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On November 29 2012 22:45 aseq wrote:Show nested quote +On November 29 2012 21:15 CptZouglou wrote:
Generalized version of a classic one:
A hundred indians are captured by cowboys. The sadistic cowboys then play a game to decide which indians to kill: They carve one of the 12 zodiac symbols on each indian's back. Then, during the massacre day, the indians are put in line, and starting from the end of the queue, each indian is asked his symbol: if he can answer correctly, he will be saved.
From their long riddle experience, the indians knew a strategy to try and save as many as they could. How many can they save, and how ?
Notes:
- The indians cannot see their own symbol, and can only see the symbols of all the indians in front of them in the queue.
- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way).
- When an indian say something, everyone else hears it
- Indians are smart + Show Spoiler +They can try something like the following, although i'm not sure it's the easiest way: They number the zodiac from 1 to 12 (are they allowed to do this?), or use their normal order if they know it. They then add all the amounts from all zodiacs they can see in front of them. Naturally, a mod 12 is used since you can't count further than 12. The back indian will answer the total of all the others and is sacrificed. The next one in line can calculate the difference between the number answered and his own calculated number, so he can save himself. The next one will subtract that number from the first, allowing him to know the difference between the total he calculated and total he counted, which is his own zodiac. This continues until the end, for every next indian is saved. Better make sure all the indians can count well, though, one mistake may cost a lot of lives  . By the way, great thread, although we should really be able to filter stuff. Posts commenting with the white/orange ball and threadmill/airplane problem are so annoying.
Correct, congrats!
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On November 29 2012 22:55 CptZouglou wrote:Show nested quote +On November 29 2012 22:45 aseq wrote:On November 29 2012 21:15 CptZouglou wrote:
Generalized version of a classic one:
A hundred indians are captured by cowboys. The sadistic cowboys then play a game to decide which indians to kill: They carve one of the 12 zodiac symbols on each indian's back. Then, during the massacre day, the indians are put in line, and starting from the end of the queue, each indian is asked his symbol: if he can answer correctly, he will be saved.
From their long riddle experience, the indians knew a strategy to try and save as many as they could. How many can they save, and how ?
Notes:
- The indians cannot see their own symbol, and can only see the symbols of all the indians in front of them in the queue.
- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way).
- When an indian say something, everyone else hears it
- Indians are smart + Show Spoiler +They can try something like the following, although i'm not sure it's the easiest way: They number the zodiac from 1 to 12 (are they allowed to do this?), or use their normal order if they know it. They then add all the amounts from all zodiacs they can see in front of them. Naturally, a mod 12 is used since you can't count further than 12. The back indian will answer the total of all the others and is sacrificed. The next one in line can calculate the difference between the number answered and his own calculated number, so he can save himself. The next one will subtract that number from the first, allowing him to know the difference between the total he calculated and total he counted, which is his own zodiac. This continues until the end, for every next indian is saved. Better make sure all the indians can count well, though, one mistake may cost a lot of lives . By the way, great thread, although we should really be able to filter stuff. Posts commenting with the white/orange ball and threadmill/airplane problem are so annoying. Correct, congrats!
I quote:
- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way).
The solution requires that the Indians are in fact able to communicate prior to the massacre.
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On November 29 2012 22:59 AmericanUmlaut wrote:Show nested quote +On November 29 2012 22:55 CptZouglou wrote:On November 29 2012 22:45 aseq wrote:On November 29 2012 21:15 CptZouglou wrote:
Generalized version of a classic one:
A hundred indians are captured by cowboys. The sadistic cowboys then play a game to decide which indians to kill: They carve one of the 12 zodiac symbols on each indian's back. Then, during the massacre day, the indians are put in line, and starting from the end of the queue, each indian is asked his symbol: if he can answer correctly, he will be saved.
From their long riddle experience, the indians knew a strategy to try and save as many as they could. How many can they save, and how ?
Notes:
- The indians cannot see their own symbol, and can only see the symbols of all the indians in front of them in the queue.
- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way).
- When an indian say something, everyone else hears it
- Indians are smart + Show Spoiler +They can try something like the following, although i'm not sure it's the easiest way: They number the zodiac from 1 to 12 (are they allowed to do this?), or use their normal order if they know it. They then add all the amounts from all zodiacs they can see in front of them. Naturally, a mod 12 is used since you can't count further than 12. The back indian will answer the total of all the others and is sacrificed. The next one in line can calculate the difference between the number answered and his own calculated number, so he can save himself. The next one will subtract that number from the first, allowing him to know the difference between the total he calculated and total he counted, which is his own zodiac. This continues until the end, for every next indian is saved. Better make sure all the indians can count well, though, one mistake may cost a lot of lives . By the way, great thread, although we should really be able to filter stuff. Posts commenting with the white/orange ball and threadmill/airplane problem are so annoying. Correct, congrats! I quote: Show nested quote +- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way). The solution requires that the Indians are in fact able to communicate prior to the massacre.
True, but it also stated in the problem that they've known this solution for generations. You never know when your tribe may end up with a situation where they paint zodiacs on your back and then ask you to name them or they kill you!
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On November 29 2012 23:03 aseq wrote:Show nested quote +On November 29 2012 22:59 AmericanUmlaut wrote:On November 29 2012 22:55 CptZouglou wrote:On November 29 2012 22:45 aseq wrote:On November 29 2012 21:15 CptZouglou wrote:
Generalized version of a classic one:
A hundred indians are captured by cowboys. The sadistic cowboys then play a game to decide which indians to kill: They carve one of the 12 zodiac symbols on each indian's back. Then, during the massacre day, the indians are put in line, and starting from the end of the queue, each indian is asked his symbol: if he can answer correctly, he will be saved.
From their long riddle experience, the indians knew a strategy to try and save as many as they could. How many can they save, and how ?
Notes:
- The indians cannot see their own symbol, and can only see the symbols of all the indians in front of them in the queue.
- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way).
- When an indian say something, everyone else hears it
- Indians are smart + Show Spoiler +They can try something like the following, although i'm not sure it's the easiest way: They number the zodiac from 1 to 12 (are they allowed to do this?), or use their normal order if they know it. They then add all the amounts from all zodiacs they can see in front of them. Naturally, a mod 12 is used since you can't count further than 12. The back indian will answer the total of all the others and is sacrificed. The next one in line can calculate the difference between the number answered and his own calculated number, so he can save himself. The next one will subtract that number from the first, allowing him to know the difference between the total he calculated and total he counted, which is his own zodiac. This continues until the end, for every next indian is saved. Better make sure all the indians can count well, though, one mistake may cost a lot of lives . By the way, great thread, although we should really be able to filter stuff. Posts commenting with the white/orange ball and threadmill/airplane problem are so annoying. Correct, congrats! I quote: - The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way). The solution requires that the Indians are in fact able to communicate prior to the massacre. True, but it also stated in the problem that they've known this solution for generations. You never know when your tribe may end up with a situation where they paint zodiacs on your back and then ask you to name them or they kill you!
"From their long riddle experience" they have a pre-arranged communications protocoll for handling situations like this?
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On November 29 2012 23:03 aseq wrote:Show nested quote +On November 29 2012 22:59 AmericanUmlaut wrote:On November 29 2012 22:55 CptZouglou wrote:On November 29 2012 22:45 aseq wrote:On November 29 2012 21:15 CptZouglou wrote:
Generalized version of a classic one:
A hundred indians are captured by cowboys. The sadistic cowboys then play a game to decide which indians to kill: They carve one of the 12 zodiac symbols on each indian's back. Then, during the massacre day, the indians are put in line, and starting from the end of the queue, each indian is asked his symbol: if he can answer correctly, he will be saved.
From their long riddle experience, the indians knew a strategy to try and save as many as they could. How many can they save, and how ?
Notes:
- The indians cannot see their own symbol, and can only see the symbols of all the indians in front of them in the queue.
- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way).
- When an indian say something, everyone else hears it
- Indians are smart + Show Spoiler +They can try something like the following, although i'm not sure it's the easiest way: They number the zodiac from 1 to 12 (are they allowed to do this?), or use their normal order if they know it. They then add all the amounts from all zodiacs they can see in front of them. Naturally, a mod 12 is used since you can't count further than 12. The back indian will answer the total of all the others and is sacrificed. The next one in line can calculate the difference between the number answered and his own calculated number, so he can save himself. The next one will subtract that number from the first, allowing him to know the difference between the total he calculated and total he counted, which is his own zodiac. This continues until the end, for every next indian is saved. Better make sure all the indians can count well, though, one mistake may cost a lot of lives . By the way, great thread, although we should really be able to filter stuff. Posts commenting with the white/orange ball and threadmill/airplane problem are so annoying. Correct, congrats! I quote: - The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way). The solution requires that the Indians are in fact able to communicate prior to the massacre. True, but it also stated in the problem that they've known this solution for generations. You never know when your tribe may end up with a situation where they paint zodiacs on your back and then ask you to name them or they kill you!
They just happen to have a number assigned to each zodiac symbol?
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On November 29 2012 23:03 aseq wrote:Show nested quote +On November 29 2012 22:59 AmericanUmlaut wrote:On November 29 2012 22:55 CptZouglou wrote:On November 29 2012 22:45 aseq wrote:On November 29 2012 21:15 CptZouglou wrote:
Generalized version of a classic one:
A hundred indians are captured by cowboys. The sadistic cowboys then play a game to decide which indians to kill: They carve one of the 12 zodiac symbols on each indian's back. Then, during the massacre day, the indians are put in line, and starting from the end of the queue, each indian is asked his symbol: if he can answer correctly, he will be saved.
From their long riddle experience, the indians knew a strategy to try and save as many as they could. How many can they save, and how ?
Notes:
- The indians cannot see their own symbol, and can only see the symbols of all the indians in front of them in the queue.
- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way).
- When an indian say something, everyone else hears it
- Indians are smart + Show Spoiler +They can try something like the following, although i'm not sure it's the easiest way: They number the zodiac from 1 to 12 (are they allowed to do this?), or use their normal order if they know it. They then add all the amounts from all zodiacs they can see in front of them. Naturally, a mod 12 is used since you can't count further than 12. The back indian will answer the total of all the others and is sacrificed. The next one in line can calculate the difference between the number answered and his own calculated number, so he can save himself. The next one will subtract that number from the first, allowing him to know the difference between the total he calculated and total he counted, which is his own zodiac. This continues until the end, for every next indian is saved. Better make sure all the indians can count well, though, one mistake may cost a lot of lives . By the way, great thread, although we should really be able to filter stuff. Posts commenting with the white/orange ball and threadmill/airplane problem are so annoying. Correct, congrats! I quote: - The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way). The solution requires that the Indians are in fact able to communicate prior to the massacre. True, but it also stated in the problem that they've known this solution for generations. You never know when your tribe may end up with a situation where they paint zodiacs on your back and then ask you to name them or they kill you!
Nvm, I get the math now
+ Show Spoiler +- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way). So this sentence syntax confuses me... is their vocabulary reduced to the twelve words of the zodiac, or can they say other words as well? + Show Spoiler +So suppose everyone has month 1 on his back, lets say its The Ram. The total is thus 99. Which zodiac name would they say, or would they say the mod12 of 99, whatever that would be?
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What I meant was:
they cannot communicate once the symbols are carved onto their backs. But they can agree on the strategy to adopt beforehand, and they are told the rules.
A more formalized answer:
+ Show Spoiler +
Each of the 12 signs is represented by an integer from 0 to 11.
The indian at the back adds up all the signs modulo 12: this gives a number C between 0 and 11. He can then communicate this number by saying the associated sign.
The next indian counts all the signs in front of him mod 12: this gives a number C2. In order to know his number, he only has to find the difference between C and C2 mod 12. This gives his sign: he is saved
All the next indian also count the signs in front of them, and add the signs told by all the previous indians (except the first). This sum is called Cn (for the n-th indian). Their sign is the difference between C and Cn mod 12. They are all saved.
So there is 99 + 1/12 indians saved in average.
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On November 29 2012 23:11 Twinmold wrote:Show nested quote +On November 29 2012 23:03 aseq wrote:On November 29 2012 22:59 AmericanUmlaut wrote:On November 29 2012 22:55 CptZouglou wrote:On November 29 2012 22:45 aseq wrote:On November 29 2012 21:15 CptZouglou wrote:
Generalized version of a classic one:
A hundred indians are captured by cowboys. The sadistic cowboys then play a game to decide which indians to kill: They carve one of the 12 zodiac symbols on each indian's back. Then, during the massacre day, the indians are put in line, and starting from the end of the queue, each indian is asked his symbol: if he can answer correctly, he will be saved.
From their long riddle experience, the indians knew a strategy to try and save as many as they could. How many can they save, and how ?
Notes:
- The indians cannot see their own symbol, and can only see the symbols of all the indians in front of them in the queue.
- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way).
- When an indian say something, everyone else hears it
- Indians are smart + Show Spoiler +They can try something like the following, although i'm not sure it's the easiest way: They number the zodiac from 1 to 12 (are they allowed to do this?), or use their normal order if they know it. They then add all the amounts from all zodiacs they can see in front of them. Naturally, a mod 12 is used since you can't count further than 12. The back indian will answer the total of all the others and is sacrificed. The next one in line can calculate the difference between the number answered and his own calculated number, so he can save himself. The next one will subtract that number from the first, allowing him to know the difference between the total he calculated and total he counted, which is his own zodiac. This continues until the end, for every next indian is saved. Better make sure all the indians can count well, though, one mistake may cost a lot of lives . By the way, great thread, although we should really be able to filter stuff. Posts commenting with the white/orange ball and threadmill/airplane problem are so annoying. Correct, congrats! I quote: - The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way). The solution requires that the Indians are in fact able to communicate prior to the massacre. True, but it also stated in the problem that they've known this solution for generations. You never know when your tribe may end up with a situation where they paint zodiacs on your back and then ask you to name them or they kill you! They just happen to have a number assigned to each zodiac symbol?
And they all somehow randomly assigned the same number to each symbol? And knowledge persists for generations without communication? Wooow.
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On November 29 2012 23:11 Ketch wrote:Show nested quote +On November 29 2012 23:03 aseq wrote:On November 29 2012 22:59 AmericanUmlaut wrote:On November 29 2012 22:55 CptZouglou wrote:On November 29 2012 22:45 aseq wrote:On November 29 2012 21:15 CptZouglou wrote:
Generalized version of a classic one:
A hundred indians are captured by cowboys. The sadistic cowboys then play a game to decide which indians to kill: They carve one of the 12 zodiac symbols on each indian's back. Then, during the massacre day, the indians are put in line, and starting from the end of the queue, each indian is asked his symbol: if he can answer correctly, he will be saved.
From their long riddle experience, the indians knew a strategy to try and save as many as they could. How many can they save, and how ?
Notes:
- The indians cannot see their own symbol, and can only see the symbols of all the indians in front of them in the queue.
- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way).
- When an indian say something, everyone else hears it
- Indians are smart + Show Spoiler +They can try something like the following, although i'm not sure it's the easiest way: They number the zodiac from 1 to 12 (are they allowed to do this?), or use their normal order if they know it. They then add all the amounts from all zodiacs they can see in front of them. Naturally, a mod 12 is used since you can't count further than 12. The back indian will answer the total of all the others and is sacrificed. The next one in line can calculate the difference between the number answered and his own calculated number, so he can save himself. The next one will subtract that number from the first, allowing him to know the difference between the total he calculated and total he counted, which is his own zodiac. This continues until the end, for every next indian is saved. Better make sure all the indians can count well, though, one mistake may cost a lot of lives . By the way, great thread, although we should really be able to filter stuff. Posts commenting with the white/orange ball and threadmill/airplane problem are so annoying. Correct, congrats! I quote: - The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way). The solution requires that the Indians are in fact able to communicate prior to the massacre. True, but it also stated in the problem that they've known this solution for generations. You never know when your tribe may end up with a situation where they paint zodiacs on your back and then ask you to name them or they kill you! Nvm, I get the math now + Show Spoiler +- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way). So this sentence syntax confuses me... is their vocabulary reduced to the twelve words of the zodiac, or can they say other words as well? + Show Spoiler +So suppose everyone has month 1 on his back, lets say its The Ram. The total is thus 99. Which zodiac name would they say, or would they say the mod12 of 99, whatever that would be?
Still have a math question  .
+ Show Spoiler + How do you distguish between 7 + 1 and 4 + 4 in such a modded sum?
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Actually, I liked a riddle that is somewhat similar to this, maybe a bit too easy but still fun:
4 gnomes are captured by a wizard who casts a spell, making them unable to move (but they can speak, ofc). The wizard arranges them like this: He puts 3 of them on a staircase, looking in the downwards direction, so the back one can see 2 others and the middle one 1. The fourth one is left in the cave, unable to see the others, and the others can't see him either. All of the gnome hats, two white ones and two red ones, are now redistributed, and the red hats are given to the top and bottom gnomes on the stairs, the white hats to the other 2. The gnomes have no idea what color hat they receive.
The wizard promises to release the gnomes as soon as one correctly states the color of his own hat. If any other word is spoken, or one guesses wrong, all are killed. Which one calls his color to free himself and his friends?
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On November 29 2012 23:17 Ketch wrote:Show nested quote +On November 29 2012 23:11 Ketch wrote:On November 29 2012 23:03 aseq wrote:On November 29 2012 22:59 AmericanUmlaut wrote:On November 29 2012 22:55 CptZouglou wrote:On November 29 2012 22:45 aseq wrote:On November 29 2012 21:15 CptZouglou wrote:
Generalized version of a classic one:
A hundred indians are captured by cowboys. The sadistic cowboys then play a game to decide which indians to kill: They carve one of the 12 zodiac symbols on each indian's back. Then, during the massacre day, the indians are put in line, and starting from the end of the queue, each indian is asked his symbol: if he can answer correctly, he will be saved.
From their long riddle experience, the indians knew a strategy to try and save as many as they could. How many can they save, and how ?
Notes:
- The indians cannot see their own symbol, and can only see the symbols of all the indians in front of them in the queue.
- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way).
- When an indian say something, everyone else hears it
- Indians are smart + Show Spoiler +They can try something like the following, although i'm not sure it's the easiest way: They number the zodiac from 1 to 12 (are they allowed to do this?), or use their normal order if they know it. They then add all the amounts from all zodiacs they can see in front of them. Naturally, a mod 12 is used since you can't count further than 12. The back indian will answer the total of all the others and is sacrificed. The next one in line can calculate the difference between the number answered and his own calculated number, so he can save himself. The next one will subtract that number from the first, allowing him to know the difference between the total he calculated and total he counted, which is his own zodiac. This continues until the end, for every next indian is saved. Better make sure all the indians can count well, though, one mistake may cost a lot of lives . By the way, great thread, although we should really be able to filter stuff. Posts commenting with the white/orange ball and threadmill/airplane problem are so annoying. Correct, congrats! I quote: - The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way). The solution requires that the Indians are in fact able to communicate prior to the massacre. True, but it also stated in the problem that they've known this solution for generations. You never know when your tribe may end up with a situation where they paint zodiacs on your back and then ask you to name them or they kill you! Nvm, I get the math now + Show Spoiler +- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way). So this sentence syntax confuses me... is their vocabulary reduced to the twelve words of the zodiac, or can they say other words as well? + Show Spoiler +So suppose everyone has month 1 on his back, lets say its The Ram. The total is thus 99. Which zodiac name would they say, or would they say the mod12 of 99, whatever that would be? Still have a math question . + Show Spoiler + How do you distguish between 7 + 1 and 4 + 4 in such a modded sum?
+ Show Spoiler + When would you ever have to? If the person behind you says 8, then it's easy to distinguish between scenarios. If you now see 7, then you know you are a 1. If you now see 4, you know that you are 4. (numbers in mod 12 of course).
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Aaagh... I should think on this stuff more... I really get the math now
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On November 29 2012 23:17 Ketch wrote:Show nested quote +On November 29 2012 23:11 Ketch wrote:On November 29 2012 23:03 aseq wrote:On November 29 2012 22:59 AmericanUmlaut wrote:On November 29 2012 22:55 CptZouglou wrote:On November 29 2012 22:45 aseq wrote:On November 29 2012 21:15 CptZouglou wrote:
Generalized version of a classic one:
A hundred indians are captured by cowboys. The sadistic cowboys then play a game to decide which indians to kill: They carve one of the 12 zodiac symbols on each indian's back. Then, during the massacre day, the indians are put in line, and starting from the end of the queue, each indian is asked his symbol: if he can answer correctly, he will be saved.
From their long riddle experience, the indians knew a strategy to try and save as many as they could. How many can they save, and how ?
Notes:
- The indians cannot see their own symbol, and can only see the symbols of all the indians in front of them in the queue.
- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way).
- When an indian say something, everyone else hears it
- Indians are smart + Show Spoiler +They can try something like the following, although i'm not sure it's the easiest way: They number the zodiac from 1 to 12 (are they allowed to do this?), or use their normal order if they know it. They then add all the amounts from all zodiacs they can see in front of them. Naturally, a mod 12 is used since you can't count further than 12. The back indian will answer the total of all the others and is sacrificed. The next one in line can calculate the difference between the number answered and his own calculated number, so he can save himself. The next one will subtract that number from the first, allowing him to know the difference between the total he calculated and total he counted, which is his own zodiac. This continues until the end, for every next indian is saved. Better make sure all the indians can count well, though, one mistake may cost a lot of lives . By the way, great thread, although we should really be able to filter stuff. Posts commenting with the white/orange ball and threadmill/airplane problem are so annoying. Correct, congrats! I quote: - The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way). The solution requires that the Indians are in fact able to communicate prior to the massacre. True, but it also stated in the problem that they've known this solution for generations. You never know when your tribe may end up with a situation where they paint zodiacs on your back and then ask you to name them or they kill you! Nvm, I get the math now + Show Spoiler +- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way). So this sentence syntax confuses me... is their vocabulary reduced to the twelve words of the zodiac, or can they say other words as well? + Show Spoiler +So suppose everyone has month 1 on his back, lets say its The Ram. The total is thus 99. Which zodiac name would they say, or would they say the mod12 of 99, whatever that would be? Still have a math question . + Show Spoiler + How do you distguish between 7 + 1 and 4 + 4 in such a modded sum?
edit: ninja'd
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On November 29 2012 23:17 Ketch wrote:Show nested quote +On November 29 2012 23:11 Ketch wrote:On November 29 2012 23:03 aseq wrote:On November 29 2012 22:59 AmericanUmlaut wrote:On November 29 2012 22:55 CptZouglou wrote:On November 29 2012 22:45 aseq wrote:On November 29 2012 21:15 CptZouglou wrote:
Generalized version of a classic one:
A hundred indians are captured by cowboys. The sadistic cowboys then play a game to decide which indians to kill: They carve one of the 12 zodiac symbols on each indian's back. Then, during the massacre day, the indians are put in line, and starting from the end of the queue, each indian is asked his symbol: if he can answer correctly, he will be saved.
From their long riddle experience, the indians knew a strategy to try and save as many as they could. How many can they save, and how ?
Notes:
- The indians cannot see their own symbol, and can only see the symbols of all the indians in front of them in the queue.
- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way).
- When an indian say something, everyone else hears it
- Indians are smart + Show Spoiler +They can try something like the following, although i'm not sure it's the easiest way: They number the zodiac from 1 to 12 (are they allowed to do this?), or use their normal order if they know it. They then add all the amounts from all zodiacs they can see in front of them. Naturally, a mod 12 is used since you can't count further than 12. The back indian will answer the total of all the others and is sacrificed. The next one in line can calculate the difference between the number answered and his own calculated number, so he can save himself. The next one will subtract that number from the first, allowing him to know the difference between the total he calculated and total he counted, which is his own zodiac. This continues until the end, for every next indian is saved. Better make sure all the indians can count well, though, one mistake may cost a lot of lives . By the way, great thread, although we should really be able to filter stuff. Posts commenting with the white/orange ball and threadmill/airplane problem are so annoying. Correct, congrats! I quote: - The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way). The solution requires that the Indians are in fact able to communicate prior to the massacre. True, but it also stated in the problem that they've known this solution for generations. You never know when your tribe may end up with a situation where they paint zodiacs on your back and then ask you to name them or they kill you! Nvm, I get the math now + Show Spoiler +- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way). So this sentence syntax confuses me... is their vocabulary reduced to the twelve words of the zodiac, or can they say other words as well? + Show Spoiler +So suppose everyone has month 1 on his back, lets say its The Ram. The total is thus 99. Which zodiac name would they say, or would they say the mod12 of 99, whatever that would be? Still have a math question . + Show Spoiler + How do you distguish between 7 + 1 and 4 + 4 in such a modded sum?
You can't distinguish between the two, but you don't have to, since you only have to subtract one number at a time (the difference between the last total and yours). How often you passed the 12 (or how much the total is) doesn't matter to you. Edit: answered already.
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On November 29 2012 23:19 aseq wrote:
Actually, I liked a riddle that is somewhat similar to this, maybe a bit too easy but still fun:
4 gnomes are captured by a wizard who casts a spell, making them unable to move (but they can speak, ofc). The wizard arranges them like this: He puts 3 of them on a staircase, looking in the downwards direction, so the back one can see 2 others and the middle one 1. The fourth one is left in the cave, unable to see the others, and the others can't see him either. All of the gnome hats, two white ones and two red ones, are now redistributed, and the red hats are given to the top and bottom gnomes on the stairs, the white hats to the other 2. The gnomes have no idea what color hat they receive.
The wizard promises to release the gnomes as soon as one correctly states the color of his own hat. If any other word is spoken, or one guesses wrong, all are killed. Which one calls his color to free himself and his friends?
+ Show Spoiler +I'd say the one in the middle.
The gnome that sees the two others doesn't see two reds or two white, therefore he doesn't speak. As he doesn't the second gnome on the stairs knows that his hat and the next hat have a different color. He can then see the color of the next gnome (red) and decide he has the other (white)
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On November 29 2012 23:28 CptZouglou wrote:Show nested quote +On November 29 2012 23:19 aseq wrote:
Actually, I liked a riddle that is somewhat similar to this, maybe a bit too easy but still fun:
4 gnomes are captured by a wizard who casts a spell, making them unable to move (but they can speak, ofc). The wizard arranges them like this: He puts 3 of them on a staircase, looking in the downwards direction, so the back one can see 2 others and the middle one 1. The fourth one is left in the cave, unable to see the others, and the others can't see him either. All of the gnome hats, two white ones and two red ones, are now redistributed, and the red hats are given to the top and bottom gnomes on the stairs, the white hats to the other 2. The gnomes have no idea what color hat they receive.
The wizard promises to release the gnomes as soon as one correctly states the color of his own hat. If any other word is spoken, or one guesses wrong, all are killed. Which one calls his color to free himself and his friends? + Show Spoiler +I'd say the one in the middle.
The gnome that sees the two others doesn't see two reds or two white, therefore he doesn't speak. As he doesn't the second gnome on the stairs knows that his hat and the next hat have a different color. He can then see the color of the next gnome (red) and decide he has the other (white)
Correct! Knew it was too easy!
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If Pinochio said my nose will grow right now, what would happen ?
this was the most obvious answer in my opinion
+ Show Spoiler +the blue fairy will change him in a donkey for creating paradoxes in fairy tales
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On November 29 2012 21:23 AmericanUmlaut wrote:Show nested quote +On November 29 2012 21:15 CptZouglou wrote:
Generalized version of a classic one:
A hundred indians are captured by cowboys. The sadistic cowboys then play a game to decide which indians to kill: They carve one of the 12 zodiac symbols on each indian's back. Then, during the massacre day, the indians are put in line, and starting from the end of the queue, each indian is asked his symbol: if he can answer correctly, he will be saved.
From their long riddle experience, the indians knew a strategy to try and save as many as they could. How many can they save, and how ?
Notes:
- The indians cannot see their own symbol, and can only see the symbols of all the indians in front of them in the queue.
- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way).
- When an indian say something, everyone else hears it
- Indians are smart I think you're missing some required information. As described, it's possible that every single Indian is marked with the same symbol, and no amount of information about the symbols marking other Indians is useful for deducing any given Indian's mark.
Solution ?
+ Show Spoiler +Represent the symbols as numbers n(i) for indian i (first one is 0, last one 99, all values are in [0..11]). Let the first indian answer with N=sum(a(1)...a(99)) mod 12.
Second indian sees a(2) ... a(99), so he can sum them up to compute A(1) = N - a(2) (mod 12) and therefore he will answer a(2)=N-A(1) (mod 12)
Recurse on indians, indian j knows a(1)...a(j-1) (correct values given by the preceding ones) and sees a(j+1)...a(99). Therefore indian j can compute A(j)=(N - a(j)) (mod 12) and his symbol is: a(j)=(N - A(j)) mod 12
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On November 29 2012 23:44 Oshuy wrote:Show nested quote +On November 29 2012 21:23 AmericanUmlaut wrote:On November 29 2012 21:15 CptZouglou wrote:
Generalized version of a classic one:
A hundred indians are captured by cowboys. The sadistic cowboys then play a game to decide which indians to kill: They carve one of the 12 zodiac symbols on each indian's back. Then, during the massacre day, the indians are put in line, and starting from the end of the queue, each indian is asked his symbol: if he can answer correctly, he will be saved.
From their long riddle experience, the indians knew a strategy to try and save as many as they could. How many can they save, and how ?
Notes:
- The indians cannot see their own symbol, and can only see the symbols of all the indians in front of them in the queue.
- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way).
- When an indian say something, everyone else hears it
- Indians are smart I think you're missing some required information. As described, it's possible that every single Indian is marked with the same symbol, and no amount of information about the symbols marking other Indians is useful for deducing any given Indian's mark. Solution ? + Show Spoiler +Represent the symbols as numbers n(i) for indian i (first one is 0, last one 99, all values are in [0..11]). Let the first indian answer with N=sum(a(1)...a(99)) mod 12.
Second indian sees a(2) ... a(99), so he can sum them up to compute A(1) = N - a(2) (mod 12) and therefore he will answer a(2)=N-A(1) (mod 12)
Recurse on indians, indian j knows a(1)...a(j-1) (correct values given by the preceding ones) and sees a(j+1)...a(99). Therefore indian j can compute A(j)=(N - a(j)) (mod 12) and his symbol is: a(j)=(N - A(j)) mod 12
Yeah, again: The description of the riddle implied that the Indians couldn't communicate prior to having to solve the problem. Thus my problem. Once you allow them to establish a communications protocoll the solution is pretty trivial.
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On November 29 2012 23:45 AmericanUmlaut wrote:Show nested quote +On November 29 2012 23:44 Oshuy wrote:On November 29 2012 21:23 AmericanUmlaut wrote:On November 29 2012 21:15 CptZouglou wrote:
Generalized version of a classic one:
A hundred indians are captured by cowboys. The sadistic cowboys then play a game to decide which indians to kill: They carve one of the 12 zodiac symbols on each indian's back. Then, during the massacre day, the indians are put in line, and starting from the end of the queue, each indian is asked his symbol: if he can answer correctly, he will be saved.
From their long riddle experience, the indians knew a strategy to try and save as many as they could. How many can they save, and how ?
Notes:
- The indians cannot see their own symbol, and can only see the symbols of all the indians in front of them in the queue.
- The indians can only say one word when asked: the name of their symbol (they cannot communicate in any other way).
- When an indian say something, everyone else hears it
- Indians are smart I think you're missing some required information. As described, it's possible that every single Indian is marked with the same symbol, and no amount of information about the symbols marking other Indians is useful for deducing any given Indian's mark. Solution ? + Show Spoiler +Represent the symbols as numbers n(i) for indian i (first one is 0, last one 99, all values are in [0..11]). Let the first indian answer with N=sum(a(1)...a(99)) mod 12.
Second indian sees a(2) ... a(99), so he can sum them up to compute A(1) = N - a(2) (mod 12) and therefore he will answer a(2)=N-A(1) (mod 12)
Recurse on indians, indian j knows a(1)...a(j-1) (correct values given by the preceding ones) and sees a(j+1)...a(99). Therefore indian j can compute A(j)=(N - a(j)) (mod 12) and his symbol is: a(j)=(N - A(j)) mod 12 Yeah, again: The description of the riddle implied that the Indians couldn't communicate prior to having to solve the problem. Thus my problem. Once you allow them to establish a communications protocoll the solution is pretty trivial.
I think it's not trivial. You can see it that way:
The cowboys give the rules to the indians. The indians discuss which strategy to use. Then they carve the symbols and from then the indians can't communicate. It's like any other strategy based riddle.
If they couldn't communicate at all before knowing the problem, then the best they can do is random or hope the previous one just gave your carving, but why would he as you haven't established any strategy ?
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EPT
