + Prisoners choose one guy to be the leader and use the following rules. 1) The leader always leaves the chalice right side up. 2) The n other prisoners always leaves it upside down, but will TURN the chalice only 2k+2 times.
When the leader has found the chalice upside down n(2k + 2) - k times he known that everyone has been in the room.
why? Here is the explanation: There can be three things that can make the leader find the cup upside down a) it may have started upside down. This can happen only once. b) the king may have turned it. This can happen only k times. c) Some of his friends may have turned it. This can happen at most k+2 times for each prisoner.
So after n(2k+2) - k times, all except k +1 have been c) happening. So he knows that at least n(2k + 2) - (k+1) times has a prisoner turned the chalice. Since each prisoner turns it max 2k+2 times, everyone must have turned it at least once by then, even. So he can be sure everyone has been in the camber. Also, whatever the starting position of the chalice, and whatever the king does with his k turns, this will always happen eventually since even if the king turns it back to normal when the prisoners has turned it upside down k times. In that case the chalice will be turned exactly n(2k+2) - k times (2k+2 times for each prisoner, minus the k times the king cancels the turn).
Orome: so we know nothing about how many colors or how many of each color? Hmm, tricky one.
this wont work if king makes the leader come in first x number of times in a row. X being the arbitrary number of times he chooses to call each of them in.
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how can that be right if the king can chose any order and any number of times he has to call in the prisoners?
Ok lets say n is 12. King choses k to be 10. King brings in each just once. That makes it so that the leader has to see the chalice upsidedown 254 times? Impossible. Also, as stated above, the king will know who the leader is and he can bring the leader in first and he wont get any information. All the other prisoners are fucked after that.
For this solution to work, you would need some constraints on the king's power.
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You missinterpreted the question. The king must keep calling in prisoners as long as they say "don't know" and he may not block any of the prisoners by stop calling him in after a while. Every prisoner must eventually be called in any number of times.
He may do it in any order he wants, but he must EVENTUALLY call in also the leader 254 times. If he chooses to call in the leader only every 100 000:th time it of course gets ridiculous, but the problem should be taken in a bit more abstract way.
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ok... i was wondering what happens if the king calls them all in x number of times and they all say dunno. Yea the solution seems to work.
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Always nice to start out with a simple one for those that haven't figured it out:
(a-x)(b-x)(c-x)(d-x)(e-x)(f-x)(g-x)(h-x)(i-x)(j-x)(k-x)(l-x)(m-x)(n-x)(o-x)(p-x)(q-x)(r-x)(s-x)(t-x)(u-x)(v-x)(w-x)(x-x)(y-x)(z-x) = ?
Note: Letters do not represent numerical order in the alphabet, so a =/= 1 and so forth.
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On July 23 2007 06:40 Elgar wrote: Always nice to start out with a simple one for those that haven't figured it out:
(a-x)(b-x)(c-x)(d-x)(e-x)(f-x)(g-x)(h-x)(i-x)(j-x)(k-x)(l-x)(m-x)(n-x)(o-x)(p-x)(q-x)(r-x)(s-x)(t-x)(u-x)(v-x)(w-x)(x-x)(y-x)(z-x) = ?
Note: Letters do not represent numerical order in the alphabet, so a =/= 1 and so forth. + Show Spoiler +
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On July 23 2007 06:53 One Page Memory wrote:Show nested quote +On July 23 2007 06:40 Elgar wrote: Always nice to start out with a simple one for those that haven't figured it out:
(a-x)(b-x)(c-x)(d-x)(e-x)(f-x)(g-x)(h-x)(i-x)(j-x)(k-x)(l-x)(m-x)(n-x)(o-x)(p-x)(q-x)(r-x)(s-x)(t-x)(u-x)(v-x)(w-x)(x-x)(y-x)(z-x) = ?
Note: Letters do not represent numerical order in the alphabet, so a =/= 1 and so forth. + Show Spoiler +
Correct sir
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you have 2 doors to choose from. one door is the good door and one is the bad door. 2 brothers know which door is good and which door is bad. you know that one brother always lies and one brother always tells the truth but you do not know which one is which. by asking one borther one question, how do you find out which door is the good door?
Edit: what is the question you need to ask to find out which door is good? remember, you do not know if the one you are asking is the one that always lie or tells the truth.
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Braavos36362 Posts
A mother pig has 9 baby pigs walking behind her. She needs to cross a river. She puts 3 on her back and carries 2 in her hands and swims across the river. When she arrives on the other side, she says "all of us are here." Why?
+ Show Spoiler [answer] +She is retarded and can't count correctly.
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Show nested quote +On July 23 2007 03:18 Chosi wrote: Inspired by the thread with this really old math riddle, which is not really a riddle I wanted to post another riddle that really took me a while to solve:
3 men discuss which of them is the smartest, so they walk all up a mountain to a very old and very wise man. They state their problem and he pulls out a sack and sais: "In this sack there are 2 black hats and 3 white hats." Then he tells them to close their eyes and puts a hat on each of them. They cannot see their own hat but the other two. Then he sais: "the first to tell me which color his hat has and why is the smartest of you". (You as the person to solve this know that one guy has a black hat on his head and two guys have a white hat on their heads.) After some minutes one of the guys jumps up and sais: "i know that my hat is .."
How did he know?
Facts in short: Sack with 5 hats, 2 black, 3 white 3 guys, one with a black hat, two with a white they can only see the others hats, not their own how can they know what color their hat has?
you see black black, you instant white because there are only 2 blacks possible.
you see black white, you slightly later instant white because if anyone else saw balck black they would instant white before you.
you see white white, you're black based on the facts you outlined.
however, (based on the word problem there's no reason to assume it's 1 black 2 white), I would white because no one else saw black white and claimed above. that means everyone must have seen white white and you have to be white.
i don't think the game can be used to determine who's the smartest because a lot depends on luck and which hats you see unless there's a better solution.
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Kau
Canada3500 Posts
On July 23 2007 07:40 mdominik86 wrote: you have 2 doors to choose from. one door is the good door and one is the bad door. 2 brothers know which door is good and which door is bad. you know that one brother always lies and one brother always tells the truth but you do not know which one is which. by asking one borther one question, how do you find out which door is the good door?
Edit: what is the question you need to ask to find out which door is good? remember, you do not know if the one you are asking is the one that always lie or tells the truth.
+ Show Spoiler +Which door would your brother say is the bad door? Both brothers would point to the right door, or at least they do in my head.
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On July 23 2007 09:06 Kau wrote:Show nested quote +On July 23 2007 07:40 mdominik86 wrote: you have 2 doors to choose from. one door is the good door and one is the bad door. 2 brothers know which door is good and which door is bad. you know that one brother always lies and one brother always tells the truth but you do not know which one is which. by asking one borther one question, how do you find out which door is the good door?
Edit: what is the question you need to ask to find out which door is good? remember, you do not know if the one you are asking is the one that always lie or tells the truth. + Show Spoiler +Which door would your brother say is the bad door? Both brothers would point to the right door, or at least they do in my head. + Show Spoiler +Right question, but you would get the bad door from them. if you asked the liar then his brother would tell him the good door and he would lie and tell you the bad door. if you asked the guy that tells the truth he would ask his brother, his brother would lie to him, point out the bad door and he would tell you that. so it is not going to be the door that they tell you.
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uh, about the above post on good/bad doors... + Show Spoiler + you'd get the good door by asking for the bad door There is always one lie (negation) along the way. you ask for the bad door, you get the good door
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On July 23 2007 09:55 EmS.Radagast wrote:uh, about the above post on good/bad doors... + Show Spoiler + you'd get the good door by asking for the bad door There is always one lie (negation) along the way. you ask for the bad door, you get the good door
+ Show Spoiler + Not true, you must ask them what would your brother say is the good door. If you ask them both "which is the bad door" the truth will point to the bad, the liar to the good, and since you don't know who is who, you are still stuck. there fore, asking them what will your brother say is the good door, the liar points to the bad door (his brother would point to the good door, but he lies), and the truth points to the bad door (he is pointing where his brother is pointing, since his brother lied about it). Then, you pick the opposite door because its the good door.
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