question and answer thread.

Well assuming all the people can have the same plan in mind before-hand, each person should name the color of the hat on the person to their left (or any other known position). If the person to their left already knows their hat color, you say the next person who doesn't know.

Each time a person is asked, some other person is saved. Even in the unlikely event that 50 people are asked and they all get it wrong, the remaining 50 people survive. More likely, 2/3 of those 50 people will die, about 34, leaving 66 still standing who have either been asked and got it right or already know.

The tricky part is remembering who knows their hat color!

Yes, they can elaborate a common plan together before the "event", so your answer is perfectly valid.

Without doing much statistical analysis, I think with your solution you would save in the mean 50% of the people. The thing with your solution is that in the worst case, only one person is saved. The chief just always asks the person to the right of the last one.

By the way, there are ways to get more people saved ;)

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Originally posted by Yves M
Yes, they can elaborate a common plan together before the "event", so your answer is perfectly valid.

Without doing much statistical analysis, I think with your solution you would save in the mean 50% of the people. The thing with your solution is that in the worst case, only one person is saved. The chief just always asks the person to the right of the last one.

By the way, there are ways to get more people saved ;)

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No, even that way, 50 people would be saved. Imagine the people are numbered 1 to 100 in order counter-clockwise in an aerial view, so that when the "chief" is going to the right he is going 1, 2, 3, etc. p1 says p100's color. p2 says p99's color. Etc., then by the time numbers 1-50 are killed, all of 51-100 know their colors.

They choose one leader to direct people by hand signals (without talking of coarse) where they should go in the circle. That leader will sort out everyone by their hat color. Then the leader will go from group to group until the people nod that he's in the correct group. Then anyone the leader asks will be able to look at the group they are in and realize which hat they wear. ;) Of coarse I assume that this will not be a valid answer.

- Kevin

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Originally posted by Yves M
By the way, there are ways to get more people saved ;)

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What it boils down to is how much interpretable data can be transmitted each time a person is asked. Therefore I ask, does the color named have to be only Red, White, and Blue? (In real life they could name any color, sacrificing their own lives to save more)

I'm also assuming that the information is limited to the utterance of the name of a color, and does not include other possible factors such as who the person is looking at before, during, and after the color is named.

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Originally posted by KevinHall
They choose one leader to direct people by hand signals (without talking of coarse) where they should go in the circle. That leader will sort out everyone by their hat color. Then the leader will go from group to group until the people nod that he's in the correct group. Then anyone the leader asks will be able to look at the group they are in and realize which hat they wear. ;) Of coarse I assume that this will not be a valid answer.

- Kevin

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You are right !








It's not a valid answer indeed ;)

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Originally posted by solarflare
What it boils down to is how much interpretable data can be transmitted each time a person is asked. Therefore I ask, does the color named have to be only Red, White, and Blue? (In real life they could name any color, sacrificing their own lives to save more)

I'm also assuming that the information is limited to the utterance of the name of a color, and does not include other possible factors such as who the person is looking at before, during, and after the color is named.

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Let me put it this way:
- If they communicate using hand-gestures, twiching in the eyes, wiggling their feet or anything like that, everyone gets killed.
- If the person who is currently questioned by the chief responds something else than "red", "blue" or "white", they all get killed.

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Originally posted by Yves M
Let me put it this way:
- If they communicate using hand-gestures, twiching in the eyes, wiggling their feet or anything like that, everyone gets killed.
- If the person who is currently questioned by the chief responds something else than "red", "blue" or "white", they all get killed.

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What I mean is, there are always variables the terrorists cannot control, such as intonation, volume, exact time before speaking, etc. Is this to be taken out of the real world so that the only thing that matters is the color named?

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P.P.S Before being rounded up, they have one hour to decide on the best common strategy that will save the most of them.

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does this not mean they can talk?...
Can they communicate in anyway?
What is the ratio of reds hats: Blue hats: Green hats ?? Or can there be just 100 white hats even

Because any person can see 99 hat colors

If he uses ration and proportion on the avaiable hats like below
He would count how many colors of each are present.
say he finds 33 Reds 32 Blue and 34 White ... he would say "blue" and survive.

The only time he would have a problem in ansering is when the count is 33 R 33 B 33 W. He can have any color so his chances of survival that time are 1/3.

Ok! this is also an invalid answer I suppose :D

Maybe I'm misunderstanding solarflare's answer, but I can't see why every other person can't name the color of the hat of the next person, and that next person can use the name said by the previous person. At least 50 people get saved, and most likely the number saved will be around 67, since about a third of the people assisting their neighbor will be correct as well. That's how I read solarflare's answer...

Or... continuing voidspace's idea...

If the distribution is not known, but the people can see the hats before hand (in that pile by the big hut), they can just count the number of each color. Then, counting the number of each color they can see, they can always figure out which color is missing and must be on their head. Then you have 100% saved!

There is another solution, which saves all hundred people: get lucky. Although if you're kidnapped by terrorists, you're probably not lucky, so that idea's out.

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What I mean is, there are always variables the terrorists cannot control, such as intonation, volume, exact time before speaking, etc. Is this to be taken out of the real world so that the only thing that matters is the color named?

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Take it as an abstract question, so the only thing that matters is the color they say.

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voidspace
What is the ratio of reds hats: Blue hats: Green hats ?? Or can there be just 100 white hats even

galathaea
If the distribution is not known, but the people can see the hats before hand (in that pile by the big hut), they can just count the number of each color. Then, counting the number of each color they can see, they can always figure out which color is missing and must be on their head. Then you have 100% saved!

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They don't have a clue about that before being put into the circle. So when they are thinking about their strategy, they don't know the distribution of hat colors. They also never see the hats all together in a big pile.

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Maybe I'm misunderstanding solarflare's answer, but I can't see why every other person can't name the color of the hat of the next person, and that next person can use the name said by the previous person. At least 50 people get saved, and most likely the number saved will be around 67, since about a third of the people assisting their neighbor will be correct as well.

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That doesn't work, because the next person to be asked is picked at random by the canibal chief.

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Originally posted by Yves M
That doesn't work, because the next person to be asked is picked at random by the canibal chief.

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The last one works if some ones that already knows his hat color just says this color (saves himself). It means that half the persons asked will give the color of someone else's hat, this person being the next one this left that doesn't know and haven't been asked yet. This saves at least 50%

Then, the theory says that there is an average of 33% saved among the other persons, meaning the at least 50% will be saved, at most 100% (if all have the same color) and and average of 66.66%.

Then if there is a better solution....