Ten hats puzzle

An alien has abducted ten logicians and placed them in a room. He explains to them that he first order them in a line, from tallest to shortest, with each person facing the direction of the next shortest person in front, so that each person may see all shorter logicians, but no taller ones. He then explains that he will place a black or white hat on each person, however nobody will be able to see the color of his own hat, only the hats of the shorter logicians. The distribution of black and white hats could be anything, not necessarily five and five.

The alien then explains that he will ask each logician, starting with the tallest, and moving down the line, the color of his hat. The logicians may hear the response of those acting before them. Other than the black/white responses, they may not communicate in any way once the game has started. If more than one logician is wrong, then they will all be eaten. If at least nine answers are correct, they will be returned safely to earth. The alien then gives them some time to strategize. What should their strategy be?

Please put answers in spoiler tags. Beer to the first correct answer. If must confess I just made this an Ask the Wizard question, so please don't cheat and look at my answer. If you have any issues with it's wording, please also put that in spoiler tags.

All logicians must answer?

Wait, that was wrong. Lemme think...

Quote: RS

All logicians must answer?

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I’m gonna say, the tallest logician says the same color hat as the shortest. Then second tallest says the same color as second shortest. Etc. that way 5 answers are guaranteed correct and the other 5 are tossups. Obv. The shortest 5 just say what their corresponding logician said (shortest repeats what tallest said, because tallest was saying what shortest has).

I think that means as long as 4/5’ths are correct, then they win, because the last 5 are guaranteed to be correct.

I’m sure this can be far improved somehow but I don’t got time for dis

Quote: CrystalMath

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The tallest logician counts the number of black hats. If it is even, he says “black” otherwise “white.”
Paying attention to each answer before your turn, you will always know if the remaining hats have an odd or even number of black hats.
For instance, the hats are bwbbwwbwbb.
The first one says white, indicating an odd number of black hats.
The second sees 5 black hats, so he knows he doesn’t have a black one, and he says white.
The third knows there are still an odd number of black hats. Observing 4 black hats ahead of him, he knows he must also have black.
The fourth now knows there must be an even number of black hats. Observing 3 ahead of him, he must also have black.
...

This is correct! I owe you a beer.

The US Department of Labor Statistics shows no occupational category called Logician.

After reading the definition of logician, I would claim that no elected official at the state or federal level is a logician.

After reading a couple of the politics-themed threads in this forum, I conclude that very few of the members here are logicians.

The Wizard challenge might have been: how in bloody hell did an alien find 10 logicians to line up in a row?

Quote: gordonm888

The US Department of Labor Statistics shows no occupational category called Logician.

I'd like to think of myself as a logician. Maybe I should say that when people ask me my profession.