57 replies to this topic

[bonanova]

 

I'm taking a slightly stricter view, that NEWS coding is not available.
Wolfgang has allowed that prisoners can either face toward or away from the door.
That is, NS (or EW, as I drew it) coding is available, and that requires two prisoners to signal a color.

That presents a particular problem for P2 on initial entry, but I think it can be worked around.

 

If only a binary signaling scheme is allowed, CaptainEd has shown that only prisoner 1 needs to change his mind. Even in the stricter NS view, there are some latitude to define a quadnary signaling scheme due to an implied necessary condition

Spoiler for because

the entering prisoners *must* be able to see the signaler rotate before taking their position. Otherwise, the last prisoner has no way to receive information about his hat color, and the puzzle is not solvable. Therefore, rotation *within sight* of entering prisoners is a necessary condition of the puzzle.

Since the entering prisoners are able to see rotation, it is then trivial to combine rotation speed, direction, and amount with NS coding to allow quadnary signals. (Again, I don't see anything in the OP prohibiting this; well, except for the 'no communication of any kind allowed', but we all know how that went). Once quadnary signals are allowed, no one needs to change position.

  You're right.NS signaling is enough.Four easily distinguishable rotations: None, 180^ocw, 180^occw,  and 360^occw.And entering prisoners must be able to see the rotation. I think we spent most of the time on this puzzle with a poor understanding of the conditions.But it was fun to finally solve something possible.It's just that the problem became teasing out the constraints that admitted a solution!Bertrand was helpful in this case.  Thanks, Wolfgang.

I want to thank you all....I was thinking like this:After the first three prisoners took their right places,they all should be facing the door, the possible combinations would be:Yellow,Green,Red,........Yellow,Green,........,BlueYellow,.........,Red, Blue.........,Green, Red, Blueso when the 4th one enters, Let him to have  X color..the X one standing in the raw will turn his face to the wall,and the new comer will stand in that raw facing the door....and when nobody turns to the wall so he should stand at the empty place facing the door.when the four raws are made, each new comer will  know where he belongs  when the man with the same color turns his face toward the wall.

The first three may not all be different.
What if all the prisoners are say red, except for the last three to make all the colors used?

Edit: ok, that's not a problem I guess, it just delays the row formation.

[phaze]

Spoiler for

Assumptions

 * that there is a set areas for each line

 * rotating or NSEW is not an option

 * prisoners can wait till the room is full with their comrades before picking a place

Each prisoner counts up the number of all colours they can see apart from that on Prisoner 1 and 2


Prisoner 1 takes note of Prisoner 2's tag

stands in Prisoner 2's row if Yellow and Green tags are both even

stands in the next row if Yellow tags are odd and Green tags are even

stands in the next row if Yellow tags are even and Green tags are odd

stands in the next row if Yellow and Green tags are both odd


Prisoner 2 now knows which row he should be in and anyone apart from 1 & 2 knows if they have a Yellow or Green hat

(it will not be odd or even as indicated by the position of P1 and the colour of P2s tag)
 


Prisoner 2 takes note of Prisoner 1's tag

stands in Prisoner 1's row if Red and Blue tags are both even

stands in the next row if Red tags are odd and Blue tags are even

stands in the next row if Red tags are even and Blue tags are odd

stands in the next row if Red and Blue tags are both odd


Prisoner 1 now knows which row he is in and anyone apart from 1 & 2 knows if they have a Red or Blue hat

(it will not be odd or even as indicated by the position of P2 and the colour of P1s tag)


All other Prisoners stand in appropriate rows

1 & 2 shift rows

Edited by phaze, 24 January 2013 - 04:28 AM.

[phaze]

Spoiler for Should even work

This should even work if you stipulate that a blindfold cannot be removed until the previous person has taken their allotted space

(albeit temporary for prisoner 1 and 2)

[bonanova]

There are two constraints from a normal reading of the OP

that, when combined, render the puzzle impossible:

1. No communication.
2. Enter and take position singly.

We've now shown that if either is relaxed the puzzle has a solution.

[Prime]

There are two constraints from a normal reading of the OP

that, when combined, render the puzzle impossible:

1. No communication.
2. Enter and take position singly.

If we drop either, the puzzle has  a solution.

If we drop (1), it's not really a puzzle.

There are more than 14 men on the death row. Which means they are either prisoners of war, or this whole thing takes place in Texas. Either way most of them are innocent in all likelyhood. With such obvious signaling as turning around, they are all doomed. I would choose some more inconspicuous signal, like someone in the formation turning the toe of his left foot inside ever so slightly.

[TimeSpaceLightForce]

Spoiler for too much beer last night

Plan: None

Too scared with the nooks hanging outside, the first prisoner...
shaking in panic ..wet his pants to much as the warden deputy
unblindfolded him..walks and stand anywhere.
Next prisoner, stepped in and notice the pool of liquid below him.
Glanced at his image ..revealed the color on his forehead. Got an
idea, and he too piss his pants on purpose. No objection from the
deputy.."they are just scared to hell", he said. 1st Prisoner notice.
The third one,wonders and look down what the stink he is standing
on..but he learns too....this goes on untill the last prisoner is

in the right lane then the first prisoner change to correct lane.

[CaptainEd]

Prime, I agree--dropping (2), as you and Rainman did, was more interesting. I was excited to see the Rainman solution, and I then admired your transformation so that people could tell where the colors are even without colored chairs.

[TimeSpaceLightForce]

This is a challenge.
A two-color version requires and permits movement after taking one's position.
So I don't think it provides useful guidance for this case

Spoiler for here it is anyway

The first two stand next to each other.
The third and subsequent persons inserts himself between differing colors, if there are any.
This requires movement of previous persons.
if all previous persons have the same colors, he takes an end position.

However, this results in a single line - just with the colors segregated.

In every way, the present puzzle is more demanding.

Great puzzle.
Eager to see the solution.

 

Spoiler for

I would like to see this work if (2) is dropped, this will force everybody
to keep in motion as to walk in circle because stoping assumes the
place. In the end the color row leaders separated one by one to line up
on their respective rows.