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3 Prisoners

3 Prisoners

These three prisoners recently escaped from "O Brother, Where Art Thou"
—compliments of the Coen Brothers.


You and two other prisoners are on death row. The warden marks each prisoner's forehead with a red X or a green X. He instructs the prisoners to stand in a circle facing each other and raise their hand if they see at least one red X on someone’s forehead. A pardon, he says, will go to the first prisoner who can determine the color of the X on his or her forehead. The other two prisoners, he warns, will be immediately executed. You see at least one red X and raise your hand. The other prisoners raise their hands also. A minute goes by, but no one says anything. Assuming that the other prisoners are as smart as you, and the warden makes sure they don't lie, what color is the X on your forehead? How do you know for sure? Don't guess. You are too young to die...


To start thinking about this problem, list all the possible ways the warden could mark the three prisoners' foreheads. Make a table in a comment below. Review table making on the Make A Table page. How many ways did you list? Is it possible he marked all with a green X? Argue for or against each set of markings. We are going to mark many things either one way or another this semester. So start marking. Click inside the circles; see if that helps. For this problem you receive 1 point for each arrangement you prove impossible.


When you have eliminated the impossible,
whatever remains, however improbable, must be the truth.

—Sherlock Holmes


Comments:

From wHolt - 10/24/06 10:56 AM

 R R G Not possible because they know if they speak up that the others would die and it could be them.

Soller - I dont understand this explanation. If prisoner A speaks correctly, he wont die.
But he wont take a chance if he does not know for sure.

From Soller - 10/23/06 11:28 PM

 P1 P2P3  Reason

 G

 G 

 G Not possible because no one would see a red x.
 G G  R Not possible because P3 would not see a red x.
 G  R G Not possible because P2 would not see a red x.
 R G G  Not possible because P1 would not see a red x.
 R R R This is possible because all three would see a red x.
 R R G Not possible because they know if they speak up that the others would die and it could be them.
 R G R Not possible because if one speaks up then the other two die and in the statement it said they hesitated so they are thinking that it could be them who would die.
 G R G Same as above.
It is not possible that all three would have green x's because they all raised their hands which meant they saw a red x.

From wHolt - 10/17/06 2:18 PM

x
    x
 x
  1 1 1Impossible; The arrangement could not occur given the facts because 1*2^2 + 1*2^1 +1*2^0=7. We have only 3 x's, not 7.
 x
   x
 x
  1 1 0 Impossible; The arrangement could not occur given the facts because 1*2^2 + 1*2^1 +0*2^0=6.

Interesting, but i dont see why the above are impossible, since each prisoner raised his hand.

From Boki - 10/17/06 10:10 AM

 

 This time I will try with conversion of the binary numbers

into decimals which gives us number of x's (or persons)

in each combination.

Me
 Prisoner 1
Prisoner 2

 binary #.:red=1

green=0 

 

   Reasoning:  conversion of the binary numbers into decimals
 x
    x
 x
  1 1 1Impossible; The arrangement could not occur given the facts because 1*2^2 + 1*2^1 +1*2^0=7. We have only 3 x's, not 7.
 x
   x
 x
  1 1 0 Impossible; The arrangement could not occur given the facts because 1*2^2 + 1*2^1 +0*2^0=6.
 x
   x
  x
  1 0 1 Impossible; The arrangement could not occur given the facts because 1*2^2 + 0*2^1 +1*2^0=5.
 x
   x
  x
  0 1 1

Possible; The arrangement could occur given the facts because 0*2^2 + 1*2^1 +1*2^0=3. This also proves that we can have max. 2 red x's.

 x
  x
  x
  1 0 0 Impossible; The arrangement could not occur given the facts because 1*2^2 + 0*2^1 +0*2^0=4.
  x
  x
  
x
  0 0 1 Impossible; The arrangement could not occur given the facts because 0*2^2 + 0*2^1 +1*2^0=1.
 x
 x
 x
  0 1 0 Impossible; The arrangement could not occur given the facts because 0*2^2 + 1*2^1 +0*2^0=2.
 x
 x
 x
  0 0 0 Impossible; The arrangement could not occur given the facts because 0*2^2 + 0*2^1 +0*2^0=0.

From wHolt - 10/15/06 1:42 PM

Boki - i cannot follow your logic.
How do the prisoners know if there are 2 or 3 red X's?

From Boki - 10/15/06 9:45 AM

In this combination (RRR), everyone will see at least one red x,

and everyone will raise hand. Since everyone actually sees exactly

red x’s, it means that everyone could think “the colour of my x is

green” and we can conclude that everyone will have a green x

which is impossible.

From wHolt - 10/13/06 3:02 PM

Boki - you say that there must be at least one green x.
Why?
Suppose everyone had a red x. 
Would not everyone raise their hand?
How do you know if there are 2 reds or 3 reds?

From Boki - 10/13/06 9:13 AM

We already know that the warden says them to “raise their hand if they
see at least one red X on someone’s forehead” and they all DID
raise their hands. It means that all of them see at least one red x.
If so, there must be also at least one green x.That means only
combinations with at lest one red or green x cold be possible. The
combination RGG (with at least one red x; consequently, there could
be max 2 green x’s) we can exclude because the prisoner who has red
x will see 2 green x’s and could NOT raise hand, but he/she DID raise
the hand. The combination GRR (with at least one green x;
consequently, there could be max 2 red x’s) is only possible
because everyone sees at least one red x, and therefore everyone will
raise his/her hand. Since there are most two red x's, the prisoner with
green x is able to determine that colour of his/her x must be green.
The other two prisoners will see 1 red and 1 green x, and they knew that
there is a possibility to have either red or green x on their forehead; so,
they were not able to determine what colour of x is on their forehead.

From wHolt - 10/12/06 7:45 PM

 x
   x
  x
Possible; everyone sees at least one red x; I will see two red x, and I see raise my hand. Since there are most two red x's, I am able to determine that colour of my x must be green. 

How can you tell this is possible, but RGR is not?
How do you know there are at most 2 red X's?
What will the other prisoners think with this arrangement?

From Boki - 10/12/06 9:10 AM

Me
 Prisoner 1
Prisoner 2
 Reasoning
 x
    x
 x
Impossible; The arrangement could not occur given the facts. It was given that everyone will see at least one red x; so there could be most 2 red x's, not 3.
 x
   x
 x
 Impossible; everyone would see at least one red x, and could raise hands. I can't determine colour of my x if I see 1 red and 1 green x. I know that could be most 2 red or most 2 green x's. So, On my forehead could be either one. 
 x
   x
  x
 Impossible; everyone would see at least one red x and could raise hands, but I can't determine colour of my x if I see 1 red and 1 green x. I know that could be most 2 red or most 2 green x's. So, On my forehead could be either one. 
 x
   x
  x
Possible; everyone sees at least one red x; I will see two red x, and I see raise my hand. Since there are most two red x's, I am able to determine that colour of my x must be green. 
 x
  x
  x
 Impossible; not everyone sees at least one red x; I will see two green x's, but I did raise hand. The arrangement could not occur given the facts.
  x
  x
  
x
 Impossible; not everyone sees at least one red x;  prisoner 2 will see two green x’s, but he/she did raise hand. The arrangement could not occur given the facts.
 x
 x
 x
 Impossible; not everyone sees at least one red x; prisoner 1 would see two green x's, but he/she did raise hand. The arrangement could not occur given the facts.  
 x
 x
 x
 Impossible; No one sees red x, the arrangement could not occur given the facts. So, no one could raise his/her hands.

From wHolt - 10/11/06 2:33 PM

Boki - of those you have labeled Possible, which ones can you eliminate by logic - without guessing?

From Boki - 10/10/06 2:34 PM

Me
 Prisoner 1
Prisoner 2
 Reasoning
 x
    x
 x
Possible; everyone sees at least one red x. So, they will raise their hands. Everyone might think that has green x on his/her forehead, but they could not be sure.
 x
   x
 x
 Possible; everyone would see at least one red x, and could raise hands. Prisoner 2 will see two red x and will raise his/her hand, but can’t say what colour is on his/her head. So, he/she will raise hand too.
 x
   x
  x
 Possible; everyone sees at least one red x. Prisoner 1 will see two red x and will raise his/her hand, but can’t say what colour is on his/her head. Other two prisoners will see at least one red x, they can raise their hands too.
 x
   x
  x
Possible; everyone sees at least one red x; I will see two red x, and I see raise my hand, but can’t say what colour is on his/her head. Other two prisoners will see at least one red x, they can raise their hands too.
 x
  x
  x
 Impossible; not everyone sees at least one red x; I will see two green x's, but I did raise hand. The arrangement could not occur given the facts.
  x
  x
  
x
 Impossible; not everyone sees at least one red x;  prisoner 2 will see two green x’s, but he/she did raise hand. The arrangement could not occur given the facts.
 x
 x
 x
 Impossible; not everyone sees at least one red x; prisoner 1 would see two green x's, but he/she did raise hand. The arrangement could not occur given the facts.  
 x
 x
 x
 Impossible; No one sees red x, the arrangement could not occur given the facts. So, no one could raise his/her hands.
 

From wHolt - 10/10/06 11:45 AM

 x
   x
 x
 Impossible; everyone would have to see at least one red x, and could raise hand; the arrangement could not occur given the facts. Prisoner 2 will see two red x and will raise his/her hand, but can’t say what colour is on his/her head.

But everyone does see at least one red x

From Boki - 10/8/06 3:43 PM

 Me
 Prisoner 1
Prisoner 2
 Reasoning
 x
    x
 x
Possible; everyone sees at least one red x. So, they will raise their hands. Everyone might think that has green x on his/her forehead, but they could not be sure.
 x
   x
 x
 Impossible; everyone would have to see at least one red x, and could raise hand; the arrangement could not occur given the facts. Prisoner 2 will see two red x and will raise his/her hand, but can’t say what colour is on his/her head.
 x
   x
  x
 Impossible; The arrangement could not occur given the facts. Prisoner 1 will see two red x and will raise his/her hand, but can’t say what colour is on his/her head. Other two prisoners will see at least one red x, they can raise their hands too.
 x
   x
  x
Impossible; The arrangement could not occur given the facts. I will see two red x, and I see raise my hand, but can’t say what colour is on his/her head. Other two prisoners will see at least one red x, they can raise their hands too.
 x
  x
  x
 Impossible; Because I will see two green x's means that I can guess that on my head is red x. Since I am not sure, I will raise my hand. Other two prisoners will see at least one red x, so they will raise their hands too.
  x
  x
  
x
 Impossible; prisoner 2 will see two green x’s and can guess that on his/her head is red x. Since is not sure, he/her will raise hand. I and prisoner 1 will see at least one red x, so we will raise our hands too.
 x
 x
 x
 Impossible; prisoner 1 would see two green x's, so he/she could not raise the hand. The arrangement could not occur given the facts. I and prisoner 2 will see at least one red x, so we will raise our hands.
 x
 x
 x
 Impossible; No one sees red x, the arrangement could not occur given the facts. So, no one could raise his/her hands.
 From 8 rows above, two have one colour, and 6 have mixed colour. All those mixed coloured rows give to each of us 75% to guess right colour on our heads. In row 1 is possible because everyone could think “on my forehead is green x.”  Rows 2, 3, 4, 5, 6, 7, and 8 also, are impossible. There is insuficient data to determine what coulour is on their forehead. So, everyone will rais his/her hand and remain silent.

From wHolt - 10/8/06 12:09 PM

So how do you eliminate 3 of your 4 remaining possibles?
Only one is correct given the facts.

From Boki - 10/7/06 3:42 PM

 Me
 Prisoner 1
Prisoner 2
 Reasoning
 x
    x
 x
Possible; everyone sees at least one red x. So, they will raise their hands. Everyone might think that has green x on his/her forehead, but they could not be sure.
 x
   x
 x
 Impossible; everyone would have to see at least one red x, and could raise hand; the arrangement could not occur given the facts. Prisoner 2 will see two red x and will raise his/her hand, but can’t say what colour is on his/her head.
 x
   x
  x
 Impossible; The arrangement could not occur given the facts. prisoner 1 will see two red x and will raise his/her hand, but can’t say what colour is on his/her head. Other two prisoners will see at least one red x, they can raise their hands too.
 x
   x
  x
Possible; because everyone I will see at least one red x, so they will raise their hands too.
 x
  x
  x
 Possible; because I will see two green x's, which means that I can guess that on my head is red x. Since I am not sure, I will raise my hand. Other two prisoners will see at least one red x, so they will raise their hands too.
  x
  x

  

x

 Possible; prisoner 2 will see two green x’s and can guess that on his/her head is red x. Since is not sure, he/her will raise hand. I and prisoner 1 will see at least one red x, so we will raise our hands too.
 x
 x
 x
 Impossible; prisoner 1 would see two green x's, so he/she could not raise the hand. The arrangement could not occur given the facts. I and prisoner 2 will see at least one red x, so we will raise our hands.
 x
 x
 x
 Impossible; No one sees red x, the arrangement could not occur given the facts. So, no one could raise his/her hands.
 From 8 rows above, two have one colour, and 6 have mixed colour. All those mixed coloured rows give to each of us 75% to guess right colour on our heads. In row 1 is possible because everyone could think “on my forehead is green x.”  Rows 4, 5, and 6 also, because I (as prisoner 2, and prisoner 1 as well) could think that on my forehead is a red x. Only rows 2, 3, 7, and 8 are impossible because no one could raise hand, but they all raised hands. Finally, none of us was sure enough to determine colour on his/her forehead. So, we all will remain silent.

From wHolt - 10/7/06 2:30 PM

x
 x
 x

why does the middle prisoner raise his hand if he sees no red X? that would not be allowed.

 

x
 x
 x

why is this arrangement impossible if everyone sees a red x?

Remember: prisoners are not allowed to guess!
Impossible means that the arrangement could not occur given the facts.
Impossible does not mean that you cannot know your color given the arrrangement.

From Boki - 10/6/06 11:43 AM

 Me
 Prisoner 1
Prisoner 2
 Reasoning

 x

    x
 x
Possible; everyone sees at least one red x. So, they will raise their hands. Everyone might think that has green x on his/her forehead, but they could not be sure.
 x
   x
 x
 Impossible; everyone would have to see at least one red x, and could raise hand. Prisoner 2 will see two red x and will raise his/her hand, but can’t say what colour is on his/her head.
 x
   x
  x
 Impossible; prisoner 1 will see two red x and will raise his/her hand, but can’t say what colour is on his/her head. Other two prisoners will see at least one red x, they can raise their hands too.
 x
   x
  x
 Impossible; because I will see two red x’s means that I couldn't determine what colour is on my forehead, so I will raise my hand. Other two prisoners will see at least one red x, so they will raise their hands too.
 x
  x
  x
 Possible; because I will see two green x's, which means that I can guess that on my head is red x. Since I am not sure, I will raise my hand. Other two prisoners will see at least one red x, so they will raise their hands too.
  x
  x
  x
 Possible; prisoner 2 will see two green x’s and can guess that on his/her head is red x. Since is not sure, he/her will raise hand. I and prisoner 1 will see at least one red x, so we will raise our hands too.
 x
 x
 x
 Possible; prisoner 1 would see two green x's and can guess that on his/her head is red x. Since not sure, he/her will raise hand. I and prisoner 2 will see at least one red x, so we will raise our hands too.
 x
 x
 x
 Impossible; No one sees red x. So, no one could raise his/her hands.
 From 8 rows above, two have one colour, and 6 have mixed colour. The row 1 is possible because everyone could think “on my forehead is green x.”  Rows 5, 6, and 7 also, because I (as prisoner 2, and prisoner 1as well) could think that on my forehead is a red x. Only rows 2, 3, 4, and 8 are impossible because no one could raise hand, but they all raised hands. Finally, none of us was sure enough to determine colour on his/her forehead. So, we all will remain silent.

From wHolt - 10/6/06 10:10 AM

But if everyone raises his hand, that means everyone sees a red x.
So why are 2 red x's and 1 green x impossible?
Don't use probability.
A minute goes by...
What is each prisoner thinking in that minute
for each row in your table?

From Taz - 9/26/06 5:59 PM

 A (Me) B C Explanation
 R G G Impossible, the prisoner with the red X can not see it.
 G R G Possible, At least one prisoner can see one red X.
 G G R Possible, At least one prisoner can see one red X.
 G G G Impossible, The prisoner can not raise their hand there is not a red X shown.
 R R R Possible, Prisoner can see at least one red X.
 R G G Possible, Prisoner can see at least one red X.
 G R G Impossible, Prisoner can not see red X on their own forehead.
 G G R Impossible, Prisoner can not see red X on their own forehead.

From wHolt - 9/20/06 8:11 PM

This page is now closed to newcomers.
Those of you who have started this puzzle,
may continue till you earn all 7 points.
Some of the assumptions you have made are:

A red x means exactly one red x,
but a red x means at least one red x.
The red x means exactly one red x.

Each prisoner only sees one other prisoner.
No ! Each prisoner sees the marks on both of the other prisoners.

Impossible means unlikely.
No! Impossible means you can explain why a specific arrangement is impossible.

Empathy means sympathy.
No! Empathy means seeing it the way the other guy sees it.
Empathy is what the warden is actually testing.

There is not enough information to disprove what seems possible.
No! A minute goes by is the only clue you need!

From TBird - 9/20/06 8:07 AM

 myself

1

cellmate

2 

cellmate

3 

reasoning 
 greenred red impossible becuase there has to be at least 2 red x's for everyone to raise their hands becuase if i could see thier two red x's i still would not be able to know what is on my head
 redred green impossible becuase if myself and cellmate 2 seen that 3 has green would we know that we had red 
 greengreen green  impossible becuase we would all not see one red x 
 greengreen red impossible becuase cellmate 3 would not see red 
 green red green impossible becuase cellmate 2 would not see red 
 redred red possible becuase we would all see red 
 redgreen red impossible becuase we would know to all raise our hands 
 redgreen green impossible becuase myself would not see red 

 

i have a red x on my head

From Brick - 9/20/06 3:48 AM

A (me)  B C Reason
 red red red Possible because everyone sees at least one red X
 green green green Impossible because everyone sees no red X's unless everyone lies
 red red green Possible because everyone sees at least one red X
 red green red Possible because everyone sees at least one red X
 red green green Impossible because I don't see a red X
 green green red Impossible because prisoner C doesn't see a red X
 green red red Possible because everyone sees at least one red X
 green red green Impossible because prisoner B doesn't see a red X

From Ivy - 9/20/06 1:37 AM

A(ME) B C REASON 
 RG G  impossible; i saw at least one red X to have raised my hand
 GR G  impossible; everyone saw at least one red X
 GG R  impossible; everyone saw at least one red X
 RR R  possible;everyone saw a red X and I would automatically say that my X is red
 RG R  impossible; unsure what color my X would be
 RR G  impossible; unsure what color my X would be
 GR R  impossible; unsure what color my X would be
 GGG impossible; everyone saw at least one red X

From Phoenix - 9/19/06 10:00 PM

 ME 2 3 REASON                                                                                                             
 G G G Impossible. At least one red X has been seen by me.
 R G G Impossible. At least one red X has been seen by me.
 G G R Impossible. Prisoner 3 raised his/her hand claiming to see a red X.
 G R G Impossible. Prisoner 2 raised his/her hand claiming to see a red X.
 G R R Impossible to prove that this arrangement in not possible. Each prisoner will see at least one red X.
 R G R Impossible to prove that this arrangement in not possible. Each prisoner will see at least one red X.
 R R G Impossible to prove that this arrangement in not possible. Each prisoner will see at least one red X.
 R R R Possible. All three prisoners raised their hands seeing at least one red X.

From Bravo - 9/19/06 10:00 PM

I think that there is only one option that allows you to see all the colors.  I think it has to be in a triangle.  if you have a diagonal line or they are across or up and down they will only see possible one or two out of the three colors.  so if they stand in a triangle they can see all the colors

 G  G  G  not possible not all see green has to be red

G  G  R  not possible not all red

G  R  R  Not possible not all red

G  R  G  Not all possible not all red

R  G  G  Not possible  not all red

R  R  G  Not possible not all red

R  G  R  Not possible not all red

R  R  R  possible.  all can see red

From CatsEyes - 9/19/06 9:59 PM

 Prisoner A (Me)

Prisoner B Prisoner C  
XX XImpossible: No prisoner sees a red X
XXXImpossible: Prisoner C does not see a red X
XXXImpossible: Prisoner B does not see a red X
XXXPossible: All prisoners see at least one red X and the X on my (Prisoner A) forehead is green. 
XXXImpossible: I (Prisoner A) do not see a red X
XXXPossible: All prisoners see at least one red X and the X on my (Prisoner A) forehead is red. 
XXXPossible: All prisoners see at least one red X and the X on my (Prisoner A) forehead is red. 
XXXPossible: All prisoners see at least one red X and the X on my (Prisoner A) forehead is red. 

From Pac - 9/19/06 9:44 PM

Me 2 3 Reasoning 
G G G Impossible because no one has a red X 
G G R Impossible because #3 doesn't see a red X 
G R G Impossible because #2 doesn't see a red X 
R G G Impossible because I don't see a red X and still raise my hand, but this would mean that my X is red 
R R G Possible as everyone sees a red X
R G R Possible as everyone sees a red X
G R R Possible as everyone sees a red X
R R R Possible as everyone sees a red X

I'm thinking to deeply into this one, as usual.  I'm sure it is something simple and I'm just not seeing it.  ARGH!!!

The only way that I can think of more impossibilities is if each person can only see one other person's X (as CenterField illustrated), if there is a 4th party that is a prisoner that isn't in the circle, or if there was more information like the prisoners and hats logic problem where there are five hats (2 of one color, 3 of another color).  I just feel like there is info missing, but everything I need is probably staring me in the face...

From RockClimber - 9/19/06 8:51 PM

 A  B C Reason
 1 X X X  This is the only possible Answer.
 2 X X X Impossible, no one sees a red X
 3 X X X Impossible, not everyone sees a red X.
 4 X X X Impossible, not everyone sees a red X.
 5 X X X Impossible, not everyone sees a red X.
 6 X X X Impossible, not everyone sees a red X.
 7 X X X Impossible, not everyone sees a red X.
 8 X X X Impossible, not everyone sees a red X.

The prisoners are standing in a circle. However, prisoner A is facing prisoner B. Prisoner B is facing prisoner C. Prisoner C is facing prisoner A. Therefore, prisoner A can only see what color Prisoner B's X is, Prisoner B can only see what color prisoner C's X is, and prisoner C can only see what color prisoner A's X is. With all three prisoner's having a red X on their forehead, each of them can see this. Prisoner A raises their hand first, then the other two follow because they both each see a red X. I cannot see the color of prisoner C's X, however I can notice that his hand is raised, which means he sees a red X on my head, So the color of my X is red, as is everyone elses.
-Rockclimber

From Draco - 9/19/06 7:31 PM

 Me P1 P2 Reason
 G G G Impossible. At least one person has a red X. 
 G G R Impossible. Since both of the prisoners raised their hands, as well as myself, their must be two red X's. 
 G R R Possible. Everyone is able to see a red X.
 R R R Possible.Everyone is able to see a red X.
 R R G Possible.Everyone is able to see a red X.
 R G G Impossible.  Both prisoners see a red X as well as myself, so one of the other prisoners must have a red X.
 R G R Possible.Everyone is able to see a red X.
 G R G Impossible.  Both prisoners see a red X as well as myself, so both  prisoners or I must have a red X.

From HoneyBee - 9/19/06 5:26 PM

 A B C Explanation
G R R Correct.  Rules state that I (A), was the first to raise my hand.  If I see 2 red 'X's, then I know I must be marked green since both colors were used.
G G G Impossible.  Rules state that both red and green are used. 
G G R Impossible.  Prisoner C cannot see a red X, which refutes the rule that each one is telling the truth in seeing a red X. 
G R GImpossible.  Prisoner B cannot see a red X, which refutes the rule that each one is telling the truth in seeing a red X. 
R G R Impossible.  If I (A) am marked green and each prisoner sees at least one red X, then prisoners B and C have no way of knowing what color they are for sure.  
R R R Impossible.  Rules state that both red and green were used.  
R G G Impossible.  Prisoner A cannot see a red X, which refutes the rule that each one is telling the truth in seeing a red X.
R R G Impossible. If I (A) am marked green and each prisoner sees at least one red X, then prisoners B and C have no way of knowing what color they are for sure.

From CenterField - 9/19/06 5:11 PM

3_Prisoners2

The only way I can think of that would reduce the four possibilities down to one would be this: The three of us are standing in a circle, all looking toward the inside of the circle, but I am facing #2, #2 is facing #3, and #3 is facing me. If that is the case and we each only see one X and still all raise our hands, then we must all see a red X. So...that would mean I am marked with a red X. The correct possibility would then be R R R.

From Bubba - 9/19/06 3:21 PM

r  r r possible if because every one would raise their hands
 r r g

 this is possible because everyone would raise their hands

 rg  r this is possible
 g rr also possible
 g g g not possible no one would raise their hands
 g g r not possible because the third prisoner would only see green
 g r g not possible because  the second prisoner would only see green
 r

 g

g  not possible because only i would see green

now in the instructions it says that i see atleast one red x it does not say that i see two red x's so assuming that at least one of the two prisoners i see has a green x then it is safe to say that i have a red x on my head but if i do not see a green x then it is impossible to say what color x is on my head

From GolfGirl - 9/19/06 1:58 PM

 ME PRISONER1 PRISONER2 EXPLANATION
 GR G This is not possible because everyone sees red. Prisoner 1 would not see red. 
 RG  G This isn't possible because I see red, and I wouldnt see red with this order.
 GG R

 This is impossible because everyone sees red, and prisoner 2 would not see red.

 R R G This is a possible answer because everyone would see red on someones forhead.
 R R R This is not possible. Everyone has either a red or green x. With this order noone would have a green one.
 G G G This is not possible because nobody would have a red x.The problem said that everyone raised their hand because they saw red.
 R G R This could work because everyone would see red on someone.
 G R R This could work because everyone would see red on someone.

From Kolin - 9/19/06 1:28 PM

 A(ME)BC REASON 
 RG G  IMPOSSIBLE i don't see a red x
 R R G POSSIBLE everyone sees a red x
 RR R  IMPOSSIBLE everyone sees a red x but noone has a green x
R GR  POSSIBLE everyone sees a red x
 GR R  POSSIBLE everyone sees a red x
 G GR  IMPOSSIBLE c doesn't see a red x
 G R G IMPOSSIBLE b doesn't see a red x
 GG G  IMPOSSIBLE noone sees a red x and noone has a red x

From SunSport - 9/19/06 11:53 AM

 A B CReasoning 
 (Me)   
 Red Green Green Impossible:  I cannot see a red x
 Red Red Green Possible:  Everyone can see at least 1 red x
 Red Green Red Possible:  Everyone can see at least 1 red x
 Red Red  Red Impossible:  Everyone can see at least 2 red x's, but warden marked prisoners with either red or green x, not all reds
 Green Red Red Possible:  Everyone can see at least 1 red x
 Green Red Green Impossible:  One person (b) cannot see red x
 Green Green Red Impossible:  One person (c) cannot see red x
 Green Green Green Impossilbe:  No-one can see red x, no-one would raise hand
    

From Soola - 9/19/06 11:38 AM

 12
3
Explanation
G G
G
 Impossible because there are hands in the air, so atleast one person must have a red x
G
G
R
 Impossible since everyones hand is in the air, atleast two people must have a red x
G
R
R
 Possible this way each prisoner could be looking at atleast one red x
G
R
G
Impossible because all hands are in the air and atleast two x's have to be red for that to work.
R
R
R
 Possible, since everyone sees a red x it is possible that they all have one
R
R
G
 Possible because every person can see a red and someone can still have a green
R
G
R
 Possible because every person can see a red and someone can still have a green
R
G
G

 Not possible there must be atleast two reds present for everyone to raise their hand.        

From Lexiowen - 9/18/06 7:25 PM

 1 23  Explanation
 G G G Impossible- no red x to be seen
 G R G # 2 does not see a red x
 G R R possible-everyone is able to see a red x
 G G R #3 is not able to see a red x
 R G G #1 is not able to see a red x
 R R R possible-everyone is able to see a red x
 R G R possible-everyone is able to see a red x
 RR  Gpossible-everyone is able to see a red x 

From Deuce - 9/18/06 6:05 PM

 PRISONER 1 (ME)PRISONER 2 PRISONER 3 REASON 
 GG G IMPOSSIBLE NO RAISED HANDS 
R G G IMPOSSIBLE I WOULDNT HAVE RAISED MY HAND 
R R G POSSIBLE EVERYONE WOULD SEE AT LEAST 1 RED X 
R R R POSSIBLE ALL WOULD SEE AT LEAST 1 RED X 
G R R POSSIBLE ALL WOULD SEE AT LEAST 1 RED 
G R G IMPOSSIBLE EVERYONE COULDNT RAISE THEIR HANDS 
G  G R IMPOSSIBLE NOT EVERY1 COULD RAISE THEIR HANDS
 R G R POSSIBLE  ALL CAN RAISE THEIR HANDS

THESE ARE THE ONLY CASES WHERE HANDS COULD BE RAISED OR NOT.  IF EVERYONE IS AS SMART AS I AM AND NOBODY CAN

LIE, THEY ARE PLAYING THE ODDS THAT ANOTHER INMATE WILL ANSWER TO EVEN THE ODDS OUT.  OR THEY REALIZED THAT

THE WARDEN DIDN'T SAY WHAT WOULD HAPPEN IF NOBODY ANSWERED RIGHT OR WRONG SO EVERYONE IS SILENT.

 

From CenterField - 9/18/06 4:59 PM

3 Prisoners

From Trixie - 9/17/06 4:41 PM

 12 3 Explanation 
 x x x Impossible-Nobody would raise their hand because nobody would see a red x.
 x x x Impossible- Only 2 people would see a red x. Therefore, all 3 people would not raise their hand.
 x x x Possible- Everyone sees atleast 1 red x. Therefore, all 3 people would raise their hand.
 x  x x Impossible- Only 2 people would see a red x. Therefore, all 3 people would not raise their hand.
 x x x Impossible- Only 2 people would see a red x. Therefore, all 3 people would not raise their hand.
 x x x Possible- Everyone would see a red x. Therefore, everyone would raise their hand.
 x x x Possible- Everyone would see atleast one red x. Therefore, everyone would raise their hand.
 x x x Possible- Everyone would see atleast one red x. Therefore, everyone would raise their hand.

From wHolt - 9/17/06 1:32 PM

Thanks to Aeneid and JooJoo.
Can you eliminate any other rows?
Zonino - 7 points!

From JooJoo - 9/17/06 8:57 AM

 A (me)B C Explanations                                                                         
 X (R) X (R) X (R) This could be true because then all 3 people would be telling the truth about seeing a red X.
 X (G) X (G) X (R) This could not be true if everyone is telling the truth. I would be telling the truth becaus I see C's red X. B would be telling the truth because he would be seeing C's red X also, but C would have to be lieing because he would see no red X.
 X (G) X (R) X (R) This could be true. I would be telling the truth because I see 2 red X's, B would be telling the truth because he sees C's red X and C would be telling the truth because he sees B's red X.
 X (R) X (G) X (R) This could be true. I would be telling the truth by seeing C's red X and B would be telling the truth by seeing 2 red X's and C would be telling the truth by seeing my red X.
 X (R) X (R) X (G) This could be true. I would be telling the truth because I see B's red X, B would be telling the truth because he sees my red X, and C would be telling the truth because he sees 2 red X's.
 X (R) X (G) X (G) This could not be true. I would be lieng because I see no red X's, but B and C would be telling the truth because they see each others red X's.
 X (G) X (G) X (G) This could not be true because no one would see a red X and then they would all be lieing.
 X (G) X (R) X (G) This could not be true. I would tell the truth and see B's red X, and C would tell the truth because he sees B's red X also, but C would be lieing because he cannot see a red X.
If all the prisoners are telling the truth, then there must be at least 2 people marked with a Red X. If they are all marked with a green X then they are all lieing. So either 2 of them are marked with a red X or all 3 of them are marked with a red X. You have a 50% chance of guessing whether or not you yourself have a green X or a red X.

From Aeneid - 9/16/06 11:31 PM

 

P1,ME

P2 P3  REASON
1  G G GIMPOSSIBLE, BECAUSE THE QUESTION STATES THAT I SEE AT LEAST ONE RED X   
2  G G RIMPOSSIBLE, THAT ALL THREE RAISED THEIR HANDS BECAUSE P3 WOULD NOT HAVE SEEN RED.  
3 G  R GIMPOSSIBLE, ALL THREE RAISED THEIR HANDS BUT COULDN'T HAVE BECAUSE P2 WOULD'NT HAVE SEEN GREEN  
4  G R R POSSIBLE, THAT ALL THREE RAISED THEIR HANDS BECAUSE P2+P3 WOULD HAVE SEEN EACH OTHERS AND (P1) WOULD HAVE SEEN THEIRS. IMPOSSIBLE THAT SOME ONE WOULD KNOW THEIR COLOR X FOR SURE WITHOUT GUESSING
5  R R R POSSIBLE, THE WARDEN COULD HAVE PLACED ALL THREE PRISONES WITH A RED X AND ALL THREE RAISED THEIR HANDS. IT'S IMPOSSIBLE TO KNOW FOR SURE THE COLOR X YOU HAD
6  R R GIT'S POSSIBLE THAT ALL THREE RAISED THEIR HANDS, BUT ITS IMPOSSIBLE TO KNOW THE COLOR X THAT YOU HAD FOR SURE. P3 COULD ASSUME THAT IF HE SAW TWO REDS THAT HIS WOULD BE GREEN. 
7  R G RIT'S POSSIBLE THAT ALL THREE RAISED THEIR HANDS, EACH (P) WOULD HAVE SEEN A RED X. ITS IMPOSSIBLE TO KNOW THE COLOR FOR SURE WITHOUT GUESSING. P2 COULD ASSUME THAT HE HAD A GREEN BECUSE THE OTHER TWO HAD RED. 
8  R G G THIS SENERIO WOULD BE IMPOSSIBLE BECUSE THE QUESTION STATES THAT I SAW AT LEAST ONE RED X. ITS IMPOSSIBLE FOR ALL THREE TO RAISE THEIR HANDS.  

THERE ARE EIGHT POSSIBLE WAYS THE WARDEN COULD HAVE MARKED THE FOREHEADS. IT IS NOT POSSIBLE THAT THE WARDEN MARKED ALL THREE PRISONERS WITH A GREEN X BECAUSE THE QUESTION NOTES THAT SAW AT LEAST ONE RED X, SO SCENERIO'S 1 + 8 ARE OUT FOR SURE. 

SCENERIO'S 1,2,3,8 ARE OUT BECAUSE ALL THREE CAN'T RAISE THEIR HANDS

From wHolt - 9/15/06 12:15 AM

Interesting ideas, EagleDrew and BassLady.
However,
the problem does state that the warden marked the foreheads with either red or green marks.
And made it unpleasant to guess. So don't guess!

 

SkoolGirl - 7 points!

From Shanja - 9/14/06 8:22 PM

Basslady that makes sense to me, in that could be a solution, but I'm almost afraid that isnt it because Mr. Holt asked if we could narrow it down from 4 to the correct 1. That aside i would agree with you because that would clearly explain why everyone hesitated because no one could have a way of knowing what color their's is.

From BassLady - 9/14/06 7:26 PM

OMG!!!  They all hesitate in guessing their color because the warden did not tell them that he only used red or green.  He only told them to raise their hand if they saw red on the other prisoners forehead.  Then he says to guess the color on their forehead.  It could have been yellow, blue or purple.  The warden did not give them the option of guessing their color to be red or green.Cool  This has to be the answer.  Oh yeah!!!

From EagleDrew - 9/14/06 3:31 PM

 trysprisoner 1  prisoner 2prisoner 3 
 1 r r r
 2 r g r
 3 r rg 
 4 g r r
 5 g g g
 6 g r g
 7 g g r
 8 r g g

 

nothing says the warden was truthful on the amount of reds and greens. what if the prisoners or at least one was colorblind! many people who are colorblind can't see a difference between red or green!

From wHolt - 9/14/06 2:34 PM

David - the Warden marked Either Green or Red does not mean both or neither.

From David - 9/13/06 10:39 AM

 a bc  Reason 
 G G GImpossible  Noone would have raised their hands
 G G RImpossible  pC would not have raised his hand
 R G GImpossible  you would not have raised your hand
 G R GImpossible  pB would not have raised his hand
 R R RImpossible Warden marked Either Green or Red not, just one 
     For these last three, the prizoners hesitated because they probably didnt know what two reds meant,  count the number of reds you see and you will know what is on your head.  (hey, you said they were as smart as meLaughing)
 G R R  If you see two reds, you know you are green
 R G R  If you see green and red you know you are red
 R R G  If you see green and red you know you are red

From wHolt - 9/13/06 9:36 AM

Boki - a 50% chance does not mean impossible. It means 50% possible also.

BassLady & Pringle - you need to prove that two reds and a green are impossible

From Pringle - 9/13/06 2:58 AM

 ME PRSIONER 1(p1) PRISONER 2(p2) REASON
 R R R Possible situation: we all raise our hands, but unable to decide what x I have on. I can't tell if p1 raise his hand because of me or p2. Same with p2. I have 50% chance to guess right. Because even if I have a green x (or red x),we all would raise our hands.
 R R GPossible Situation : we all raise our hands. And I know that I have a red x. Since p2 has a green x, P1 would raise his hand because of the red x on me.
 R G R Possible Situation: we all raise our hands . And I know that I have a red x. Since p1 has a green x, p2 would raise his hand because of the red x on me
 R G G impossible situation: I wouldn't raise my hand becasue I don't see any red x. But I can tell I have a red x. Because p1 and p2 would raise their hands and I know neither of them has red x.
 G G G impossible situation:no one would raise their hands. But I know I have a green x, because nobody raise their hands up. This means there is no red x.
 G G R impossible situation: p2 wouldn't raise his hand. But I know I have a green x. Because p1 and I would raise our hands, but p2 wouldn't.
 G R R possible situation but unable to decide what x I have on me. I can't tell if p1 raise his hand because of me or p2. I have 50% chance to guess right. Because even if I have a red x(or green x), we all would raise our hands up.
 G R G impossible situation:p1 wouldn't raise his hand up. But I know I have a green x. Since p1 wouldn't raise his hand, p2 raise his hand because of p1's red x.

From BassLady - 9/12/06 8:42 PM

If Prisoner A has a Red X and Prisoner B has a Green X - Then Prisoner C cannot have a green X.  Prisoner A would not see a red X.

If Prisoner A has a Green X and Prisoner B has a Red X - Then Prisoner C cannot have a green X.  Prisoner A would not see a red X.

If Prisoner B has a Red X and Prisoner C has a Green X - Then Prisoner A cannot have a green X.  Prisoner B would not see a red X.

If Prisoner B has a Green X and Prisoner C has a Red X - Then Prisoner A cannot have a green X.  Prisoner B would not see a red X.

If Prisoner C has a Red X and Prisoner A has Green X - Then Prisoner B cannot have a green X.  Prisoner C would not see a red X.

If Prisoner C has a Green X and Prisoner A has a Red X - Then Prisoner B cannot have a green X.  Prisoner C would not see a red X.

Prisoner A, B, and C all three cannot have a green X. No one would see a red X.

Now I have proved 7 theories cannot be true because with each theory, one of the 3 cannot see a red X.

From Boki - 9/12/06 2:32 PM

 You Prisoner 1Prisoner 2 
 XX X

 Possible; all of them would see two red x’s on the others’ forehead.

 X X X Impossible; everyone would have to see at least one red x. If all had a green X then no one would raise their hand.
 X X X Impossible; everyone will see at least one red x and will raise his/her hand.
 X X X

 Impossible; because one of the prisoners will see two green x's meaning he couldn't raise his hand.

 X  X X Impossible; because prisoner 1 will see two green x's, which means he can't raise his hand.
  X X  X Impossible; everyone will see at least one red x and will raise his/her hand.
 X X X Impossible; prisoner 2 would see two green x's and will not raise his/her hand.
 X X X Impossible; all of them see at least one red x and will raise his/her hand.
    

 

 

From wHolt - 9/12/06 1:36 PM

CLARIFICATION!
Prisoners do not hesitate to raise their hands.
Everyone sees at least one red X.
Prisoners hesitate, however,  in declaring the color of their X.

From BassLady - 9/12/06 12:29 PM

 MeBC  
 X X X

 This is impossible.  No prisoner would see a red X.

 X X X This is impossible.  Prisoner A would not see a red X.
 X X X This is impossible.  Prisoner B would not see a Red X.
 X X X This is impossible.  PrisonerC would not see a Red X.
 X X X If the others are as smart as I am.  This is impossible.  None of the 3 prisoners rushed to raise their hand to tell what color X they each had. All 3 prisoners would have rushed to raise their hand.  Each thinking they had a Green X after seeing 2 red X's on the others.
 X X X If the others are as smart as I am.  This is impossible.  None of the 3 prisoners rushed to raise their hand to tell what color X they each had. Prisoner B would have rushed to raise his hand thinking he had a Green X after seeing 2 red X's on the others.
 X X X If the others are as smart as I am.  This is impossible.  None of the 3 prisoners rushed to raise their hand to tell what color X they each had. Prisoner C would have rushed to raise his hand thinking he had a Green X after seeing 2 red X's on the others.
 X XX  The only logical solution is that I have a Green X.

From Fro - 9/11/06 9:58 PM

 A B C (me) Reason
 G R R each will see 1 red X and raise their hand
 R R G  each will see 1 red X and raise their hand
 R G R each will see 1 red X and raise their hand
 R R R each will see 2 red Xs, raise their hand and think they have the green = all die
(impossible if a green X was used)
 G GR  Only 2 can raise their hands (impossible)
 R G G Only 2 can raise their hands (impossible)
 G G R Only 2 can raise their hands (impossible)
 G G G Nobody would raise their hands (impossible)
    If the others are as smart as me and they don't speak up, it's because they can see the green x on my head and know they're gonna die! Wink

From Poovey - 9/11/06 6:48 PM

 Prisoner A (me) B C Comments
 g r r this one everybody will raise hand because a,b,c all see one red x
 r g r possible because again everyone sees a red x
 r r g possible because again everyone sees a red x
 g g r not possible because everyone would not see a red x
 g r g not possible because everyone would not see a red x
 r g g impossible because I would not raise a hand
 g g gimpossible nobody would raise a hand and then we know we all have green x
 r r r everyone would raise their hand and you can possibly assume you have a red x
    

From wHolt - 9/11/06 10:56 AM

Taurus - why are rows 1 and 5 possible, but not row 2?
you cannot eliminate a row based on chance. use logic only.

Nice job, Capricorn. 7 points!

From Bigfoot - 9/10/06 6:53 PM

 A-ME BC WHY B/C i said so
XXX

This would be possible a,b,c will see a red x 

XXX

This would be possible a,b,c will see a red x on at least one person

XXXThis would be possible a,b,c will see a red x on at least one person
XXXI cant raise my hand because I am the suspect Impossile
XXXNo body can raise their hand because they are all green Impossile
XXXB cant raise his hand because he is the suspect Impossile
XXXC cant raise his hand because he is the suspect Impossile
XXXThis would be possible a,b,c will see a red x on at least one person

From Harkar - 9/10/06 5:38 PM

 Me Prisoner A Prisoner B Explanation
 G G G This is not possible as no prisoner would see a red X.
 G G R This is not possible as Prisoner B would not see a red X.
 G R G This is not possible as Prisoner A would not see a red X.
 R G G This is not possible as I would not see a red X.
 G R R This is possible because everyone would see a red X.  If I knew there had to be one Green X then I would know I had a Green X, but that is not explicit in the problem.
 R G R This is possible because everyone would see a red X.
 R R G This is possible because everyone would see a red X.
 R RR  This is possible because everyone would see a red X. 

From Taurus - 9/10/06 11:11 AM

 ME (1)CELLMATE 2  CELLMATE 3EXPLANTION 
 R R G IMPOSSIBLE, THERE HAS TO BE AT LEAST 2 RED X'S FOR EVERYONE TO RAISE THEIR HANDS.  SO IF ME AND #2 SEE A GREEN X WE BOTH KNOW WE ARE RED, AND WOULD IMMEDIATELY RESPOND.
 G R R IMPOSSIBLE, THERE HAS TO BE AT LEAST 2 RED X'S FOR EVERYONE TO RAISE THEIR HANDS.  SO IF I SEE 2 RED X'S I WOULD NOT KNOW WHAT COLOR MY X IS, BUT # 2 AND # 3 WOULD IMMEDIATELY RESPOND B/C THEY WOULD EACH SEE ONE RED AND ONE GREEN AND KNOW THAT FOR EVERYONE TO RAISE THERE HANDS THERE HAS TO BE AT LEAST 2 RED X'S.
 G G G IMPOSSIBLE, EVERYONE WOULD NOT SEE AT LEAST 1 RED
 R R RPOSSIBLE, SINCE WE WOULD EACH SEE 2 RED X'S, NEITHER OF US WOULD KNOW WHAT COLOR THE X IS ON OUR HEADS.  SO WE WOULD ALL HESITATE TO ANSWER.
 R G RIMPOSSIBLE, THERE ARE 2 RED X'S, AND # 3 AND I WOULD SEE ONE RED AND ONE GREEEN AND KNOW FOR ALL OF US TO RAISE OUR HANDS THERE MUST BE AT LEAST 2 RED X'S.
 G R G IMPOSSIBLE, # 2 WOULD NOT SEE RED
 R G G IMPOSSIBLE, I WOULDN'T SEE RED
 G G R IMPOSSIBLE, # 3 WOULDN'T SEE RED

Well, it's obvious that there will be at least 2 people marked with a red X or else all three of us couldn't raise our hands.  Any scenario where there are 2 green Xs one of the cellmates would not see a red. But if there are only 2 red x's and 1 green, the two people that would see one red and one green would know that theirs is red (because there has to be at least 2 red x's for all hands to be raised).  They would answer immediately.  But since we all just stood around not saying anything, we all saw 2 red x's and wouldn't know the color on our forehead- because we didn't answer immediately.  Therefore my head is marked with a red x.

From Tiger - 9/10/06 12:50 AM

 A (Me) B C Argument
 X X X No one would see a red X. Impossible
 X X X Prisoner C would not see a red X. Impossible
 X X X Prisoner B would not see a red X. Impossible
 X X X Everyone would see a red X. Possible
 X X X Everyone would see a red X. Possible
 X X X Everyone would see a red X. Possible
 X X X I would not see a red X. Impossible
 X X X Everyone would see at least one red X. Possible

I think the answer is everyone has a red X, I just don't know how to prove it.

 

From wHolt - 9/9/06 9:49 PM

Soller- sorry cannot picture what you did. Missing a piece of the explanation.

From Soller - 9/9/06 2:58 PM

Originally I got 4 possibles and 4 impossibles, but I figured if there was a circle on the ground and the prisoners were standing inside the circle where 2 prisoners are facing one which would leave only one possible solution.

From wHolt - 9/9/06 2:34 PM

Assume that each prisoner can see the marks on the other two prisoners.

From SuperDuke - 9/8/06 9:11 PM

Soller, I am confused by your chart. If they are standing in a circle looking at each other that means each prisoner see's the other TWO prisoners.

I must disagree with some of your statements on your chart because of this. 

From Butterfly - 9/8/06 7:48 PM

  AB C P or I  Reason
 1.G G G Impossible None of the prisoners would see a red X. 
 2.R G G Impossible Prisoner A would not see a red X. 
 3.G R G Impossible Prisoner B would not see a red X. 
 4.G G R Impossible Prisoner C would not see a red X. 
 5.R R G Possible All prisoners would see at least one red X. 
 6.R G R Possible All prisoners would see at least one red X. 
 7.G R R Possible All prisoners would see at least one red X. 
 8.R R R Possible All prisoners would see more than one red X. 
      

From Soller - 9/8/06 6:11 PM

 Prisoner 1Prisoner 2 Prisoner 3 Reason 

 Red

 Red Red This is possible because everyone would be able to see a red x.
 Red Green Red This is impossible if they are standing inside a circle facing prisoner 2; prisoner 1 and 3 would only see a green x.
 Red Red Green This is impossible if they are standing inside a circle with prisoner 1 and prisoner 2 facing prisoner c; prisoner 1 and 2 would only see a green x.
 Red Green Green This is impossible because priosoner 1 would not see a red x. 
 Green Green Green This is impossible because no one would see a red x.
 Green Red Green This is impossible because prisoner 2 would not see a red x. 
 Green Green Red This is impossible because prisoner 3 would not see a red x.
 Green Red Red This is impossible if prisoner 2 and 3 are side by side facing prisoner 1. prisoner 1 would be the only one who would see a red x.
 There is no chance that all would have a green x.  I would have a red x because if we were standing inside a circle and the other 2 prisoners are standing side by side facing me and if they raise thier hands then I would know that i would have a red x.

From wHolt - 9/8/06 11:00 AM

Who can use logic to go beyond the 4 row limit?

Aeneid - which of your reasons explain the impossible?

From DirtyBird - 9/7/06 7:03 PM

 A B C 
 G G GNot possible because nobody can see a red x. 
 G G R Person C could not see a red x.
 G R R Possible because everybody could see a red x.
 R R R Possible because everybody could see a red x.
 R R G Possible because everybody could see a red x.
 R G G Not possible because person A could not see a red x.
 R G R Possible because everybody would see a red x.
 G R G Not possible because person B could not see a red x.
It would seem that I have a 75% chance of living and a 25% chance of being executed.

From Melewen - 9/7/06 5:27 PM

 Prison 1 (Me)
Prisoner 2
Prisoner 3
Reason
 X X X Impossible. There are no red X's, so no one would raise their hand.
 X X
 X Impossible. Prisoner 3 wouldn't see a red X, so he wouldn't raise his hand.
 X
 X
 X
 Impossible. Prisoner 2 wouldn't see a red X, so he wouldn't raise his hand.
 X  X X Possible. Since there are two X's total, each prisoner would see at least one (I [prisoner 1] would see prisoner 2's and prisoner 3's; prisoner 2 would see prisoner 3's; prisoner 3 would see prisoner 2's).
 X X X Impossible. I (Prisoner 1) would only see green X's, so I wouldn't raise my hand.
 X X X Possible. Since there are two X's total, each prisoner would see at least one (I would see prisoner 3's; prisoner 2 would see prisoner 3's and mine; prisoner 3 would see mine)
 X X X Possible. Since there are two X's total, each prisoner would see at least one (I would see prisoner 2's; prisoner 2's would see mine; prisoner 3 would see prisoner 2's and mine).
 X X X Possible. Since there are no green X's, everyone would have to raise their hand.

From wHolt - 9/7/06 11:21 AM

There seems a consensus that there are 8 arrangements to consider.
Most of you have eliminated some of them with basic logic.
But how many of you can eliminate all except one of your rows?
That may require a bit more logic, and a dash of empathy,
which is not the same as sympathy.
No guessing allowed, of course...

From SuperDuke - 9/7/06 9:23 AM

 I have to give Mr. Holt his dibs here. You have to really be paying attention. If you'll notice he says he will award 7 points for 7 impossibles. Thats the reason I kept grinding on this one till...... EUREKA!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

From Slick - 9/7/06 8:47 AM

  Me 1   2    Explanation                                          
 GG G  Impossible, no hands raised 
 G G R Impossible, only 2 hands will raise
 GR  R Possible, All hands could raise
 RR  RPossible, All hands could raise 
 R R GPossible, All hands could raise 
 RG