# The Overcrowded Prison

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A prison was overcrowded - not simply crowded, you understand, overcrowded. So the warden decided to offer freedom to a prisoner to help relieve the overcrowdedness. But he premised freedom on a test.

Three prisoners were brought into a room and each was ordered to put on a blindfold and reach into a duffel bag and take a hat and put it on his head. In the duffel bag were two red hats and three black hats.

After removing the hats and putting one on his own head, the first prisoner was ordered to take off his blindfold, permitting him to see the other two prisoners' hats, but not his own. If he could tell the color of the hat on his own head, he would be pardoned immediately. If he guessed, and was incorrect, he would be shot immediately. So nobody guesses.

After removing blindfolds,

First prisoner: "I don't know."

Second prisoner: "I don't know."

Third prisoner, who is blind: "I know."

Does he? Explain.

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I'm obviously missing something - I don't see how he could possibly know. If we call the prisoners A,B and C and the hats R and B, then the possible combinations are

A-B-C

1) B,B,B

2) B,R,R

3) B,R,B

4) B,B,R

5) R,B,B

6) R,B,R

7) R,R,B

The eight variation R,R,R is impossible because there are only 2 red hats.

If A says don't know, it excludes 2), and if B says don't know, it excludes 6), but it still leaves 1),3),4),5) and 7). Four of these has him with a black hat, but the fifth with a red one. Given that there are more black than red, the probability of 4) being the case is quite small so perhaps C is taking a fairly safe bet.

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The other two are wearing red hats.

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I don't understand the spoiler - even if that were the case, there are the others I listed above which were possible

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I don't understand the spoiler - even if that were the case, there are the others I listed above which were possible

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I'm obviously missing something - I don't see how he could possibly know. If we call the prisoners A,B and C and the hats R and B, then the possible combinations are

Agreed. The only thing the blind guys knows for certain is that both he and one other person are not wearing red hats, otherwise one of the first two would have known that they wore a black hat.

Therefore it is possible that both of the first two prisoners are wearing black (in which case a black hat would remain) or that one is wearing black and one is wearing red (in which case a red hat would remain).

Hence, the blind guy doesn't know with certainty the color of his hat.

Edited by zapatos
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Agreed. The only thing the blind guys (sic) knows for certain is that both he and one other person are not wearing red hats, otherwise one of the first two would have known that they wore a black hat.

Therefore it is possible that both of the first two prisoners are wearing black (in which case a black hat would remain) or that one is wearing black and one is wearing red (in which case a red hat would remain).

Hence, the blind guy doesn't know with certainty the color of his hat.

This puzzle has been viewed 89 times and nobody in this august crowd has been able to figure out the solution.

There is an important lesson here. Given the same set of facts, many if not most people are unable to reach what is a clearly valid conclusion.

Even AFTER zapatos acknowledged that the blind prisoner "knows for certain" that he is "not wearing" a red hat, he still claims "the blind guy doesn't know with certainty."

Amusing, no?

Solution: Prisoner #1 does NOT see 2 red hats.

Prisoner #2 does NOT see 2 red hats on #1 and #3, BUT IN ADDITION, he does NOT see a red hat on #3, for IF HE DID, he would know his own hat was black.

Prisoner #3, who is blind, recognizes the value of information gleaned from prisoner's #1 and #2 and says, "My hat is black. Buh bye."

All the blather and bluster here about intellectualism and rationalism seem rather misplaced.

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Even AFTER zapatos acknowledged that the blind prisoner "knows for certain" that he is "not wearing" a red hat, he still claims "the blind guy doesn't know with certainty."

Amusing, no?

Of course, that isn't what I said, is it? What is amusing is your inability to actually read what I write (you are now two for two).

Here, I'll copy it below as you seem to having trouble reading my posts the first time around.

"The only thing the blind guys knows for certain is that both he and one other person are not wearing red hats"

Perhaps you'd benefit from Googling 'conjunctions'.

Did you come to this site because you ran out of local people to be rude to?

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Of course, that isn't what I said, is it? What is amusing is your inability to actually read what I write (you are now two for two).

"Hence, the blind guy doesn't know with certainty the color of his hat." - Zapatos, in the post in question

Yes, that IS what you said. It is wrong. He DOES know with certainty the color of his hat.

First you said he does, then you countered yourself and concluded with "he doesn't know."

I repeat, 89 viewers and not one of you could get it right in this totally brilliant science forum.

And speaking of rudeness, I find your childish attacks on The Lord to be extremely rude and offensive.

Edited by GeniusIsDisruptive
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I repeat, 89 viewers and not one of you could get it right in this totally brilliant science forum.

Nursing some hurt feelings?

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Nursing some hurt feelings?

"Hence, the blind guy doesn't know with certainty the color of his hat." - Zapatos, in the post in question

Prisoner #3's hat was black. You were wrong, but can't admit it. Genius is disruptive.

"There are only two kinds of people, decent and indecent." - Elie Wiesel

Your footnotes clearly show which kind you are.

Edited by GeniusIsDisruptive
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This puzzle has been viewed 89 times and nobody in this august crowd has been able to figure out the solution.

There is an important lesson here. Given the same set of facts, many if not most people are unable to reach what is a clearly valid conclusion.

Even AFTER zapatos acknowledged that the blind prisoner "knows for certain" that he is "not wearing" a red hat, he still claims "the blind guy doesn't know with certainty."

Amusing, no?

Solution: Prisoner #1 does NOT see 2 red hats.

Prisoner #2 does NOT see 2 red hats on #1 and #3, BUT IN ADDITION, he does NOT see a red hat on #3, for IF HE DID, he would know his own hat was black.

Prisoner #3, who is blind, recognizes the value of information gleaned from prisoner's #1 and #2 and says, "My hat is black. Buh bye."

All the blather and bluster here about intellectualism and rationalism seem rather misplaced.

Your egotistical rant might make some kind of sense if you were right.

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Your egotistical rant might make some kind of sense if you were right.

1. You do not so much as make even a feeble attempt to demonstrate how I am "wrong." Very unscholarly and rude of you.

2. I am not the subject. The subject is "The Overcrowded Prison" and your collective failure to solve the puzzle. Obviously this angers you greatly to the extent that you must call ME "egotistical."

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I too have a riddle - How long before "GeniusIsDisruptive" gets banned?

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I too have a riddle - How long before "GeniusIsDisruptive" gets banned?

I have the answer. Not long because you folks are tragically intolerant. You are, in the words of Harvard scholar, Ruth Wisse, "A Herd of Independent Minds."

A simple puzzle has your panties twisted into knots, and your "Moderators" are hustling to close any thread I might originate.

There is a telling article by the National Association of Scholars, titled "A Crisis of Confidence - The Corrupting Effect of (Leftist) Political Activism at the University of California." It describes this forum's members perfectly. Perfectly. And this explains the disastrous state of public education throughout America.

"Public education is a socialist monopoly, a real one." - The Late Milton Friedman

Now, why don't all of you call up some more of your friends. The more crap you throw up on the wall, the more you believe will stick. I cited zapatos' glaring mistake, and he sniveled and withdrew.

Then comes Manticore to suggest I am wrong, but how, he cannot and will not say.

Now the whining koti wants me banned and quickly, because all of you together can't stand to be taught even simple lessons.

You are blinded by your pride. And it's ugly. It's destructive. It makes you very uncomfortable to the extent that you demand I go away, such is your inability to deal with truth.

the probability of 4) being the case is quite small so perhaps C is taking a fairly safe bet.

One chance in 7 is "quite small"? When death is on the line?

That's "fairly safe"?

Talk is cheap.

Edited by GeniusIsDisruptive
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I'd actually like you to stay and see you make some proggress. Before you get banned at least try to understand where your error is in accusing Zapatos of an error which is not there. While at it, you could continue your progress by stoping projecting your insecurities on this forum to a point in which a group of 12 year olds could see them...not to mention a bunch of PHD's who you are trying to "disrupt" with your bulshit. There are 14 year olds on this forum writing more coherent and valusble posts than you. Your choice...stay and learn or get banned and go back to the dark place.

Edited by koti
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I don't suppose if anyone really cares about your problem that you got from a book. You probably didn't think it up yourself. There are plenty of problems that I am sure many of the intelligent people here won't be able to solve - so what? No-one cares. I rather suspect no-one wants to put in the effort to play your game - especially if they are going to be insulted for not getting it right.

You clearly have your own rigid agenda which you are immovable from. Why are you even here if you do not want to talk or learn science? No-one wants to hear your ignorant angry rants except your brainwashed mates.

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I'd actually like you to stay and see you make some proggress. (sic) Before you get banned at least try to understand where your error is in accusing Zapatos of an error which is not there. While at it, you could continue your progress by stoping (sic) projecting your insecurities on this forum to a point in which a group of 12 year olds could see them...not to mention a bunch of PHD's who you are trying to "disrupt" with your bulshit. (sic) There are 14 year olds on this forum writing more coherent and valusble (sic) posts than you. Your choice...stay and learn or get banned and go back to the dark place.

Zapatos CONCLUDED with this error:

"Hence, the blind guy doesn't know with certainty the color of his hat."

The blind guy DOES know with certainty the color of his hat. It is black.

"Valid criticism does you a favor." - Carl Sagan

Now why don't YOU try writing something coherently and try to learn, if you can.

"Public education is a socialist monopoly, a real one." - The Late Milton Friedman

Edited by GeniusIsDisruptive
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It ha

1. You do not so much as make even a feeble attempt to demonstrate how I am "wrong." Very unscholarly and rude of you.

2. I am not the subject. The subject is "The Overcrowded Prison" and your collective failure to solve the puzzle. Obviously this angers you greatly to the extent that you must call ME "egotistical."

It has already been explained to you by others exactly why you are wrong.

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I don't suppose if anyone really cares about your problem that you got from a book. You probably didn't think it up yourself. There are plenty of problems that I am sure many of the intelligent people here won't be able to solve - so what? No-one cares. I rather suspect no-one wants to put in the effort to play your game - especially if they are going to be insulted for not getting it right.

You clearly have your own rigid agenda which you are immovable from. Why are you even here if you do not want to talk or learn science? No-one wants to hear your ignorant angry rants except your brainwashed mates.

Ah yes, nobody "really cares" so much that there have been 154 hits in just over a day. Compare that frequency with others in the thread.

Nor did I claim that I thought it up myself. You are desperately searching for something - anything to impugn me because you and your pals could not solve this simple puzzle. And in your collective embarrassment, you smear me in the pettiest ways imaginable, claiming that I come from a "dark place."

As to who has a "rigid agenda," look in the mirror. At least I can talk about atheism without screaming and ranting "ban him, ban him!"

I communicated at length with Richard Dawkins, Carl Sagan, and Isaac Asimov to name but a few. So don't try impressing me with your PHD "bulshit" (sic).

This is NOT a science topic, in case you had not noticed. But if you wish to discuss science, then by all means, start your own thread and teach to your heart's content. Give me a link and I'll happily join in... if you Leftists can tolerate a shred of reasoned counterpoint.

So far, you're incapable of doing that.

Incidentally, your pretend to be in a "light place," far removed from the "dark place" you have foisted upon me in your all too imitable style. How kind and thoughtful and intellectual of you. Really.

Edited by GeniusIsDisruptive
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Read back through the thread carefully and see who starts being an arsehole first. This isn't about science or facts here - this is the first time you and I have ever engaged in a conversation. I have no embarrassment over this puzzle. I'm trying to impress no-one, I'm not the one who is name dropping. I'm not trying to teach you anything, it's just an observation. You come across really angry about stuff - probably because that is synonymous with the kind of fear and loathing bred by right wing propaganda in people that believe it. It's sad.

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GeniusIsDisruptive - You come across as someone who would like acknowledgement from the people in this thread that you posted a very difficult riddle which is too hard to figure out for the ignorant, leftist idiots like myself and the rest of the people reading this thread. This is actually not how you come across, it is exactly what you are saying in your posts. Do you realise how cardinaly dumb your stance is and do you realise what a complete fool you are making of youreself? Would you care to reconsider the above and reconsider your attacks on every single person who engages with you in this thread?

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I communicated at length with Richard Dawkins, Carl Sagan, and Isaac Asimov to name but a few. So don't try impressing me with your PHD "bulshit" (sic).

Pestering them via eMail or Facebook until they block you doesn't count as communication.

I've read some of your posts. Your threads are not getting closed because the mods are intolerant. It's because they are complete drivel. I mean, you came in tried to disprove global warming by pointing out that global changes in temperature are smaller than the changes between seasons. You think no one has noticed this in the years of researching global warming. I mean, you must be a complete idiot.

And then you also attempt to disprove evolution and preach Christianity as fact. You have no idea what you are talking about and none of what you say is scientific in the slightest. I know you think you're some sort of genius, when in reality, you're an average moron who read something on the New World Order or some other crackpot site and you think you're going to ''save christianity'' and ''disprove science''. I have not read a single intelligent thing by you. Perhaps you should learn some science.

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Read back through the thread carefully and see who starts being an arsehole first. This isn't about science or facts here - this is the first time you and I have ever engaged in a conversation. I have no embarrassment over this puzzle. I'm trying to impress no-one, I'm not the one who is name dropping. I'm not trying to teach you anything, it's just an observation. You come across really angry about stuff - probably because that is synonymous with the kind of fear and loathing bred by right wing propaganda in people that believe it. It's sad.

zapatos has this at the bottom of every single post he makes:

And the Lord spake, saying, "First shalt thou take out the Holy Pin. Then shalt thou count to three, no more, no less. Three shall be the number thou shalt count, and the number of the counting shall be three. Four shalt thou not count, neither count thou two, excepting that thou then proceed to three. Five is right out. Once the number three, being the third number, be reached, then lobbest thou thy Holy Hand Grenade of Antioch towards thy foe, who, being naughty in my sight, shall snuff it. -MP

"As a good christian, I'm always going to disagree with any proof you try to give me." -Peter BE cimp

THAT, DrP, is "who starts being an arsehole first." AND THEN, on top of that, even AFTER I point out that he CONCLUDED his post with the quote that I repeatedly cited, not ONE of you has the courage to admit that he truly was wrong. Instead you attack me.

As to your ignorant remark about "fear and loathing bred by the right wing propaganda machine," why don't you address that in a separate thread. I will accomodate you with facts and analysis to which you are unaccustomed.

It is NOT the "right wing" that has repeatedly rioted, and set fires, and attacked Trump supporters, it is YOUR side.

It is NOT the "right wing" that shot up congressmen on a baseball field in Virginia. It was YOUR side.

It is NOT "right wing" professors who have been in the news for radical, insane, hateful actions. It was exclusively YOUR SIDE.

I direct you to the scholarly paper cited earlier, "A Crisis of Competence". It describes you and your PhD Leftist friends here perfectly.

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zapatos has this at the bottom of every single post he makes:

"As a good christian, I'm always going to disagree with any proof you try to give me." -Peter BE cimp[/size]

Peter BE Cimp, a good Christain, said that. I just thought it was so telling that I quoted him. If you have a problem with it please take it up with him.

And the Lord spake, saying, "First shalt thou take out the Holy Pin. Then shalt thou count to three, no more, no less. Three shall be the number thou shalt count, and the number of the counting shall be three. Four shalt thou not count, neither count thou two, excepting that thou then proceed to three. Five is right out. Once the number three, being the third number, be reached, then lobbest thou thy Holy Hand Grenade of Antioch towards thy foe, who, being naughty in my sight, shall snuff it. -MP[/size]

Again, not a quote from me. It's a quote from a Monty Python movie. You know who to talk to if you don't like it. Perhaps they'd be willing to change their movie so you are not offended.

Here's another movie quote for you:

Edited by zapatos
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