57 replies to this topic

[wolfgang]

Another point to clarify.

 

Must the rows be parallel, and in particular Y-G-R-B order?

OP seems to suggest this condition.

 

+-------------------------+

|                         |

|      Y Y Y Y Y . . .    |

|      G G G . . . . .    |

Door   R R R R R R . .    |

|      B B B B B . . .    |

|                         |

|                         |

+-------------------------+

 

Or could the rows e.g. all start at the middle of the room, and grow outward toward the four walls, in any sequence?

Say Yellow to the north, Green to the south, Red to the east and Blue to the west?

Yes...the raws should be as you mentioned in your diagram,but all should face one direction

[Prime]

If the crooks who have already formed 4 neat rows start turning around in their places upon the entry of the next criminal -- that should be deemed as a form of communication by the warden. If they stay put until the newcomer takes his place, he has 3/4 chance of spoiling that neat formation.

If you arrange randomly, say, 16 men in 4x4 formation, no consecutive change of which way they face can guaranty thus newly formed rows' order and same colors in each row.

[bonanova]

Another point to clarify.
 
Must the rows be parallel, and in particular Y-G-R-B order?
OP seems to suggest this condition.
 
+-------------------------+
|                         |
|      Y Y Y Y Y . . .    |
|      G G G . . . . .    |
Door   R R R R R R . .    |
|      B B B B B . . .    |
|                         |
|                         |
+-------------------------+
 
Or could the rows e.g. all start at the middle of the room, and grow outward toward the four walls, in any sequence?
Say Yellow to the north, Green to the south, Red to the east and Blue to the west?

Yes...the raws should be as you mentioned in your diagram,but all should face one direction

"All" in one line? Or "All" in the whole room?

Say the the persons in the red line face the door.
Can the persons in the green line face away from the door?

This is like nailing jello to a tree.

[bonanova]

 

 

I can add something which may help you... The raws may face the door or the opposit direction!

 

Continuing with the community solve approach, can we clarify:

1. Must all the persons in a particular row face the same direction?
2.  
3. If prisoners in say the Yellow row can face in differing directions does that constitute [illegal] communication?
4.  
5. Can the first two prisoners choose the time that they [legally] alter their position, at any time up to the last prisoner takes his place?
6.  

 

During making raws...some of them  can be..back to back (in any raw)...but by reaching the last prisoner,they all shoud be at the same direction

 

But only the first two prisoners can move.

 

This means the seventh prisoner, say can come into a row back to back with someone else in that row, then at a later time switch his direction so that at the end all in that row have the same direction. So as long as a prisoner stays in the same position, he can flip his direction back and forth during the formation of rows. 

 

That sounds like communication.

 

Another piece of jello fell off the nail...

[wolfgang]

 

 

 

I can add something which may help you... The raws may face the door or the opposit direction!

 

Continuing with the community solve approach, can we clarify:

1. Must all the persons in a particular row face the same direction?
2.  
3. If prisoners in say the Yellow row can face in differing directions does that constitute [illegal] communication?
4.  
5. Can the first two prisoners choose the time that they [legally] alter their position, at any time up to the last prisoner takes his place?
6.  

 

During making raws...some of them  can be..back to back (in any raw)...but by reaching the last prisoner,they all shoud be at the same direction

 

But only the first two prisoners can move.

 

This means the seventh prisoner, say can come into a row back to back with someone else in that row, then at a later time switch his direction so that at the end all in that row have the same direction. So as long as a prisoner stays in the same position, he can flip his direction back and forth during the formation of rows. 

 

That sounds like communication.

 

Another piece of jello fell off the nail...

 

Yes....in my OP I said....each prisoner should choose his raw and once he did,he is not allowed to change his mind,but turning around himself was not mentioned

[bushindo]

 

 

 

 

I can add something which may help you... The raws may face the door or the opposit direction!

 

Continuing with the community solve approach, can we clarify:

1. Must all the persons in a particular row face the same direction?
2.  
3. If prisoners in say the Yellow row can face in differing directions does that constitute [illegal] communication?
4.  
5. Can the first two prisoners choose the time that they [legally] alter their position, at any time up to the last prisoner takes his place?
6.  

 

During making raws...some of them  can be..back to back (in any raw)...but by reaching the last prisoner,they all shoud be at the same direction

 

But only the first two prisoners can move.

 

This means the seventh prisoner, say can come into a row back to back with someone else in that row, then at a later time switch his direction so that at the end all in that row have the same direction. So as long as a prisoner stays in the same position, he can flip his direction back and forth during the formation of rows. 

 

That sounds like communication.

 

Another piece of jello fell off the nail...

 

Yes....in my OP I said....each prisoner should choose his raw and once he did,he is not allowed to change his mind,but turning around himself was not mentioned

 

 

This seems to imply that turning around (spinning or rotating) is allowed, even though switching rows isn't allowed. Isn't that a contradiction of the requirement of the OP, which I list below

 

An unknown number of prisoners( more than 14)were told a day before their execution, that they are going to be blind folded, and a colored paper(either.. yellow,green,red or blue) will be  glued on forehead of each one of them( no one can see his own paper), then they should inter a big hall one by one to make 4 raws in this order( Yellow,Green,Red,Blue)i.e. a raw of Yallows, a raw of Greens  etc.,each one will be unfolded when he inters the hall.No one of them is allowed to arrenge the others,each one should himslf choose where to stay, once he did,he can not change his place( only the first 2 prisoners can change their minds only once). Any kind of comunication between them is not allowed. If any one of them stands in a wrong raw, all of them will die!
All colores were used.
They should make a plane which saves all of them, can you help them?

 

Communication is defined as 'the imparting or exchanging of information or news', so by any reasonable interpretation, turning-in-place is considered a violation of the rules. If communication is allowed, then the puzzle becomes trivial. In fact, we don't even need to allow the first 2 prisoners to change their minds if we allow them to communicate.

[bonanova]

Agree that now it's not difficult.

But the first two might need change row locations.

Suppose the first three prisoners were [1] all red, [2] all different colors.

[CaptainEd]

OK, I think we are agreeing that we have to relax our interpretation of Wolfgang's proscription against communication.

The first two prisoners can establish the locations of all 4 colored rows, before the third one enters the room.

Then, the prisoners can inspect each arriving prisoner, rotate their positions to indicate the newcomer's color, and the newcomer can take his place in the appropriate row.

Spoiler for Details of establishing the locations

* Let's consider that there are (invisible) row numbers, from -4 to +4.
* Prisoner A enters and stands at 0, asserting his own color to be Yellow (regardless of his actual color, which he doesn't know). So at his right hand (position 1) should be Green, next (position 2) Red, further right (position 3) is Blue.
* Prisoner B enters, takes his position according to A's actual color. That is, B goes to the row A SHOULD be in = Row(Color(A)). Now A knows his own color and that of B.
* Prisoner A now changes the color framework by moving himself so that B is in the row B should be in. That is, A moves to Row(Color(A) + Row(B) - Color( B ) ). At this point, both prisoners know their own colors, and any observer can tell the new color framework, which may or may not be 0 = Yellow.

Spoiler for Examples:

1) A is Green, B is Blue. A enters, establishes location of 0. B enters, sees that A is Green, so he moves to (Row(Color(A)) = 1. Now A knows A is Green and B is Blue. Now A moves to (Row(Color(A) + Row(B) - Color( B ) ) = (1+1-3) = -1. At this point, in absolute terms, A is in position -1, B is in position 1. However, to the remaining prisoners, A (visibly Green) is therefore at position 1 and B (visibly Blue) is at position 3. Anybody knows where Yellow and Red go.

2) A is Green, B is Green. A enters. B enters, moves to 1. A now knows that both A and B are Green, so A moves to  (Row(Color(A) + Row(B) - Color( B ) )= (1+1-1)= 1 (ie. stands in the same row, directly behind or ahead of B). Now remaining prisoners can tell where Green is, therefore can infer where Red, Yellow and Blue are.

3) A is Green, B is Yellow. A enters. B enters, moves to 1. A now knows that A is Green and B is Yellow, moves to (Row(Color(A) + Row(B) - Color( B ) ) = (1 + 1 -0) = 2. Now remaining prisoners see B is Yellow and A is Green; they can easily infer where Red and Blue belong.

Spoiler for Conveying position to next arrival

When prisoner K enters, two chosen prisoners tell him his color by facing him or facing away from him, giving two bits of information, therefore a number from 0 to 3. Which two chosen prisoners? We have a number of ways to establish a sequence; here are two ways:
* If the prisoners were permitted to choose their order of arrival, then prisoner K looks at prisoners I and J, who just entered before him.
* Alternatively, consider the sequence of all prisoners in the Yellow row, followed by Red row, followed by Green row, followed by Blue row. Take the first two prisoners in this sequence. They are the ones who will tell prisoner K his color.

Edited by CaptainEd, 21 January 2013 - 05:14 PM.

[CaptainEd]

Spoiler for I always have typos...

Conveying position to next arrival. Consider the sequence of prisoners in rows Y, G, R, B. The first two of those prisoners will convey the newcomer's color to him.

 

Also, To match Bonanova's picture, I should say that Prisoner A, facing the door, starts in location 0, with his LEFT hand pointing to Position 1 = Green, further LEFT is Position 2 = Red, even further LEFT is Position 3 = Blue. The negative values are to his RIGHT.

[wolfgang]

Spoiler for I always have typos...

Conveying position to next arrival. Consider the sequence of prisoners in rows Y, G, R, B. The first two of those prisoners will convey the newcomer's color to him.

 

Also, To match Bonanova's picture, I should say that Prisoner A, facing the door, starts in location 0, with his LEFT hand pointing to Position 1 = Green, further LEFT is Position 2 = Red, even further LEFT is Position 3 = Blue. The negative values are to his RIGHT.

 

OK, I think we are agreeing that we have to relax our interpretation of Wolfgang's proscription against communication.

The first two prisoners can establish the locations of all 4 colored rows, before the third one enters the room.

Then, the prisoners can inspect each arriving prisoner, rotate their positions to indicate the newcomer's color, and the newcomer can take his place in the appropriate row.

Spoiler for Details of establishing the locations

* Let's consider that there are (invisible) row numbers, from -4 to +4.
* Prisoner A enters and stands at 0, asserting his own color to be Yellow (regardless of his actual color, which he doesn't know). So at his right hand (position 1) should be Green, next (position 2) Red, further right (position 3) is Blue.
* Prisoner B enters, takes his position according to A's actual color. That is, B goes to the row A SHOULD be in = Row(Color(A)). Now A knows his own color and that of B.
* Prisoner A now changes the color framework by moving himself so that B is in the row B should be in. That is, A moves to Row(Color(A) + Row(B) - Color( B ) ). At this point, both prisoners know their own colors, and any observer can tell the new color framework, which may or may not be 0 = Yellow.

Spoiler for Examples:

1) A is Green, B is Blue. A enters, establishes location of 0. B enters, sees that A is Green, so he moves to (Row(Color(A)) = 1. Now A knows A is Green and B is Blue. Now A moves to (Row(Color(A) + Row(B) - Color( B ) ) = (1+1-3) = -1. At this point, in absolute terms, A is in position -1, B is in position 1. However, to the remaining prisoners, A (visibly Green) is therefore at position 1 and B (visibly Blue) is at position 3. Anybody knows where Yellow and Red go.

2) A is Green, B is Green. A enters. B enters, moves to 1. A now knows that both A and B are Green, so A moves to  (Row(Color(A) + Row(B) - Color( B ) )= (1+1-1)= 1 (ie. stands in the same row, directly behind or ahead of B). Now remaining prisoners can tell where Green is, therefore can infer where Red, Yellow and Blue are.

3) A is Green, B is Yellow. A enters. B enters, moves to 1. A now knows that A is Green and B is Yellow, moves to (Row(Color(A) + Row(B) - Color( B ) ) = (1 + 1 -0) = 2. Now remaining prisoners see B is Yellow and A is Green; they can easily infer where Red and Blue belong.

Spoiler for Conveying position to next arrival

When prisoner K enters, two chosen prisoners tell him his color by facing him or facing away from him, giving two bits of information, therefore a number from 0 to 3. Which two chosen prisoners? We have a number of ways to establish a sequence; here are two ways:
* If the prisoners were permitted to choose their order of arrival, then prisoner K looks at prisoners I and J, who just entered before him.
* Alternatively, consider the sequence of all prisoners in the Yellow row, followed by Red row, followed by Green row, followed by Blue row. Take the first two prisoners in this sequence. They are the ones who will tell prisoner K his color.

 

your method is successful with the first two prisoners, but you should find a very simple,uncomplicated way for the 3rd one,if you find it, the rest will be  very easy and straight forward job.