I got one.

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Do the figures in this diagram look like some sort of hybrid of model rockets and lawn gnomes?

Yes
130
97%
No
4
3%
 
Total votes: 134

James
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I got one.

Postby James » Sat Apr 29, 2006 3:10 pm UTC

This is one we found long ago, although I just now found this diagram and I hate it.

4men.gif
4men.gif (4.74 KiB) Viewed 9127 times
Image

The four men shown above are buried up to their necks in the ground, and are about to be executed. They cannot move and can only see what is ahead of them. Between A and B is a brick wall which which prevents everyone else from seeing A, and A from seeing anyone else. They know that each of them is wearing a hat, and that two hats are black and two are white, but no one knows which color they are wearing themselves. They will be freed if anyone can determine what color hat they themselves are wearing, all four men will be freed. Also, each person only gets to say either "My hat is white/black," and cannot yell, for example, "Hey, you're wearing a white hat."* However, if this first guess is wrong, they will all be immediately executed. Do the men go free? If so, how?

* Because Kira isn't allowed to cheat.
Last edited by James on Sun Apr 30, 2006 1:30 pm UTC, edited 1 time in total.
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Postby kira » Sun Apr 30, 2006 8:43 am UTC

i fear i may be confused. couldn't D just yell over to B, "hey, you're wearing a white hat!"?

i guess that'd be cheating. but it doesn't specifically say they can't do that, does it?

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Postby James » Sun Apr 30, 2006 1:33 pm UTC

No, you can't do that. You can only guess as to what color your own hat is. And it says so now, but good point. The guy who typed this up originally left out a lot of detail and added in a lot of stuff you don't need. (eg: model rocket elves.)
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Sure

Postby Spamtek » Sun Apr 30, 2006 2:45 pm UTC

Everybody waits a second. Gnome D can't respond, since he can only see one white hat and one black hat, which means there's still a white or black hat he could be wearing. Gnome C realizes this, and since gnome B is wearing a white hat, it means he must be wearing a black one. Gnome C says he's wearing a black hat and they all go free.

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Postby Shoofle » Sun Apr 30, 2006 4:48 pm UTC

This is the only difficult logic puzzle I know, and I had it explained to me, but I'm still proud that I understand it.

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Postby kira » Tue May 02, 2006 5:18 am UTC

problem. does C know that D is behind him?

because if C can only see what's in front of him and D can't say anything (since he doesn't know what color hat he's wearing), then how does C know that D isn't on the other side of the wall, or that D even exists?

CONUNDRUM.

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Postby Shoofle » Tue May 02, 2006 11:12 am UTC

Uhhh, C heard them digging the hole for D, or at least D getting into his hole.

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Postby xkcd » Tue May 02, 2006 12:19 pm UTC

problem. does C know that D is behind him?

They know the arrangement, yes.

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Postby kira » Tue May 02, 2006 10:46 pm UTC

ok, that solves everything. move along, nothing to see here.

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Postby Nerd Girl » Wed May 31, 2006 5:38 pm UTC

I've been lurking here for some time--the comics are awesome, hey Jello, yadda yadda yadda. But then I stumbled upon something, and I knew I had to come here and show it off:

Sure, the diagram's bad, but it could be worse. :lol:

It actually couldn't get worse, as I just stole the image from here because the other one has evaporated - jestingrabbit

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Postby Shoofle » Wed May 31, 2006 8:57 pm UTC

That's... precisely what we have been talking about, with another bad diagram.

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Postby xkcd » Wed May 31, 2006 11:07 pm UTC

That's... precisely what we have been talking about, with another bad diagram.


Yeah -- I think that's what she's pointing out.

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Postby Shoofle » Thu Jun 01, 2006 3:21 am UTC

Oh! I misunderstood. I actually think that diagram might be a little bit better. It doesn't appear to have the rocket fins.

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Postby James » Thu Jun 01, 2006 8:02 am UTC

Really though, what are the rocket fins supposed to depict? It that their collars or something?
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Postby Shoofle » Thu Jun 01, 2006 9:37 pm UTC

My best guess is that they are the sand that is piled up against their necks.

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Postby davean » Thu Jun 08, 2006 5:29 am UTC

Since we are debating which is worse, I propose a solution in challenging someone to come up with a universally WORSE diagram, laying to rest the question of which is worse in the sure knowlege that they are both compairably good. I'll be handing out used loli-pops, please collect in person.

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Postby James » Thu Jun 08, 2006 6:39 am UTC

I think I may have come up with one:

Image

I mean, people's ordering, relative positions, hat color is not only unclear, but oftentimes flat-out misleading. So I guess it could be worse.
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xkcd
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Postby xkcd » Thu Jun 08, 2006 10:01 am UTC

Impressive!

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Postby Shoofle » Thu Jun 08, 2006 11:12 am UTC

Most impressive.

(Haha, I said it!)

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Postby davean » Tue Jun 13, 2006 1:15 pm UTC

James wrote:I think I may have come up with one:

Image

I mean, people's ordering, relative positions, hat color is not only unclear, but oftentimes flat-out misleading. So I guess it could be worse.


Problem solved! They are both GREAT.

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Re: Sure

Postby Enzo Dragon » Tue Jul 04, 2006 7:43 am UTC

Spamtek wrote:Everybody waits a second. Gnome D can't respond, since he can only see one white hat and one black hat, which means there's still a white or black hat he could be wearing. Gnome C realizes this, and since gnome B is wearing a white hat, it means he must be wearing a black one. Gnome C says he's wearing a black hat and they all go free.
Problem! Gnome C can't know that he's wearing a black hat, since he only sees that which is in front of him: the white hat. He could easily be wearing the second white hat, since he can't see D, behind him.

D sees C (black), and B (white), and can only conclude that he could be wearing the second of either color.

C sees B (white), and can only conclude that he could be wearing the second white hat, or either of the two black hats.

B sees no one, and so knows nothing of his hat color.

A sees no one, and so knows nothing of his hat color.

I don't see a solution in any of that information. =/

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Postby xkcd » Tue Jul 04, 2006 3:23 pm UTC

Problem! Gnome C can't know that he's wearing a black hat, since he only sees that which is in front of him: the white hat. He could easily be wearing the second white hat, since he can't see D, behind him.

No; this is the key to the puzzle. If Gnome C were wearing a white hat, Gnome D would know his hat was black and would respond out loud. When Gnome C doesn't hear him respond out loud, he knows he's not wearing a white hat, and his hat is therefore black.

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Postby RealGrouchy » Thu Jul 06, 2006 8:02 am UTC

That assumes that D isn't a wuss.

D could very well see two white hats, but be too scared and/or stupid to conclude that that would mean he has a black hat on.

...also, the third diagram is better because it has colour.

:evil:

- RG>
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Mighty Jalapeno wrote:At least he has the decency to REMOVE THE GAP BETWEEN HIS QUOTES....
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Postby Vonkwink » Tue Jul 18, 2006 8:17 pm UTC

I think to make this question more clear we should add the following like (somewhat borrowed from the blue eyes puzzle): "all gnomes in the puzzle are perfect logicians, and will call out their hat color as soon as they know it."

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Postby RealGrouchy » Wed Jul 19, 2006 1:31 am UTC

These last few posts are just begging for a smartass response, but one isn't coming to me at the moment. Must be the flu.

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Jack Saladin wrote:etc., lock'd
Mighty Jalapeno wrote:At least he has the decency to REMOVE THE GAP BETWEEN HIS QUOTES....
Sungura wrote:I don't really miss him. At all. He was pretty grouchy.

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Postby Bahtaw » Sun Aug 13, 2006 3:19 am UTC

Achtung!!

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Postby Verysillyman » Mon Aug 21, 2006 1:28 am UTC

Baby

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Postby brimstone » Mon Sep 11, 2006 2:12 pm UTC

Okay, so you have Gnome C saying Black. Because he's relying on a response from the gnome team, and since there's none, he has to answer for D can see B/W can cannot determine his hat, B can't see anything and A can't see anything.

But the solution you guys have only lets gnome C get off free.

Okay, so C is free, you have

A | B D

A is Black, B is White and D is white.

A can't see anything, so obviously he's the last to say his colour from deduction.

There's only 1 Black hat left and 2 whites, but how does D know that he has a white one? He can see that B is white, but cannot see A. So he still has a 50/50 chance of knowing his hat colour right? Did i miss something?


[edit]
Nevermind, I reread the question and saw that only one guy needed to answer the question right.

I thought that they needed to save themselves...

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Re: Sure

Postby Marrow » Mon Sep 11, 2006 8:09 pm UTC

Spamtek wrote:Everybody waits a second. Gnome D can't respond, since he can only see one white hat and one black hat, which means there's still a white or black hat he could be wearing. Gnome C realizes this, and since gnome B is wearing a white hat, it means he must be wearing a black one. Gnome C says he's wearing a black hat and they all go free.


I'll agree that this is the MOST correct solution. It does, however, seem to assume that Gnome C and D know what the other is thinking. I know they can't say what color another gnomes hat is directly, but are they allowed any other form of communication? Because we are looking at them all at once, it would me much harder to find out the answer if the diagram only depicted gnome C's perspective.

If gnome C were able to ask D if he knew what color hat he was wearing and D could say that he did not know without stating the color of B or C's hats then I am perfectly satisfied. Otherwise I am going to whine about the general annoyance I feel for logic puzzles and not bother anyone since I they can just immagine what that is like for themselves.
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Re: Sure

Postby McMillian » Wed Sep 13, 2006 11:11 pm UTC

Marrow wrote:
Spamtek wrote:Everybody waits a second. Gnome D can't respond, since he can only see one white hat and one black hat, which means there's still a white or black hat he could be wearing. Gnome C realizes this, and since gnome B is wearing a white hat, it means he must be wearing a black one. Gnome C says he's wearing a black hat and they all go free.


I'll agree that this is the MOST correct solution. It does, however, seem to assume that Gnome C and D know what the other is thinking. I know they can't say what color another gnomes hat is directly, but are they allowed any other form of communication? Because we are looking at them all at once, it would me much harder to find out the answer if the diagram only depicted gnome C's perspective.

If gnome C were able to ask D if he knew what color hat he was wearing and D could say that he did not know without stating the color of B or C's hats then I am perfectly satisfied. Otherwise I am going to whine about the general annoyance I feel for logic puzzles and not bother anyone since I they can just immagine what that is like for themselves.
Why don't we just assume that they are all perfect logicians (which should be assumed anyway), and that if there was any way for any of them to know 100% what the color of their hat was, they would instantly say it. As such, when C doesn't hear D instantly say his hat color, he knows that he cannot be wearing the same color hat as the person in front of him because if he was, then D would've known his own hat, and thus C comes to the conclusion his hat is black.

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Postby katsielyonz » Thu Sep 14, 2006 1:03 am UTC

I could just be nit-picking but my problem with the solution is that it assumes that Gnome D can see Gnome B. According to the graph all the gnomes are the same exact size, and according to the problem NONE of them can move AT ALL. If that's the case than Gnome D can't see Gnome B and thus Gnome's C's opinion is based on false logic. Gnome D just isn't saying anything because he can't surmise anything from where he's at. It's just that Gnome C has a 50% chance of being right even under false premises.
Yah yah, poo.

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Postby McMillian » Thu Sep 14, 2006 10:15 pm UTC

katsie that's retarded. Would it ease your mind to think that gnome D was bigger than the other gnomes and is further away, so can see B and C but from our perspective looks the same size?

It's a logic riddle, the diagram was just to show you the color pattern

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Postby katsielyonz » Fri Sep 15, 2006 1:11 am UTC

Yes, yes it would.

'Sides, there's nothing wrong with creative thinking. I mean without specification how do we know that Gnome C isn't some poor fellow who suffers from Giantism and thus blocks the vision of Gnome D? Either I have to assume the diagram is 100% correct OR I have to allow for the possibility of different sized Gnomes going on OR maybe the executions DIDN'T put them in perfect alignment and so Gnome D CAN see the color of both Gnome's hats; because the word problem says specifically they can't move at all.
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Postby Marlayna » Sun Sep 17, 2006 5:54 pm UTC

So, they're all perfect logicians, but does each one know that the others are perfect logicians?

Boy oh boy I love nitpicking :P
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Postby katsielyonz » Mon Sep 18, 2006 3:18 am UTC

Whoa, I didn't even think about that nitpick.
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Postby Marrow » Tue Sep 19, 2006 10:12 am UTC

Actually only gnome C has to be the perfect logician, as long as A, B and D are not stupid C has a good chance of figuring things out before the others do something to condemn them all. However this is not something one should expect from gnomes since they are being put to death in the first place they can't be all too genius.
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Postby Verysillyman » Tue Sep 19, 2006 12:57 pm UTC

This is in a country where is it illegal to be a perfect logician, especialy if you look like a rocketship. That's why they're being put to death.

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Postby Teaspoon » Tue Sep 19, 2006 1:57 pm UTC

Of course. Nobody likes a smartarse.

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Postby Binary.Tobis » Mon Sep 25, 2006 10:22 pm UTC

I feel silly for not getting the answer sooner. :)
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Re: I got one.

Postby ch103 » Tue Oct 23, 2007 6:18 am UTC

C calls out that he is wearing a black hat. Why is he 100% certain of the colour of his hat ?


This is the real answer!

After a while, C comes to the realization that he must answer.

This is because D can't answer, and neither can A or B.

D can see C and B, but can't determine his own hat colour. B can't see anyone and also can't determine his own hat colour. A is in the same situation as B, where he can't see anyone and can't determine his own hat colour.

Since A, B, and D are silent, that leaves C. C knows he is wearing a black hat because if D saw that both B and C were wearing white hats, then he would have answered. But since D is silent, C knows that he must be wearing a black hat as he can see that B is wearing a white hat.


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