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Mind Challenge.

Zetsubou
Posts: 4,933
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8/28/2010 11:14:22 PM
Posted: 6 years ago
Four inmates are to be Executed.

Objective
For the group to be freed, one of inmates must know and tell the Executioner what colour hat he is wearing.

Facts
They are all buried up to their shoulders in sand.
They cannot rotate their heads or move.
They cannot talk to each other, only the executioner.
Only one of them can talk to the Executioner once.
They do not know what color hat they are wearing.
They each know that between them 2 will wear white hats and 2 will wear black hats.
Man A is wearing a white hat.
Man B is wearing a black hat.
Man C is wearing a white hat.
Man A is wearing a black hat.

Positioning
They are all buried in this Position: http://www.debate.org...

In worded terms:
From East to West: A - Wall - B - C - D
A wall covers the few of man A from the rest of the group(B, C, D) and vice versa.
Man A is facing East.
Man B is facing West
Man C is facing West
Man C is facing West.
Man A sees only the wall.
Man B sees only the wall.
Man C sees man B and the wall.
Man D sees man B, man C and the wall.
When a man sees another man they also see the other man's hat and it's colour.

I think this is quite hard but there is a answer.

Hint: Try and disprove it.
'sup DDO -- july 2013
lovelife
Posts: 14,629
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8/28/2010 11:17:31 PM
Posted: 6 years ago
That dude has a KKK hat? Anyway is the wall see through or something? What about the guys behind the other ones that see them from behind?
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LaissezFaire
Posts: 2,050
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8/28/2010 11:18:46 PM
Posted: 6 years ago
C knows he has a white hat. He sees that B has a black hat. He knows that if he had a black hat, D would see two black hats, tell the executioner his hat color, and they'd be freed. Since D doesn't do this, he knows that he must have one of the white hats.
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Zetsubou
Posts: 4,933
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8/28/2010 11:20:49 PM
Posted: 6 years ago
At 8/28/2010 11:17:31 PM, lovelife wrote:
That dude has a KKK hat?
Yeah, and what.
Anyway is the wall see through or something?
No, opaque.
What about the guys behind the other ones that see them from behind?
What about "the guys behind the other ones that see them from behind"?
'sup DDO -- july 2013
lovelife
Posts: 14,629
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8/28/2010 11:23:09 PM
Posted: 6 years ago
At 8/28/2010 11:20:49 PM, Zetsubou wrote:
At 8/28/2010 11:17:31 PM, lovelife wrote:
That dude has a KKK hat?
Yeah, and what.
Anyway is the wall see through or something?
No, opaque.
What about the guys behind the other ones that see them from behind?
What about "the guys behind the other ones that see them from behind"?

They can tell the color of hat of the people ahead of them so they can figure the odds of each hat color. If it is in the WBWB pattern they will likely guess what their color is, and will tell the guard I guess.
Without Royal there is a hole inside of me, I have no choice but to leave
wush
Posts: 330
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8/28/2010 11:24:10 PM
Posted: 6 years ago
the 3rd guy can tell he has a white hat as the 4th would say he had a white hat if the 3rd guy had a black hat. so the third guy knows he has a white hat
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Zetsubou
Posts: 4,933
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8/28/2010 11:25:07 PM
Posted: 6 years ago
At 8/28/2010 11:23:09 PM, lovelife wrote:
At 8/28/2010 11:20:49 PM, Zetsubou wrote:
At 8/28/2010 11:17:31 PM, lovelife wrote:
That dude has a KKK hat?
Yeah, and what.
Anyway is the wall see through or something?
No, opaque.
What about the guys behind the other ones that see them from behind?
What about "the guys behind the other ones that see them from behind"?

They can tell the color of hat of the people ahead of them so they can figure the odds of each hat color.
Go on...
If it is in the WBWB pattern they will likely guess what their color is, and will tell the guard I guess.
Be more specific.
'sup DDO -- july 2013
wush
Posts: 330
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8/28/2010 11:30:53 PM
Posted: 6 years ago
oh no someone bet me to it....
BE HAPPY!! =D
you are beautiful, don't let anyone tell you you're not
you're 100X more beautiful when you smile, not that you need it
LeafRod
Posts: 1,548
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8/29/2010 12:00:21 AM
Posted: 6 years ago
If Man D sees B and C with the same color hat he knows his immediately and says so. Since he doesn't say so, Man C knows that his is the opposite of Man B's. Seems pretty easy. There are much more difficult variations.
Ren
Posts: 7,102
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8/29/2010 5:52:52 PM
Posted: 6 years ago
Hint: Try to disprove it.

At 8/28/2010 11:18:46 PM, LaissezFaire wrote:
C knows he has a white hat. He sees that B has a black hat. He knows that if he had a black hat, D would see two black hats, tell the executioner his hat color, and they'd be freed. Since D doesn't do this, he knows that he must have one of the white hats.

This could only be true given that all of the inmates knew the exact position of the other, including the direction in which each were facing. If they cannot turn their heads, C could not have possibly known that D could see them both unless he were told or they were buried in a given order, starting with D.

Thus, this may not follow unless certain specific information not included in the riddle applies.
lovelife
Posts: 14,629
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8/29/2010 9:43:26 PM
Posted: 6 years ago
At 8/29/2010 9:38:12 PM, LeafRod wrote:
Good point Ren. However, in that case it's impossible.

I believe Ren was trying to disprove it.
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Zetsubou
Posts: 4,933
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8/29/2010 9:52:03 PM
Posted: 6 years ago
At 8/29/2010 5:52:52 PM, Ren wrote:
Hint: Try to disprove it.

At 8/28/2010 11:18:46 PM, LaissezFaire wrote:
C knows he has a white hat. He sees that B has a black hat. He knows that if he had a black hat, D would see two black hats, tell the executioner his hat color, and they'd be freed. Since D doesn't do this, he knows that he must have one of the white hats.

This could only be true given that all of the inmates knew the exact position of the other, including the direction in which each were facing.
They do, didn't I say.
If they cannot turn their heads, C could not have possibly known that D could see them both unless he were told or they were buried in a given order, starting with D.

Thus, this may not follow unless certain specific information not included in the riddle applies.

I'll add this in future.
'sup DDO -- july 2013