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 Forum index » Diversions » Perplex City Puzzle Cards » PXC: Yellow Puzzle Cards
[puzzle] #80 Cruel and unusual
Moderators: AnthraX101, bagsbee, BrianEnigma, cassandra, Giskard, lhall, Mikeyj, myf, poozle, RobMagus, xnbomb
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chichiri
Decorated

Joined: 31 Oct 2005
Posts: 207

oliverkeers13 wrote:
Though after Charlie works out what colour hat he has, bella can work out what she has on, as it would be the other colour to Charlie's hat.


No she couldn't, because only dave knows that they both have different colour hats on, bella would still be unsure whether she was the remaning black or one of the whites because she can't see anyone else.

no da

PostPosted: Thu Dec 08, 2005 10:13 am
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oliverkeers13
Entrenched


Joined: 23 May 2005
Posts: 917
Location: London, UK

Yes, she could. She'd realise that if Dave stayed silent, she'd have to be a different colour to Bella, the same as Charlie. She can't see anyone else, however, but after Charlie says his colour, she knows she's the other colour.
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PostPosted: Thu Dec 08, 2005 1:15 pm
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BrianEnigmaModerator
Entrenched


Joined: 05 Oct 2003
Posts: 1199
Location: Pacific Northwest

oliverkeers13 wrote:
Yes, she could. She'd realise that if Dave stayed silent, she'd have to be a different colour to Bella, the same as Charlie. She can't see anyone else, however, but after Charlie says his colour, she knows she's the other colour.

Going on the assumption that you can hear statements, but not really be certain of the direction (e.g. someone talking behind you vs. voices coming from the other side of the wall) or the identity of the person in front of you based on the back of their head (hairstyle, etc.), neither Andrea nor Bella know what color hat they have.

Dave can state "I see two hats in front of me. The one facing the wall is white and the one behind that is black."
Charlie can corroborate that statement versus what he sees--namely someone wearing a white hat facing a wall--and know he is wearing the black hat because nobody else is in the same situation and nobody can offer a counteractive statement of fact.
Both Andrea and Bella are facing a wall and (given the above assumptions) can't tell if anyone is behind them, so neither one knows if they are the white hat that Dave talked about.
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PostPosted: Thu Dec 08, 2005 3:24 pm
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Scott
Entrenched


Joined: 11 Sep 2004
Posts: 1140
Location: 390 Chestnut Ridge Rd, Rochester NY, 14624, USA

If you really wanted to get technical, all people could simply jar their heads fForward so their hat fFalls off. Given the picture, they don't appear to be held on very well. But i suppose that goes against the spirit of the question. And indeed, they may be bobby pinned in place. All of this assumes they didn't see the hats coming (suggesting they were blindfolded fFor the be-hatting).
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PostPosted: Thu Dec 08, 2005 4:35 pm
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PuzzledPineapple
Unfettered


Joined: 07 Apr 2005
Posts: 352

Generally the point of this challenge is that no one is allowed to say anything apart from the one person who chooses to guess what colour their hat is. Once that person says the right colour, they are all freed and can happily ask each other whatever question they like including, but not limited to, what colour their hat is, who the strange guy who did this to them is and what on earth anyone did to deserve it. Hence it doesn't really matter if anyone knows what colour their hat is after Charlie speaks, they're all free anyway.

The card neglects to mention whether anyone is allowed to speak other than to say the colour of their own hat, so technically, if they can actually tell who the person in front of them is (given hairstyles it shouldn't be too difficult), both Dave and Charlie could just tell Charlie and Bella respectively the colour of their hats and it would be incredibly easy. But MC rely on people like us having heard this puzzle before and remembering that there should be the extra clause about no chatting amongst themselves.

PostPosted: Fri Dec 09, 2005 12:06 pm
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sabsay
Kilroy

Joined: 07 Feb 2006
Posts: 2

so here goes for my first solve on this forum:

Spoiler (Rollover to View):
The answer is Charlie. He knows that Bella and him are different colours or else Dave would have known his colour. Since Charlie can see that Bella is White, he knows that he must be Black.


PostPosted: Tue Feb 07, 2006 6:41 am
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EkoeEkoe
Greenhorn

Joined: 04 Mar 2006
Posts: 3

Don't forget:
Spoiler (Rollover to View):
to give the king some credit. I'm sure he know there's no challenge (or humor if you're the king) in this scenario if the prisoners a) know all the hats available and b) put two like color hats in plain view of Dave, allowing Dave to answer before the game has even begun. All the diferent logic to solve this depends on the fact that Dave isn't supposed (or able) to be able to answer despite it being obvious he should be able to.


All in all this makes for a great interview question. Wink

PostPosted: Mon Mar 06, 2006 4:27 pm
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mcboyt
Greenhorn

Joined: 26 Mar 2006
Posts: 7

Spoiler (Rollover to View):
Seems like since Bella's hat is bright white, perhaps Charlie might be able to see some sort of a reflection off of it, considering his hat is black.


PostPosted: Sun Mar 26, 2006 3:33 am
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DrKra37
Decorated

Joined: 22 Mar 2006
Posts: 160
Location: Colorado, USA

This is similar to a question posed by my Symbolic Logic professor the first day of class this semester. In our version there were three prisoners who could each one see the other two, and the fourth hat was simply thrown away.

PostPosted: Mon Apr 10, 2006 7:12 pm
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forensick
Greenhorn

Joined: 26 Apr 2006
Posts: 9
Location: Macomb, IL

I solved this puzzle by just figuring out that
Spoiler (Rollover to View):
Charlie
had the best odds of guessing his/her hat color. Just for future reference or whatever, were we to assume they could chat about what hats they could see?

My logic:

Spoiler (Rollover to View):
Charlie and Dave are the only two who can see hats in front of them. Dave can see a white and black, which gives him 50% odds of guessing his hat color. Charlie can see a white, which gives him a 66% chance of being right about a black guess.


PostPosted: Sun Apr 30, 2006 12:49 am
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lonadar
Boot


Joined: 30 Jan 2007
Posts: 50
Location: Indiana, USA

Spoiler (Rollover to View):
I still don't get why Dave can't just go "Hey, Charlie, your hat is Black", so Charlie goes "My hat is Black". Following that, either of the men could have "saved the day". Nothing on the card says they can't talk (or for that matter tip their heads forward so xyz person could see the color of the person behind them).


PostPosted: Tue Feb 20, 2007 12:35 am
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