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LeoTheLion
China958 Posts
On September 10 2010 06:07 0nega wrote: Hello! lurked at this site for some time and couldn't resist EDIT but didn't have the solution... EDIT + Show Spoiler + i don't think they get to pick which hat they take. the hats are placed on the prisoners' heads | ||
Aesop
Hungary11291 Posts
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jiabung
United States720 Posts
On September 10 2010 06:05 Aesop wrote: I wonder how the prisoners have a chance of 66% by guessing randomly. If they pick 1 / 7 (given they know the seven available colors), they have a 14% chance of getting it right. Doing it 7 times is 100%, so statistically one should get it right. Or am I missing something? If there were 6 prisoners who had to roll a die and guess the number they were going to get beforehand, each one would have a 1/6 chance of getting it right. Doing it 6 times does not mean one of them is going to get it right. Same thing with guessing the color of a hat with 1/7 chance, since the OP specifies that the hats could be the same color. | ||
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Slithe
United States985 Posts
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LunarDestiny
United States4177 Posts
On September 10 2010 06:07 0nega wrote: Hello! lurked at this site for some time and couldn't resist to post the solution(hopefully) + Show Spoiler + Before they get the hats, they agree, that they will all take the colour of the hat of one guy, this guy instead takes the colour which no hat he sees has hmm... Situation XXX: Hat color is ROY G BLV TEH guys is red. Other dudes are ROY G BL. The other dudes picks red->got owned. TEH guys picks V-->>got owned. | ||
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saltywet
Hong Kong1316 Posts
On September 10 2010 06:08 seRapH wrote: even then its mathematically impossible to have a 100% correct rate PER PERSON. your hat color is not affected by anyone else's. the only solution i can think of is if the prisoners get to talk beforehand: The first person will write a color of a hat he sees, show it to everyone, and give it to the king. everyone else writes that same color. but this involves a form of communication, and so feels gimmicky  OP states that they cannot communicate AFTER they are seated. meaning they can come up with strategy beforehand. secondly, the sheets are directly handed to the king without possibility being shown to others @OP my solution is for seven people to agree on all looking at one color hat, say white or black, if someone is already looking at a white hat, look at another white hat. if there are no white hats, look at the table say each person is labeled A,B,C,D,E,F,G person A is responsible to look at person B's hat, person B for C, and so on if person A sees that person B is looking at his hat, A knows he's wearing a white hat, vice versa. | ||
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Seth_
Belgium184 Posts
On September 10 2010 06:02 AcrossFiveJulys wrote:i think they know the colors in the pool, otherwise in the example i brought up there's no way to win 100% when all colors are different. I agree. This is complicated though: Image you see a 2:4 distribution of colors, you might have a completely different color (so 5 possibilities) but if you try to guess, you'll need to be sure that if your guess fails someone else's guess must be right. You could also be on the 2 team (making it 3:4) or on the 4 team (so 2:5) If you're in 3:4 then 4 players will see a 3:3 and 2 other players will see a 2:4 like you did. If you're in 2:5 then 2 players will see a 1:5 and 4 other players will see a 2:4 like you did. Oh and if it's 1:2:4, then 2 players will see 1:1:5 and 4 will see 1:2:3. This will get really complicated. Edit: *this was answered in the OP's edit* Can we have different rules for the different players? Like player 1 will side with the 'color 1 team' and player 2 will side with the 'color 2 team' if they see a 2:4?? | ||
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The_Pacifist
United States540 Posts
2) The prisoners cannot communicate in any way to each other after being seated on the table. So then, before they sit down and get the hats, they are able to communicate, right? If so, here is my answer: + Show Spoiler + Before sitting down on the table and getting the hats, the prisoners agree to write down the color of the hat of the person sitting clockwise to them once they sit down and get the hats. Afterwards, they all pass their papers clockwise by one person and turn in the answers. Do I get a cookie now? | ||
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AcrossFiveJulys
United States3612 Posts
On September 10 2010 06:14 saltywet wrote: OP states that they cannot communicate AFTER they are seated. meaning they can come up with strategy beforehand. secondly, the sheets are directly handed to the king without possibility being shown to others @OP my solution is for seven people to agree on all looking at one color hat, say white or black, if someone is already looking at a white hat, look at another white hat. if there are no white hats, look at the table say each person is labeled A,B,C,D,E,F,G person A is responsible to look at person B's hat, person B for C, and so on if person A sees that person B is looking at his hat, A knows he's wearing a white hat, vice versa. On September 10 2010 06:14 The_Pacifist wrote: So then, before they sit down and get the hats, they are able to communicate, right? If so, here is my answer: + Show Spoiler + Before sitting down on the table and getting the hats, the prisoners agree to write down the color of the hat of the person sitting clockwise to them once they sit down and get the hats. Afterwards, they all pass their papers clockwise by one person and turn in the answers. Do I get a cookie now? These both use communication after the hats are passed out, therefore should not be valid solutions. | ||
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Slithe
United States985 Posts
On September 10 2010 06:14 saltywet wrote: OP states that they cannot communicate AFTER they are seated. meaning they can come up with strategy beforehand. secondly, the sheets are directly handed to the king without possibility being shown to others @OP my solution is for seven people to agree on all looking at one color hat, say white or black, if someone is already looking at a white hat, look at another white hat. if there are no white hats, look at the table say each person is labeled A,B,C,D,E,F,G person A is responsible to look at person B's hat, person B for C, and so on if person A sees that person B is looking at his hat, A knows he's wearing a white hat, vice versa. Observing the direction that people look is a form of communication, and is not allowed. The prisoners can only see the hats for some reason. | ||
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tissue
Malaysia441 Posts
If you could see another person's paper, answer is: + Show Spoiler + First guy writes down a color he sees. Everyone copies it. and it seems an injustice to even assume such a horrible answer. | ||
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Darby.mcg
United States16 Posts
On September 10 2010 06:13 LunarDestiny wrote: hmm... Situation XXX: Hat color is ROY G BLV TEH guys is red. Other dudes are ROY G BL. The other dudes picks red->got owned. TEH guys picks V-->>got owned. you fail. only one guy has to get it right. Situation XXX: hat colors are ROY G BIV(perhaps there's a reason you used L for Indigo, but I don't know it). the one guys is Red. Other guys are ROY G BI. They choose red, R gets it right. First guy doesn't even have to bother answering. EDIT. in the case that he is Violet instead(since that was the one missing from your prior example) and when they guess his they get it wrong, by choosing the one that isn't there (V) he gets it right. | ||
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Klive5ive
United Kingdom6056 Posts
On September 10 2010 06:18 AcrossFiveJulys wrote: These both use communication after the hats are passed out, therefore should not be valid solutions. This but the problem is impossible otherwise. As I said before there must be a trick so these answers are just as valid as the "real" answer. | ||
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Slithe
United States985 Posts
On September 10 2010 06:19 tissue wrote: I think that the answer is probably a gimmick, and that no player can see another person's paper. If you could see another person's paper, answer is: + Show Spoiler + First guy writes down a color he sees. Everyone copies it. and it seems an injustice to even assume such a horrible answer. The answer is not a gimmick, it is a math-type problem. | ||
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revy
United States1524 Posts
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Black Gun
Germany4482 Posts
so do they know that there are as many colors possible as there are prisoners? | ||
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Phant
United States737 Posts
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The_Pacifist
United States540 Posts
+ Show Spoiler + Prisoners meet and introduce themselves before getting the hats and sitting at the table. One person introduces himself as "Bob," and all the prisoners agree to write down the color of Bob's hat, whatever it happens to be, once they all sit down and get hats. Cookie nao? :3 EDIT: Aww, crap. 0nega beat me, and I didn't notice. My bad. In that case, I'll go with 0nega's answer. | ||
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AcrossFiveJulys
United States3612 Posts
On September 10 2010 06:07 0nega wrote: Hello! lurked at this site for some time and couldn't resist to post the solution(hopefully) + Show Spoiler + Before they get the hats, they agree, that they will all take the colour of the hat of one guy, this guy instead takes the colour which no hat he sees has I think this is the solution. If all the hats are a different color the chosen guy gets it right, if there are repeats then the other guy wearing the same color as the chosen guy gets it. Well done. | ||
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getSome[703]
United States753 Posts
+ Show Spoiler + All the prisoners before hand pick one guy. The six other players agree that if the designated prisoner is wearing a certain colored hat, one of them will begin write that hat color down on their paper (so one of the players will begin to write if the designated one is wearing a red hat, another will begin to write if he is wearing an orange hat, etc). The designated prisoner, seeing the person who is writing, will then know his hat color. If none of the prisoners are writing down anything, then his hat is the seventh color. He writes down his hat color and everyone goes free | ||
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