MATH: How can you figure this out?

[Attic]

I hope you didn't waste your time producing that. It is clear from the context that Albert's first comment was made in the presence of Bernard because Bernard said he didn't know but does now. Now clearly meaning now that he has heard Albert's comment.

You have all the information you need. The king could choose all black hats if he wants to. You no the number and alignment of rows: one row. They can't turn their heads.

I figured out another solution if my original solution is deemed inappropriate because it depends on what I think is an unintentional loophole.

Spoiler

All prisoners agree that guy in rear will say black if he sees an odd number of black hats and red if he sees an even number of black hats. He again has 50-50 shot of being right. Everyone else can count and keep track of whether or not there is an even number of black hats left.

Example:
Prisoner in back sees 35 red hats and 64 black hats.
He says red because 64 is an even number. He dies if his hat is black.
Next guy counts black hats in front.
If he sees 64 (even number) black hats, he knows his is red.
If he sees 63 (odd number) black hats he knows his is black.
If he says red, next guy knows there is still an even number of black hats.
If he says black, next guy knows there is now an odd number of black hats left.
Cycle continues to end: 99-100 survivors.

Agree with that solution. Basically

Spoiler

99.5

can survive if running the logic through infinite situations.

 

[dank69]

We don't know, and have no information. There are potentially 3 "people" they could be talking to.

...

We do know. We know that it does not make sense for someone to say "then I ..." without being prompted first. It makes zero sense, so the possibility that they were not speaking in front of each other can be ruled out.

 

[mrjminer]

Based on many assumptions, sure. But look at the actual "facts"...as I posted in that photo. Without making opinionated guesses you cant come to any clear conclusion. And any conclusion based on opinionated guesses can not be stated as fact. Regardless of how many people make similar opinionated guesses.

I don't make any opinionated guesses. My answer is 100% correct, worked through logically. If you choose to remain ignorant, you choose to remain wrong.

 

[DrPizza]

Actually it is. They don't specify a setting for Albert and Bernard.

You're right. No setting was specified. The setting is logically deduced.

I find it weird that so many people had trouble deducting what the setting was:
"At first I don't know when Cheryl's birthday is, but I know now."
"THEN I ALSO know when Cheryl's birthday is."

I'm wondering if someone can actually come up with a reasonable context where they're not saying those lines in the presence of each other.

 

[DrPizza]

What if they were lined up single file across from one another. If they can't look to the side they would have no information at all and would each have a 50% chance of guessing right/wrong.

And if nobody is in front, none of them will see what gets placed on another.
Never was it stated as a rule that the "line" would be one in front of the other.
Or that such a line would then be run through front to back.

You guys and your damn assumptions. To narrow minded to properly think things through.

Line them up side by side if they cant move their heads.
Various start positions and/or random prisoner picks.
Line around corner or bend, or in the dark.
Move or change prisoners and or/hats.
Shoot them all anyway.
Align by height.
Etc etc...

They will not be able to see what's placed on their own head, or on the head of those behind them, but will be able to see all of the hats as they're being placed on the men in front of them.

You're kind of slow, aren't you? There isn't an in front of, or behind, if they're lined up side by side or in multiple rows, or all the other incorrect circumstances that are contrary to the problem, in an effort to rationalize for yourself that you're not slow - the problem just isn't fair.

And, the problem in the OP is a logic problem. If you can't logically deduce that they could hear each other speak, then I guess this question from Singapore weeded you out pretty well.

 

[dullard]

You're kind of slow, aren't you? There isn't an in front of, or behind, if they're lined up side by side or in multiple rows, or all the other incorrect circumstances that are contrary to the problem, in an effort to rationalize for yourself that you're not slow - the problem just isn't fair.

And, the problem in the OP is a logic problem. If you can't logically deduce that they could hear each other speak, then I guess this question from Singapore weeded you out pretty well.

You forget his name, EliteRetard.

To EliteRetard,
1) He adds rules such as no moving heads. A line side-by-side is even easier to solve (although the maximum expected result is still the same) since they can see everyone's head but their own by moving their heads.

2) He adds rules such as the guards choose the order (when clearly the text says "a prisoner correctly identifies the color of hat on his head"). It doesn't say a guard forces a prisoner to instantly identify the color of the hat on his head. It says the prisoner himself or herself identifies. But EliteRetard will add that rule and assume we all must follow his new rule.

3) His mathematical "lines" bend around corners. I suppose we are now in a non-Euclidean geometry?

4) He adds rules that the King and Guards can change the rules.

5) He ignores that it says the prisoners "will be able to see" but then says it is too dark to see or that people are hidden from view around corners.

6) He thinks that order matters. Sure swap people around, you still can use the same technique.

7) He thinks that "a row" might mean multiple rows.

Etc.

 

[dank69]

He says "Cheryl gives us this list of comments" which was never stated in the original text.

He says Cheryl is asking us when her birthday is when that is never stated in the original text.

If we "assume" anything, we can't think but he can assume whatever he wants I guess.

 

[Darwin333]

I think one of my favorites in this genre is "100 prisoners, to be executed the next day. But, the King decides to give them a chance. The next morning, the prisoners are to be lined up in a row. Each will have either a red or black hat randomly chosen to be placed on their head. They will not be able to see what's placed on their own head, or on the head of those behind them, but will be able to see all of the hats as they're being placed on the men in front of them. If a prisoner correctly identifies the color of hat on his head, he is allowed to live. If any prisoner says anything other than "red" or "black", every one of them is shot on the spot. If any prisoner cheats in any way, they're all shot on the spot. The prisoners know what is to happen, and the night before, plot to determine a way to ensure that a maximum number of them possible will survive.

What is the maximum number that can be guaranteed to survive, if the prisoners correctly follow an agreed upon procedure.

I'll refrain from giving the answer for a day or two. It's more than most people would suspect. A lot more.

I can logically deduce that it has been more than two days.

 

[DrPizza]

I can logically deduce that it has been more than two days.

The solution was given by another poster.

This is just another version of this very old logic puzzle:Cannibals ambush a safari in the jungle and capture three men. The cannibals give the men a single chance to escape uneaten.

The captives are lined up in order of height, and are tied to stakes. The man in the rear can see the backs of his two friends, the man in the middle can see the back of the man in front, and the man in front cannot see anyone. The cannibals show the men five hats. Three of the hats are black and two of the hats are white.

Blindfolds are then placed over each man's eyes and a hat is placed on each man's head. The two hats left over are hidden. The blindfolds are then removed and it is said to the men that if one of them can guess what color hat he is wearing they can all leave unharmed.

The man in the rear who can see both of his friends' hats but not his own says, "I don't know". The middle man who can see the hat of the man in front, but not his own says, "I don't know". The front man who cannot see ANYBODY'S hat says "I know!"

How did he know the color of his hat and what color was it?

That's not a very good logic puzzle, since there's no penalty for anyone guessing wrong. Seeing 3 black hats, and only 2 white hats, with 3 prisoners, instead of the rear prisoner saying, "I don't know," if he were smart, and since his life depended on it, he would use the trivial solution, rather than rely on his partners to be smart. I.e., if his partner was one of the "elite" posters above, he's doomed. "Black?" Nope. 2nd prisoner: "black?" "Nope." At which point, the first prisoner, understanding the pigeonhole principle, would say, "black."

 

[Darwin333]

The solution was given by another poster.

That's not a very good logic puzzle, since there's no penalty for anyone guessing wrong. Seeing 3 black hats, and only 2 white hats, with 3 prisoners, instead of the rear prisoner saying, "I don't know," if he were smart, and since his life depended on it, he would use the trivial solution, rather than rely on his partners to be smart. I.e., if his partner was one of the "elite" posters above, he's doomed. "Black?" Nope. 2nd prisoner: "black?" "Nope." At which point, the first prisoner, understanding the pigeonhole principle, would say, "black."

The above, while quite similar, isn't the logic question that you presented. The above I can easily figure out, the "guaranteed" qualifier in your question makes it a bit tougher. I'd guess 99 but since you included "random" and disqualified cheating I am not quite sure.