If they are only allowed to say the words black or white, the first person can say the next person's hat color and then guess their own. The next person would say the hat colour of the person in front of them and then say the color of his hat that the previous person said. Continue on and you end up with up to one death. This is, of course, allowing the each person to only say black or white, but it was never specified that they can only say ONE word.

Idea 2:
They simply move their eyes upward like any thinking being and say the color they see.

Lulz nice try but no. One word only and they can't see their own hat.

Hmm... I know a way if they didn't have to go in order. And it appears that through my way of thinking, there is only an optimal strategy for odd numbered groups.

Post has been edited 1 time(s), last time on Dec 3 2008, 4:55 am by A_of-s_t.

Most people have these things called "skulls", y'know. ;o
What kind of hat was never specified, and many varieties don't extend significantly beyond one's forehead.

Feeling too lazy to try thinking of an answer right now, but for whenever I do, and possibly whomever may get to it sooner than I - they do know whether or not the person/people behind them have died, correct?

The first person counts the number of black and white hats he sees. If B>W, he should guess W since this is random (giving a 50/50 chance). No matter what he answers, the next person will know the hat color, and now will have a hint at their own hat color, if they said white B>W, so they now count the hats and use the same method, white if B>W and black with W>B. Each time someone goes, the next person's information becomes greater and their probability of living increases.

This is the most optimum strategy I can think of using your rules . I've seen the question presented a different way and they most optimum stategy was (n-1)/n for odd numbers.

That sounds very close...but I think something might be slightly off...

I don't think it matters if they know whether or not the person behind them dies. For the sake of making the puzzle uber-hard, I'm going to say they don't know since my solution does not require it. But go ahead and try to solve it if they know (or don't), I'd like to see what you come up with regardless.

There is no "randomness" for the answer, except the first guess since that guy has absolutely no clues to help him. Poor guy..

Actually, he does. Combination says he has a greater chance of getting his hat color right if he guesses his hat color based on which color has less.

Guys... this is the same thing as 100 brown eyes and 100 blue eyed people on an island. The first one (who has no clue about his color) is the Guru (green eyes).

The first one counts all hats and the says the color that he counted most hats of. Then all others can logically deduct their hat color.
Check http://www.staredit.net/105126/ to see how this logic actually works.

They can only say black or white. Obviously...

Like I said, the optimal strategy allows at most one death (the first guy) so randomness doesn't have to be a part of it.

And it's not like the color of eye thing. At all. Except you use some logic... *wink wink*.

wut
I think we're assuming the hats are given 50% chance of either color, not based on other rolls. ;o

wut
The person behind you, the first guy, says "black". You see 26 black, and 5 white. What color are you?
Whichever you are would still be able to satisfy the condition of "black is the color he counted most hats of".

Srsly, I can understand sub-optimal answers ( i.e. 75% success rate ) , but making blatantly false statements confuses me.

Eh, I'm going to sleep, maybe I'll figure something out by tomorrow morning.

Yeah. I doubt anyone's going to get it anytime soon. And the answer DOES guarantee (n-1) survival rate.

The colours of the stars and the endless space. Ursa Major.

I got it! As I was sleeping, I began to dream of this scenario and the person behind me was taking forever to answer -- 120 seconds to be exact -- and then said white triumphantly. I only saw 119 white hats in front of me and waited 119 second to proudly exclaim white as my hat color.

All people agree that they will count the number of white hats they see and wait that many seconds before answering the question. The first person starts this, and only has an educated guess (going with which color has the least), but the next person now know how many hats he had seen with him ONLY saying white or black. If the next person sees fewer white hats then the time the previous person took, he knows his hat was white. If equal, his hat is black. This continues on to the last person, with EVERY person getting their hat color correct except -- perhaps -- the first one.

This stategy means no one needs to know who dies NOR do they need to know the previous person's hat color -- they only need to count white hats and count how many seconds it takes the person behind them to answer.

DONE.

Wtf, why is their like 2-3 puzzles going on since 3-4 pages ago?... Dam i can't even find which puzzles haven't or have been solved. STOP POSTING PUZZLES until you get the green light from the dam poster :C

Remember Fatal exception? nuff said.

Yeah, that's, unfortunately, the wrong kind of thinking. Like I said, it's not a trick. There's no subtle communication going on. If you were one of the guys in line and it's your turn, all you know is this: all the hats in front of you and all the answers the people behind you said. Nothing about when they said it, how they said it, etc; only what they said and in what order.

Let me give you guys a hint. The first person's response provides the "answer" for all the other people.

First guy counts how many White Hats to Black Hats, and says "White", where he dies. (White being the most populated).
Next guy says white and so forth...

Edit: You know what, A_of-s_t's solution proves to be the most effective.

I just now looked it up and this is actually the type of solution that Wikipedia and every other site uses. I have no fucking idea how cheeze does it.