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Author Topic: Red and Blue hats  (Read 6468 times)

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Offline Builderboy

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Red and Blue hats
« on: July 21, 2012, 12:49:42 am »
So a large village of people lives by a forest that is terrorized by a goblin.  Occasionally when a large group of villagers go out to hunt, the goblin takes kidnaps them and plays a cruel game with them.  The goblin first forces the villagers to stand in a single file line with each villager facing the one in front of him, and then places either a red or a blue hat on each villager such that they do not know what color hat they have on.  If any villagers move or make any sort of signal, the goblin kills all of the villagers immediately.  The goblin then starts from the back of the line (starting with the villager with nobody behind him that is) and asks them which color hat they are wearing.  The villagers must either answer red or blue, and any variation or movement once again gets all the villagers killed.  If the villager is wrong, he gets his head bitten off, and if he is correct, he is permitted to live, but must stand in his location without moving until the goblin is finished.  After the goblin is finished asking each villager, all the ones still alive are permitted to leave safely.

The villagers (or at least the survivors) over time have come to learn the goblins game very well, and so set out to determine if there is a best strategy they can use to ensure the highest survival rate on average.  They keep in mind that all villagers can hear the responses of all villagers before them, and a villager will know when a fellow villager answers incorrectly based on the sound of their head being eaten.  All villagers can also see the hat color of all villagers in front of them.

So the question stands, if all of the villagers can come up with a strategy beforehand, what would the most optimal strategy be?
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Offline Hayleia

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Re: Red and Blue hats
« Reply #1 on: July 21, 2012, 02:57:29 am »
PMed my answer :)
I can save at least N-2 villagers (considering N>2)
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Offline Builderboy

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Re: Red and Blue hats
« Reply #2 on: July 21, 2012, 05:07:31 am »
You can save N-1 villagers with just a slight modification of your logic :)
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Offline Scipi

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Re: Red and Blue hats
« Reply #3 on: July 21, 2012, 06:41:07 am »
Well, if any of the villagers in the line have ADHD, they're all screwed :P jk

Is there an even number of red and blue hats or are the numbers arbitrary?
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Wait... This just in, the Omnimagians have sent the UN a list of demands that must be met or else the world will be "submitted to the wrath of Netham45's Lobster Army". Such demands include >9001 crates of peanuts, sacrificial blue lobsters, and a wide assortment of cherry flavored items. With such computing power stored in the hands of such people, we can only hope these demands are met.

In the wake of these events, we can only ask, Why? Why do these people make these demands, what caused them to gather, and what are their future plans...

Offline cyanophycean314

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Re: Red and Blue hats
« Reply #4 on: July 21, 2012, 10:02:21 am »
Hmmm.... maybe this has something to do with sacrificing to let other people know in front of you what they're wearing?  ???
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Offline Hayleia

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Re: Red and Blue hats
« Reply #5 on: July 21, 2012, 10:07:56 am »
Quote from: Builderboy on July 21, 2012, 05:07:31 am
You can save N-1 villagers with just a slight modification of your logic :)
PMed you my update :P
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Offline thepenguin77

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Re: Red and Blue hats
« Reply #6 on: July 21, 2012, 03:39:23 pm »
Perhaps I'm misunderstanding the rules. But I'm fairly certain I can save all but the first villager.

Spoiler For Spoiler:
If the person in front of you has a red hat, you respond with a high pitch voice.

If the person in front of you has a blue hat, you respond with a low pitch voice.
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Offline parserp

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Re: Red and Blue hats
« Reply #7 on: July 21, 2012, 03:44:12 pm »
But are they asking from the front person to the back person? If so, thep's answer wouldn't work. :-\

EDIT: didn't read the whole post :P Looks like thep's answer saves all but .5 of the first person. (He has a 50% chance of guessing what hat he has on) :P
« Last Edit: July 21, 2012, 03:46:30 pm by parserp »
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Offline thepenguin77

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Re: Red and Blue hats
« Reply #8 on: July 21, 2012, 04:03:23 pm »
Mine would work, but I'm fairly certain it's cheating.
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Offline Builderboy

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Re: Red and Blue hats
« Reply #9 on: July 21, 2012, 04:31:11 pm »
Lol yeah that is cheating
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Offline Scipi

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Re: Red and Blue hats
« Reply #10 on: July 22, 2012, 10:41:57 am »
Sent in my answer. It assumes the villagers know how many red and blue hats there are though :P
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Spoiler For IMPORTANT NEWS!:
Late last night, Quebec was invaded by a group calling themselves, "Omnimaga". Not much is known about these mysterious people except that they all carried calculators of some kind and they all seemed to converge on one house in particular. Experts estimate that the combined power of their fabled calculators is greater than all the worlds super computers put together. The group seems to be holding out in the home of a certain DJ_O, who the Omnimagians claim to be their founder. Such power has put the world at a standstill with everyone waiting to see what the Omnimagians will do...

Wait... This just in, the Omnimagians have sent the UN a list of demands that must be met or else the world will be "submitted to the wrath of Netham45's Lobster Army". Such demands include >9001 crates of peanuts, sacrificial blue lobsters, and a wide assortment of cherry flavored items. With such computing power stored in the hands of such people, we can only hope these demands are met.

In the wake of these events, we can only ask, Why? Why do these people make these demands, what caused them to gather, and what are their future plans...
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