14 COMMENTS
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Posted on January 15, 2007
Hey Jordan, in my humble opinion guy #1 is wearing a black
hat. I may be sorry if I end up getting executed for it, but I'm willing to take the chance. I happen to know that inmates #2 and #3 are both NT’s so I’m basing my answer on the assumption that they too, possess the great logic and reasoning skills of the NT population in general (let’s hear it for NT’s!) Ok so here goes. First off, I haven’t done this riddle before and I didn’t Google for the answer. (Or obviously read other posts.) so if I’m right, I played fair and square, if I’m wrong…well, I guess I should have Google’d it first. Alright so back to the prison yard with the intimidating, but obviously not NT prison guard, (perhaps he’s an SF? Sorry, couldn’t resist) and our 3 inmates with cool headgear. #1 is wearing a black hat, #2 has a 50/50 chance of wearing any hat that fell out of the box, and #3 would be staking his life on a 1 out of 3 chance of correctly guessing what he had on. #3 looks in front of him and either sees a black hat and a red hat, or 2 black hats so he knows there is still at least 1 red hat and 1-2 black hats left, one of which he’s wearing. If the two guys
in front of him were wearing red hats he would know he had a black hat on and would have guessed what he was wearing. Since he wasn’t confident enough to make a guess we have to assume he was staring at something other than 2 red hats, which would leave him in doubt about what he had on. #2 sees #1 with a black hat in front of him so he knows there are still 2 red and 2 black hats, one of which are sitting atop his head. In that case, his chances of guessing the correct color of his fashionable accessory is 50/50 and he’d rather live with the hopes that #1 is an NT, will guess correctly, and someday come back to rescue him from prison. So he gives up. We’ll be back right after this **Commercial break** We come back to see that #1 is now standing there alone with his fate literally hanging over his head. He gets to thinking. If #3 had seen two red hats he would have guesses he was wearing a black hat. If #3 had guesses, #2 would have know that #3 saw two red hats which would have made #2 guess. If #2 had guesses that would have meant that he, #1 was wearing a red hat. But since #2 lacked that confidence, the only logical conclusion is that he, #1 was wearing a black hat. And that my friend, is natural selection at it’shighest. (And you wonder why there are so many ENTP’s?!) Thank God for non NT prison guards! Poor guy didn't see that one coming!

David Voeller
San Antonio, Texas

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Posted on January 15, 2007
Ok, I couldn't sleep, so I got bored and decided to visit your blog and check out that riddle you were telling me about, and I think I figured it out. I am assuming that these guys know there are 5 hats and that 3 are black and 2 are red. By the way, for simplicity, I am gonna call the third guy in line "3" the second, "2" and the first, "1". Here it goes: 3 sees the colors of 2 and 1. He knows if they are both wearing red, he has to be wearing black. But since he didn't know his color, that means 2 and 1 are either both wearing black or one is wearing black and the other is wearing red. In any case, 3 is gone. 2 would realize that 3 would have guess his own color if they were both wearing red. He sees the color of 1's hat, and realizes that if it were red, then his has to be black. However, if 1's hat is black, then 2's could be black or red. So there you have it, 1 is wearing black.

Josef
Georgia

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Posted on January 15, 2007
By the way, I just realized something. You gave this challenge out to all the NT's but at the end, you only singled out ENTP's as being the ones who'd look on the comments page to cheat... why's that?? Don't hate us just because we're better than all other NT's.. :)

Josef
..

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Posted on January 15, 2007
1 and 2 have at least one black hat between the two of them,
because if they were both red, 3 would know he is black. 2
now knows there is at least 1 black hat between the two of
them. If 3 is red, 2 knows he's black, so 3 must have been
black. BTW, these three must have been clever smooth
criminals, because I don't think I would've figured that out
on the spot like that. Love the question, and Kalea is the
cutest thing ever!

Luke
New Milford, NJ

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Posted on January 15, 2007
i got the riddle. the first guy has a black hat, and he
knows it because he knows the third guy would know what hat he had on if the first 2 guys both had red hats. therefore,
by the third guy quitting, the remaining 2 now know that
between themselves, one of them must have a black hat. then the second guy quits because he sees the first guy's hat is black, and hes not sure if he himself has a red or a black hat. had the second guy seen a red hat on the first guy, he would know that his was black, because he knew that one of them must have a black hat. He saw a black hat though, therefore he was unsure and quit. The first guy knew all this information, and therefore realized his hat must be
black............i know it could be a little difficult to understand what i said, but if u indeed cracked the riddle, you will understand what i said. good riddle Jordan, you had me going crazy in front of my computer for a good 10-15 minutes haha.

Mark, Luke's brother

New Milford, NJ

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Posted on January 15, 2007
I think I have the answer. I said at first, there is a 3-2
chance for the black so go along with that. Problem is that
I'm not certain. I spent the last 30-45 minutes on it and I
think that I have it. Reason (here goes): I started with how
many possibilites there were BBB, BBR, BRB, RBB, RBR, RRB, BRR. Guy number 3 can't figure it out his own hat color so it CAN'T be the BRR. What he must be seeing then in front of him is a BB or a RB or BR. Mr. inmate 2, if he sees a black he still doesn't know what he is, but if he sees a red then he knows that he is black!(look at the combinations left) He does NOT know what he is or he would have said, so the guy in front of him can't be wearing a red! Number 1 must know that information as the other guys couldn't get their own hat colors. Answer: Number 1 is wearing a Black hat. (unless of course one of them were color blind) Wow, I started the comment writing down a completly different idea but ran into a wall with it. I have re-written is so many times. Now, someone tell me I'm wrong. ;-) It's funny because we were just talking about brain teasers in church yesterday. I'll
have to bring this one. Thanks Jordan. That was a lot of fun..........More?

Matthew
Massachusetts

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Posted on January 15, 2007
#1 is wearing a black hat. And I could explain my reasoning
but, honestly, it's the exact same reasoning that all of the above comments are using so I therefore see no point in
stating it once again. I hope that's OK. If it isn't (and you all don't trust me *wink*) I'll type the whole thing for you. Clever riddle, Jordan. You gave me the good idea to post some riddles on my own site... I love riddles. :-) You should post them more often.

Katie C.
GA

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Posted on January 15, 2007
ee! that's too much brain power for an infj like me. i'd
rather write an essay or proofread a dictionary. thx. : )

k
snowville, mo

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Posted on January 15, 2007
Man that's really tough. What were these guys in for anyway?
JFly

JFly
MA

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Posted on January 16, 2007
Whow, that's a brain fryer for sure! After much hard and
grueling thought, I came to pretty much the same conclusion
as Josef. 1 must be wearing black, and for the reasons Josef explained, I won't type em all out again. Great thinking
riddle Jor! Oh my word!! I can't believe how long it's been
since I've seen our Brad and Kyle interviews! I was literally laughing out loud, hard, watching that clip! I have to go back and watch the rest now.

Nathan
SoCal

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Posted on January 16, 2007
If you hadn't have warned ENTP's not to cheat, I would have
cheated. However the only thing that I find more enticing
than taking a shorty cut is protecting other people's
perception of my own intelligence. Therefore I figured the
riddle out on my own, and came up with the same (correct)
conclusion that everyone else did.

David Robison
The OC

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Posted on January 17, 2007
Well, we certainly have some braniacs here. Congrats! David, long-winded, but good job ... Josef, good job, and when I made that ENTP comment, I had you as well as a few other ENTPs in mind :-D ... Luke, I think you got it, but you just confused #3 with #1 midway in your answer ... Mark, great job ... Matthew, excellent ... Katie, I'll take your word for it ;-) ... K, I know how you feel, so no worries :-D ... JFly, I think they were in for hate speech or something .... Nathan, I'll also take your word for it :-) ... David R, I wouldn't have taken your word for it had not you explained it to me over IM, so you're off the hook. Anyway, I never knew my blog readers were of such high academic caliber! You make me proud! :)

The Jordan
so mo

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Posted on January 17, 2007
yea i did ...can't believe i didn't catch that.

luke
nj

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Posted on January 18, 2007
I figured it out ... YEA! I didn't look at the comments either :-) The first man is wearing a black hat. The reason he was so sure was because he would have known that man 1 and 2 didn't have a red hat otherwise man 3 would have known. Thus, man 2 would know that if man 1 has a red hat on he would not, but since man 2 and three gave up it leaves man one with a black hat. Thanks for posting, we always enjoy your blog.

Melanie Thomas
Massachusetts

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