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Re: Re: (OT) Meditate on this brain-teaser
by dragonchild (Archbishop) on Dec 12, 2001 at 19:05 UTC
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The point isn't in what someone sees, the point is in what someone doesn't see. C knows that his hat is either white or blue. Now, let's say that C's hat is white. That means that A sees a white and a blue (because we know B's hat is blue). A can't make any decisions, for the very reason you stated.
So, let's see what B thinks. (Remember, C's hat is white at this moment, and that A didn't do anything.) Since A didn't do anything, B knows his hat cannot be white. (If B's hat was white and C's hat was white, A would say his hat is blue.) So, B knows that his hat must be blue.
But, B doesn't do anything, either. So, since A didn't stand up and B didn't stand up, then C must be able to stand up because his hat isn't white.
Does that make sense?
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We are the carpenters and bricklayers of the Information Age. Don't go borrowing trouble. For programmers, this means Worry only about what you need to implement. | [reply] |
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Tut, tut Dragonchild,
There are a lot of assumptions being made here: That the players are rational thinkers and intelligent enough to realise this kind of strategy etc... I just find these problems incredibly annoying because I'm not very good at them and people who get the answer right tend to do so not because of induction but more because they've seen it before! It rather reminds me of a physics joke I once heard.
A horseracing fan wins a million dollars/pound/shekels in the lottery and decides to invest it in an interesting proposition: He will find out how to predict the winner of a horserace with 95% accuracy based on the build, weight and past form of a horse. To do this he goes to a racehorse trainer, a molecular biologist and a theoretical physicist: He gives them each $10000 just for working for one year and promises the winner $250,000 more if they win.
After the year is up he returns to each. The horse trainer is pleased to report than he can get it right 75% of the time and the fan is impressed, but his heart heavy he wanders on. The molecular biologist is delighted to report that he got to 80% but progressed no further. Eventually the fan comes to the physicist, who replies, "Yes, I can predict which horse will win any race with 99.5% probability of success with one minor catch."
Needless to say, the racing fan is impressed and offers the physicist the prize money in return for the analysis, however the physicist being an honest man says he must tell him the catch first:"It must be a spherical horse running in a vacuum!"
"A nerd is someone who knows the difference between a compiled and an interpreted language, whereas a geek is a person who can explain it cogently over a couple of beers"
- Elgon
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Those are cogent issues with this type of brainteaser. However, it is a common assumption for the brainteaser that all subjects are intelligent and rational.
The idea isn't to find the real-world solution, but to find the correct solution (for some value of correct).
I guess the way I think about it is that a chess GM can say "Mate in 8 moves." Ok, that's great. However, it's mate in 3 moves unless your opponent does the perfectly correct move. The GM has to assume perfect play when making that assertion, not normal play.
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We are the carpenters and bricklayers of the Information Age. Don't go borrowing trouble. For programmers, this means Worry only about what you need to implement.
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Consider how different the puzzle would be if a correct
guess spared only the guessers' head, an incorrect guess
doomed them all and there was a time limit (which if not
met, doomed them all as well). Now it's more like a game of
chicken which will end with a 50-50 chance of three heads
rolling.
--Jim
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Ummh. No. As stated a player can only be sure of their hat color if they see two white hats as the only stated condition is at least one blue hat. All players see at least one blue hat. None of the players see two whites. They are all in the position of seeing at least one potentially lethal blue hat.
In fact A and B are identical in all respects. They are better denoted A and A'. They both see B-X where X is C's hat color. C sees B-B. No one sees the required W-W combination. There is no logical solution. The lack of response on all player's behalfs is logical. C is a punter
cheers
tachyon
s&&rsenoyhcatreve&&&s&n.+t&"$'$`$\"$\&"&ee&&y&srve&&d&&print
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Yes, you're right. All players do see at least one blue hat. But, the puzzle depends on this:
C is trying to determine if the other players see one blue hat or two blue hats!
Another thing that might be confusing you is that this is a proof by negation. The proof isn't that C has a blue hat on his head. The proof is that C doesn't have a white hat on his head. Since !white == blue, C has a blue hat.
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We are the carpenters and bricklayers of the Information Age. Don't go borrowing trouble. For programmers, this means Worry only about what you need to implement.
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[d/l] |
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Lets look at this from an outsiders point of view...
From this new perspective there are only three scenerios --- 1 blue hat in the group, 2 blue hats in the group, and 3 blue hats in the group
- One blue hat - Guy wearing the blue hat sees two white hats, jumps up immediately and yells "BLUE" - Time to play 10 seconds.
- Two blue hats - One of the guys wearing a blue hat realizes that if his own hat was white, the other guy would have yelled "BLUE" 10 seconds into the game. Since this didn't happen, his own hat must be blue. Time to play: 5 minutes.
- Three blue hats - Someone realizes that if his own hat was white, one of the other two would have jumped up and yelled "BLUE" at the 5 minute mark. Since that didn't happen, his own hat must be, "BLUE!" - Time to play 20 minutes.
-Blake
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