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 Forum index » Diversions » TimeWasters
Riddle help for class
Moderators: Giskard, ndemeter, ScarpeGrosse
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kleinfehn
Greenhorn

Joined: 06 Sep 2007
Posts: 3

Riddle help for class

Alright, here is a riddle I have for one of my classes in school for extra credit and I would really like some help. If possible, before tomorrow at noon since that is when school will start for me. Anyway, here is the riddle:

Three men are captured and put in a hole. All three of the men are wearing hats that are either black or white, but all three of them can't be the same color. A guard watching them says that if they can say the correct color of their hat they will let all three of them go.

They are all facing one way so the front guy just sees the wall, the second guy can see the front guy and his hat, and the third guy can see the first and second guys hat. If any of them move they will be shot, or if they say something besides their color. None of the guys know what their hat color is.

Now, which one of them has a 100% possible chance of knowing their hat color? I don't think it is the third one since if the first guy is wearing a black hat and the second guy is wearing a white hat he will not have a 100% chance of knowing.

PostPosted: Thu Sep 06, 2007 10:25 pm
Last edited by kleinfehn on Thu Sep 06, 2007 10:41 pm; edited 1 time in total
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catherwood
I Have 100 Cats and Smell of Wee

Joined: 25 Sep 2002
Posts: 4109
Location: Silicon Valley, CA

puzzles like this often involve a delay, such that the last guy knows his color *only* because the other guys didn't respond immediately. I don't know if this is the case with this puzzle, but I know i've seen it before, and the answer is probably on the internet somewhere.

PostPosted: Thu Sep 06, 2007 10:31 pm
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GuyIncognito
Decorated


Joined: 20 Jul 2006
Posts: 295

catherwood wrote:
I don't know if this is the case with this puzzle, but I know i've seen it before, and the answer is probably on the internet somewhere.

Actually, look no further than unfiction's own Perplex City Puzzle Card section. (Picture here.) While it's not exactly the same puzzle, as catherwood said, the logic is the same. You'll figure it out ...

PostPosted: Thu Sep 06, 2007 10:51 pm
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kleinfehn
Greenhorn

Joined: 06 Sep 2007
Posts: 3

Alright I got it.

It is the second or third guy because if both the first guys are wearing either a black or white hat he will know his color but if the third guy is quite then the second guy will know that his hat is a different color then the first guys since the third guy wouldn't want to answer with a 50-50 chance. Alright, thanks guys.

PostPosted: Thu Sep 06, 2007 10:53 pm
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Blue K
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Joined: 20 Mar 2006
Posts: 192
Location: NW/Chicago

Re: Riddle help for class

B= Black; W= White

B1-B2-W3 -or- W1-W2-B3= #3 knows 100%...he can clearly see the other hats.

B1-W2-B3 -or- W1-B2-W3= #2 knows 100% by seeing #1's color, combined with#3's silence.

Okay, you've got that worked out right here:

kleinfehn wrote:
Alright I got it.

It is the second or third guy because if both the first guys are wearing either a black or white hat he will know his color but if the third guy is quite then the second guy will know that his hat is a different color then the first guys since the third guy wouldn't want to answer with a 50-50 chance. Alright, thanks guys.


But, per the riddle, you have a problem:

kleinfehn wrote:
Now, which one of them has a 100% possible chance of knowing their hat color?


Both #2 and #3 only have a 100% chance of knowing their hat color 50% of the time. The riddle asks which one, but the answer in the above scenario is either/or. Either the puzzle is poorly worded or the answer is none.
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PostPosted: Fri Sep 07, 2007 12:15 am
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kleinfehn
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Joined: 06 Sep 2007
Posts: 3

Re: Riddle help for class

Blue K wrote:


Both #2 and #3 only have a 100% chance of knowing their hat color 50% of the time. The riddle asks which one, but the answer in the above scenario is either/or. Either the puzzle is poorly worded or the answer is none.


It is probally the wording, since I wrote it down quickly in a notebook and might have missed a few words.

PostPosted: Fri Sep 07, 2007 8:20 am
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Blue K
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Joined: 20 Mar 2006
Posts: 192
Location: NW/Chicago

Re: Riddle help for class

kleinfehn wrote:
It is probally the wording, since I wrote it down quickly in a notebook and might have missed a few words.


Cool...just wanted to make sure your teacher wasn't trying to trip you up.
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PostPosted: Fri Sep 07, 2007 8:35 am
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thebruce
Dances With Wikis


Joined: 16 Aug 2004
Posts: 6899
Location: Kitchener, Ontario

On the surface, none of the men have a 100% chance of guessing right.
(solution below!)

If we say #2, he only has a guaranteed correct if #3 (after he guesses right or wrong) has the same colour as #1 which he can see. Otherwise it's a 50-50 guess for him.
If we say #3, he only has a guaranteed correct if #1 and #2 have the same colour. Otherwise it's a 50-50 guess for him.
#1 has a guaranteed correct if he waits until #2 and #3 guess right or wrong, and both have the same colour. Otherwise it's a 50-50 guess for him.

Gotta take it a step further, and be able to 'read people'...

#3 would say his colour with certainty IF #1 and #2 were the same colour.
If #3 doesn't guess right away, or is uncertain in his guess, then the other two guys would know that they must be opposite colours. BUT, only #2 knows the other person's colour, so he'd just guess the opposite.

#1 = white
#2 = white
#3 = knows it's black

#1 = white
#2 = black
#3 = doesn't guess or hesitates

...#3 therefore doesn't have a guaranteed correct

#1 = white
#2 = white
#3 = correctly guesses black
(#2 is safe already because #3 is right)

#1 = white
#2 = black
#3 = doesn't guess or hesitates
(#2 knows therefore that his hat must be black, since #3's colour could be either, it doesn't matter - his hat MUST be black) - guaranteed 100%

So the answer is- the guy in the middle has 100% guaranteed freedom if he deduces #3's certainty: if #3 knows his colour, he doesn't have to guess; if #3 doesn't know his colour, he guesses the opposite colour to the #1's hat.

nifteh!
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PostPosted: Fri Sep 07, 2007 10:11 am
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Uberg33k
Entrenched


Joined: 10 Apr 2006
Posts: 905
Location: Atlanta

thebruce wrote:
On the surface, none of the men have a 100% chance of guessing right.
(solution below!)

If we say #2, he only has a guaranteed correct if #3 (after he guesses right or wrong) has the same colour as #1 which he can see. Otherwise it's a 50-50 guess for him.
If we say #3, he only has a guaranteed correct if #1 and #2 have the same colour. Otherwise it's a 50-50 guess for him.
#1 has a guaranteed correct if he waits until #2 and #3 guess right or wrong, and both have the same colour. Otherwise it's a 50-50 guess for him.

Gotta take it a step further, and be able to 'read people'...

#3 would say his colour with certainty IF #1 and #2 were the same colour.
If #3 doesn't guess right away, or is uncertain in his guess, then the other two guys would know that they must be opposite colours. BUT, only #2 knows the other person's colour, so he'd just guess the opposite.

#1 = white
#2 = white
#3 = knows it's black

#1 = white
#2 = black
#3 = doesn't guess or hesitates

...#3 therefore doesn't have a guaranteed correct

#1 = white
#2 = white
#3 = correctly guesses black
(#2 is safe already because #3 is right)

#1 = white
#2 = black
#3 = doesn't guess or hesitates
(#2 knows therefore that his hat must be black, since #3's colour could be either, it doesn't matter - his hat MUST be black) - guaranteed 100%

So the answer is- the guy in the middle has 100% guaranteed freedom if he deduces #3's certainty: if #3 knows his colour, he doesn't have to guess; if #3 doesn't know his colour, he guesses the opposite colour to the #1's hat.

nifteh!
Good call. Party on, Wayne.

PostPosted: Fri Sep 07, 2007 10:22 am
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Blue K
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Joined: 20 Mar 2006
Posts: 192
Location: NW/Chicago

#2 looks at #1 and sees that #1's hat is black. He waits what he considers a reasonable amount of time for #3 to speak up, and when #3 says nothing, #2 confidently says to the guard, "My hat is white."

The guard shoulders his rifle and shoots #2 dead.

#3 then proclaims, "My hat is white," to which the guard replies "You are free to go." "Tell me," the guard says to #3, "You could clearly see that both #1 and #2 were wearing black hats, so why didn't you speak up?" to which #3 replies, "I never could stand that son-of-a-bitch."

So much for 100%. Smile
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PostPosted: Fri Sep 07, 2007 1:52 pm
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thebruce
Dances With Wikis


Joined: 16 Aug 2004
Posts: 6899
Location: Kitchener, Ontario

*tsk*
trick question'd!

foil'd agaaaaaiin!
Flaming Nutter
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PostPosted: Fri Sep 07, 2007 1:56 pm
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Vman
Veteran


Joined: 26 Aug 2007
Posts: 107
Location: Kent

haha classic, a tricked trick question reversesrever psychology!
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PostPosted: Sat Sep 08, 2007 4:08 am
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