Yellow,Green,Red,Blue

[wolfgang]

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?

[phaze]

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 January 24, 2013 by phaze

[phaze]

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]

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

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.

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.