MATH: How can you figure this out?

[dank69]

Yeah, the 'tense' threw me off. As I read it I didn't take Albert's initial statement to mean that Bernard 'could not' know, just that he does not know - but I suppose that is redundant.

Either way I didn't quite make the connection between Albert's statement and removing May/June, I thought it was a premise, not something that he had actually determined.

If it was a premise it would have been false.

 

[disappoint]

That isn't "math". That's a logic problem.

The first information given rules out May and June because if the month is either of those, then the second person could know the date (only months with 18 and 19).

Now that I've gotten you started, you should be able to figure out the rest.

I was told there would be maths. There wasn't.

 

[mrjminer]

Yeah, the 'tense' threw me off. As I read it I didn't take Albert's initial statement to mean that Bernard 'could not' know, just that he does not know - but I suppose that is redundant.

Either way I didn't quite make the connection between Albert's statement and removing May/June, I thought it was a premise, not something that he had actually determined.

That's what actually took me so long. The way the wording is, it's like they are making guesses, not statements you are supposed to take as facts. If you can wrap your head around everything them saying being a fact, it makes it a little easier.

 

[Aikouka]

I'd be there with you if nobody was able to figure it out with the wording presented, but people are figuring it out as written. Don't blame the question if other people are getting it right.

That's rather short-sighted of you. Not everyone processes information the same way, and it's certainly understandable if someone reads that and has an issue with the way its written. I shouldn't be surprised to see a comment like this since humans are usually quite terrible at things involving not thinking about yourself for more than a damn second (e.g. empathy).

Procedure is for each person to say red or black normally if that is the true color of the hat in front of them, and say red or black in an abnormal accent if it is not the color of the hat in front of them. Start with person in the back who has a 50-50 shot of his hat matching the one in front of him. The other 99 live. I am certain this isn't the answer you are looking for. Instead of normal/accent they could also do whisper/normal or whisper/yell or normal/yell.

I was thinking about something like this, but I had one huge problem: he vaguely stated how they would be lined up (by mentioning that they could see the hat in front of them), but he never said in what order they would be questioned. That's important because your method doesn't work if they go front to back. Now, you can assume that it's back to front, but frankly... if we're asking a logic question, then goddamnit, I expect a fully-formed logical question!

EDIT:

Logic is a type of math.

I don't agree. Forms of math may use logic (that was the majority of my geometry class in high school), but that does not mean all logic is math. How about you go take a Philosophy course that involves philosophical proofs and attempt to pass it off as a Math credit. I doubt you'll get far.

 

[dank69]

...



I was thinking about something like this, but I had one huge problem: he vaguely stated how they would be lined up (by mentioning that they could see the hat in front of them), but he never said in what order they would be questioned. That's important because your method doesn't work if they go front to back. Now, you can assume that it's back to front, but frankly... if we're asking a logic question, then goddamnit, I expect a fully-formed logical question!

...

That was my first thought as well but then I figured that if it wasn't stated, it was the prisoners' option to decide the order.

 

[EliteRetard]

 

[EliteRetard]

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'm going to say we need more information, whats the number of hats of each color? The king could randomly decide to give them all black hats. If they knew there were 50 of each and it was single file the guy in the back could simply count hats and figure out his. The next guy would then be able to do the same etc until they were all free. Without knowing the number or alignment of rows, and the number of each possible hat I don't think it would be possible to guess your own. Can they look to the side? 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.

 

[irishScott]

I'd be there with you if nobody was able to figure it out with the wording presented, but people are figuring it out as written. Don't blame the question if other people are getting it right.

Reminds me of :

Huh? By that logic we shouldn't allow students to ask for clarification during exams, because some students are getting it right! Even the most notorious and anal of my engineering professors would occasionally make allowances for or even completely retract exam questions that were ambiguously stated and led a good chunk of people to different conclusions. Sometimes they'd even draw explanatory pictures on the board during exams to clarify what they were asking. They did this because they wanted to test your engineering knowledge, not your language parsing/guessing skills.

I got the question right too, after I cleaned up the conditions and realized what was going on. That doesn't mean it was a good question nor does it make it immune to critique.

 

[dank69]

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.

I'm going to say we need more information, whats the number of hats of each color? The king could randomly decide to give them all black hats. If they knew there were 50 of each and it was single file the guy in the back could simply count hats and figure out his. The next guy would then be able to do the same etc until they were all free. Without knowing the number or alignment of rows, and the number of each possible hat I don't think it would be possible to guess your own. Can they look to the side? 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.

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.

 

[EliteRetard]

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.

It is not clear at all.
Though, as stated at the bottom, if you attempt to make an assumption about those comments...the assumption would be that they told each other the answer. None of this changes the facts you are given however, and it is impossible to determine the correct answer based on fact alone.

 

[dank69]

It is not clear at all.
Though, as stated at the bottom, if you attempt to make an assumption about those comments...the assumption would be that they told each other the answer. None of this changes the facts you are given however, and it is impossible to determine the correct answer based on fact alone.

No assumptions needed. It is clear that the comments are part of a conversation. When Albert says "Then ..." it has to be a response to Bernard's statement.

 

[EliteRetard]

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.

You would be killed, since you fail at thinking. I already posted one scenario that would defeat both your "solutions".

With the extremely vague "rules" given I can come up with several other scenarios that would eliminate all but random luck.

 

[dank69]

You would be killed, since you fail at thinking. I already posted one scenario that would defeat both your "solutions".

With the extremely vague "rules" given I can come up with several other scenarios that would eliminate all but random luck.

How does the king using all black hats defeat any of my solutions?

 

[Exophase]

I remember having to solve a problem like this using Prolog.

Should I feel embarrassed that it took me like 10 minutes to get it?

 

[EliteRetard]

No assumptions needed. It is clear that the comments are part of a conversation. When Albert says "Then ..." it has to be a response to Bernard's statement.

It is not clear.
It doesn't "HAVE' to be response to Bernard.
That is all just supposition on your part.

There is virtually no information given, and all the facts that are clearly stated are laid out in the photo above.

If we can assume anything we wish about any portion of what a person says, then we can claim any number of facts about you with just this one post.

 

[dank69]

It is not clear.
It doesn't "HAVE' to be response to Bernard.
That is all just supposition on your part.

There is virtually no information given, and all the facts that are clearly stated are laid out in the photo above.

If we can assume anything we wish about any portion of what a person says, then we can claim any number of facts about you with just this one post.

So your theory is that people blurt out statements that start with "then I ..." without being prompted by someone else?

 

[EliteRetard]

How does the king using all black hats defeat any of my solutions?

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...

 

[JujuFish]

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.

That's what I was thinking.

Spoiler

One person to be a parity bit, so to speak, and the rest can then deduce from there.

Of course, it only works if the prisoners are asked in reverse order.

 

[Newell Steamer]

Cheryl is playing head games with these guys - probably to get free pot or drugs or booze from them.

They need to move on, because split roasting a wasted skank is gross.

 

[JujuFish]

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...

Almost all of these are invalid. You might want to reread what DrPizza wrote:

but will be able to see all of the hats as they're being placed on the men in front of them.

 

[EliteRetard]

So your theory is that people blurt out statements that start with "then I ..." without being prompted by someone else?

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

And as stated, if any assumption is to be made, why would you assume they don't just share their information. To me the logical conversation with the given information would be like this:

A: "Neither of us knows the complete date right? She did tell me it was X month."
B: "I didn't know the complete date, but I do now, since she said day was Y"
A: "Ah, well I guess I know the correct and complete date now too."

But perhaps they're just interjecting:

C: "Do either of you know what my birth date is now?"
A: "Of course not, B doesn't know either"
B: "I didn't know before, but I do now"
A: "Yeah, I do too."

Now how the heck does that help us at all? The fact is Cheryl is giving incomplete and very vague information. Based on what she has told us, or what we think we know, there are many assumptions that can be made, and they can clearly vary significantly. How can we make any accurate assumptions about a conversation we did not hear, but was relayed to us by an unreliable source?

How can you claim to know the answer for a fact, based on your opinionated assumptions? You cant, therefore you don't have a factual answer.

As another poster put it: Cheryl is a conniving bitch, prone to half truths.

That answer wouldn't give you a grade though, so the best option is to try to lay the "facts" out as they are presented. If her birth date really does lie on one of the 10 dates she has given us, then the answer is simply a 1 in 10 guess for us. All the other crap is just hearsay and is there to obfuscate the truth.

Like that one sig I saw floating around here:

"Make them think they're thinking and they'll love you. Make them really think and they'll hate you."

Cheryl is just messing with you, and she won.

 

[EliteRetard]

Almost all of these are invalid. You might want to reread what DrPizza wrote:

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.

 

[mrjminer]

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

And as stated, if any assumption is to be made, why would you assume they don't just share their information. To me the logical conversation with the given information would be like this:

A: "Neither of us knows the complete date right? She did tell me it was X month."
B: "I didn't know the complete date, but I do now, since she said day was Y"
A: "Ah, well I guess I know the correct and complete date now too."

But perhaps they're just interjecting:

C: "Do either of you know what my birth date is now?"
A: "Of course not, B doesn't know either"
B: "I didn't know before, but I do now"
A: "Yeah, I do too."

Now how the heck does that help us at all? The fact is Cheryl is giving incomplete and very vague information. Based on what she has told us, or what we think we know, there are many assumptions that can be made, and they can clearly vary significantly. How can we make any accurate assumptions about a conversation we did not hear, but was relayed to us by an unreliable source?

How can you claim to know the answer for a fact, based on your opinionated assumptions? You cant, therefore you don't have a factual answer.

As another poster put it: Cheryl is a conniving bitch, prone to half truths.

That answer wouldn't give you a grade though, so the best option is to try to lay the "facts" out as they are presented. If her birth date really does lie on one of the 10 dates she has given us, then the answer is simply a 1 in 10 guess for us. All the other crap is just hearsay and is there to obfuscate the truth.

Like that one sig I saw floating around here:

"Make them think they're thinking and they'll love you. Make them really think and they'll hate you."

Cheryl is just messing with you, and she won.

It is definitely possible to work through to the correct answer. However, it's not easy, especially with the shitty wording. See my post for the walkthrough: http://forums.anandtech.com/showpost.php?p=37331672&postcount=30

 

[EliteRetard]

It is definitely possible to work through to the correct answer. However, it's not easy, especially with the shitty wording. See my post for the walkthrough: http://forums.anandtech.com/showpost.php?p=37331672&postcount=30

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.

 

[dank69]

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.

The puzzle states that the prisoners will be lined up in a row. One row, not rows. The puzzle states that they will be able to see the hats on the prisoners on front of them, and will not be able to see the hats on those behind them. This means they have to be lined up front to back since they can't have people in front or behind if they are in a single row side to side.