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| The Last Dance (Posted on 2004-02-04) |
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When Zablon asked how the last dance went, he got information from the four different people. Just like last year, the four people (Epotram, Forgam, Golkam, and Holdram) decided to mix up what they wore again, and together these four wore red, blue, green, and white of something. However, this year the four friends got tired of dancing earlier and each dropped out from dancing at a different time, such that only one of them made to the last dance. When Zablon asked four people about the last dance, each person told what he knew about what was asked. One of them was a liar; every one of his statements was a lie.
Z: What do you know about the person that was in the last dance?
A: I know the person with the white shirt wasn't in it. The person with the white shirt was the one that stopped right after the person with the red shirt.
Z: What else did you notice?
A: I know the person with the red shirt wore green suspenders.
Z: What do you know about the person that was in the last dance?
B:I know he wore blue suspenders, or that might have been the person that stopped first, I'm not sure. I do know that I looked at the people dancing when the person with the white shirt stopped, and there wasn't a person at all there that was wearing a red tie.
Z: What else do you know?
B:I know the person with the red tie didn't stop directly before the person with the red shirt. I remember Epotram wore only one thing that was red. Actually, I remember that two different people, the person with the white suspenders and the person with the white shirt, were talking to each other about the fact that nobody wore more than one thing that was red.
Z: What do you know about who stopped dancing last?
C: I know the person that stopped dancing second had something blue on. This person stopped dancing directly before or after Forgam. This means Forgam didn't stop dancing last.
Z: What else do you know?
C: Everyone liked to wear white for this, since it was snowing outside, and this meant nobody wore more than one white thing. Forgam eventually volunteered that the others could wear white things and he would not wear anything white.
Z: What do you know about who stopped dancing last?
D: I remember seeing Epotram, the person with the green shirt, and the person with the red tie, all three of them watching that person.
Z: What else do you know?
I know Golkam wore a white tie, but didn't wear anything blue.
(Solving notes: When B says "there wasn't anyone there at all wearing a red tie", he includes people outside the four people that the solution pertains to. If he's lying, you can't infer anything from that statement.)
(Note: When figuring the "lies" (where the inverse of everything that person says is true), don't count "story" elements. For example, when B says "I also know the person with the white suspenders and the person with the white shirt were talking to each other", if he was lying, it means the person wearing the white suspenders also wore the white shirt. The idea that B could be lying merely because these two people actually didn't talk to each other even though the person with white suspenders wasn't the person with the white shirt is disallowed.)
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Submitted by Gamer
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Rating: 1.8000 (5 votes)
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Solution:
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(Hide)
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If both A and B were telling the truth, we can figure out part of the solution:
Given _ _ _ is shirt, tie, suspenders in that order, we can conclude what three in order are by A's statements.
R_G W__ ___
Since the red tie wasn't worn by anyone after the white shirt, it wasn't worn any person before the person wearing the red shirt, and it wasn't worn by the person wearing the red shirt, it must have been worn by the person wearing the white shirt. Then, this person couldn't have worn the red suspenders since he is already wearing a red tie, he can't wear the green suspenders since the person wearing the red shirt is already wearing them, and he can't be wearing the white suspenders (since he's wearing a white shirt), so he must be wearing blue suspenders.
R_G WRB ___
This poses a contradiction because then the person wearing the blue suspenders can't be last (or else the person with the white shirt would be last), and if the person with the blue suspenders was first, the person with the red shirt couldn't be before him. This means that either A or B is lying.
If A was telling the truth and B was not, we can start off the same way as last time. This time we can conclude the person with the red tie came before the person with the red shirt.
_R_ R_G W__ ___
From what C and D say (which must be true), we can figure that Forgam must be first or third. Forgam can't be third, because Forgam isn't wearing anything white. Since Forgam is first, he isn't wearing the white suspenders. The person who stopped second is already wearing green suspenders, and the person who stopped dancing third is already wearing a white shirt. This means the person who stopped dancing last wore the white suspenders. Then since the last two people to stop are already wearing something white and Forgam didn't wear anything white, the person who stopped second must be wearing the white tie. From what D says, this person is Golkam. He didn't wear anything blue like D said.
F-_R_ G-RWG W__ __W
This conflicts with what D's first statement which says Epotram, the person with the green shirt, and the person with the red tie are all different people; none of them last. Epotram must be the person with the white shirt, and Forgam is the person with the red tie. Golkam can't be wearing the green shirt because he is already wearing the red shirt. Since this contradiction came about from thinking that B was the liar and A was not, we know the opposite must be true.
So, we know that A was the liar, and that B, C, and D all made truthful statements. We also know the 4 people named two different ways. Forgam, the person with the white shirt, the person with the white tie, and the person with the white suspenders. Also, we know them as Epotram, the person with the green shirt, the person with the red tie, and the person who came in last. If we can match up these lists, we would know more about the solution.
We know that the person with the white shirt was the last one to stop because A said the inverse. C says the three others not including Forgam wore something white. D says Epotram wasn't the last to stop, so what Epotram wore that was white wasn't the white shirt. Also, D says Golkam wore the white tie instead of Epotram. So Epotram must have been wearing the white suspenders.
To figure out what shirt Golkam wore, we can match up the four people D describes. Golkam wasn't Epotram, he wore the white tie instead of the red tie or white shirt (the person who stopped last), so Golkam must be the only person left, the person with the green shirt. Then, we know Forgam didn't wear the white shirt, so he must have been the person with the red tie.
By figuring this out, we can conclude Forgam was third instead of first. If Forgam was first, we come to a contradiction because nobody wore the red shirt. Forgam wore the red tie, so he couldn't have worn the red shirt. By what B says, the person with the red shirt wasn't directly after the person with the red tie. If the person with the red tie came third, it would mean that the person with the red shirt came right before the person with the white shirt who stopped last and make one of A's statements not a lie. Lastly, the person with the red shirt couldn't have stopped last because the person with the white shirt stopped last.
Since Forgam stopped third, he didn't stop last, and D says Epotram didn't stop last either. Since Golkam is already known to be wearing the green shirt, he couldn't be the last one to stop since that person was wearing the green shirt. So Holdram was the last person to stop and wore the white shirt.
E-__W, G-GW_, F-_R_, H-W__ or
G-GW_, E-__W, F-_R_, H-W__
Since the second person to stop dancing wore something blue, the first possibility must have Golkam wearing blue suspenders. This poses a contradiction because B says the person wearing blue suspenders was either first or last. This means Golkam was first to stop and Epotram was second to stop.
G-GW_, E-__W, F-_R_, H-W__
Since Holdram is wearing the white shirt, and Golkam is wearing the green shirt, they can't be wearing the red shirt. Forgram is already wearing the red tie, so he isn't wearing the red shirt. This means Epotram is wearing the red shirt and Forgam is wearing the blue shirt.
G-GW_, E-R_W, F-BR_, H-W__
Since B says the second person to stop wore something blue, Epotram must have worn the blue tie. This means Holdram must have worn the green tie.
G-GW_, E-RBW, F-BR_, H-WG_
Golkam didn't wear anything blue, so the person who stopperd first didn't wear the blue suspenders. Instead, Holdram (who stopped last) wore the blue suspenders. Since Forgam is already wearing a red tie, he couldn't have worn the red suspenders. Golkam wore the red suspenders, and Forgam wore the green suspenders.
G-GWR, E-RBW, F-BRG, H-WGB
First: Golkam who wore a green shirt with his white tie and red suspenders,
Second: Epotram who wore a red shirt with his blue tie and white suspenders,
Third: Forgam who wore a blue shirt with his red tie and green suspenders,
Fourth: Holdram who wore a white shirt with his green tie and blue suspenders
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