3 Prisoners

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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 either 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.
In the REASON column, argue for or against each arrangement.

How many ways did you list?
Is it possible the warden marked all with a green X?
The warden knows that each of the prisoners is equally smart, or otherwise.
So what is the warden actually testing?
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.
If your monitor is too bright, you will not see the color they see.
For this problem you receive 5 points if you can eliminate all but one arrangement.

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

—Sherlock Holmes

Comments:

From wHolt - 1/3/09 9:14 AM

Thanks to all who solved this one,
but let's give others a chance also

From wHolt - 10/5/08 9:48 AM

The object of this puzzle is to eliminate all but one set of markings.

First count how many ways the warden could mark the prisoners' foreheads.

LIST ALL these ways in your table !!!

Then eliminate all but one of the ways.

Remember: they all raise their hand because they all see at least one red X.
At least means, maybe 1, or more.

From Ashley Walker [198.146.87.128] - 9/16/08 11:24 AM

A	B	C	Reason
R	R	G	One person sees at least one red X which means the person who see the red X could be red.
G	G	R	The person who see the red X could also be green.
R	R	G	The other two prisoners raise their hands which means the first person is a red X.

From Marian A. Grice [76.22.201.34] - 9/14/08 2:01 PM

1	2	3	Reason
R	R	G	Cause all of them see a red x
G	R	R	Cause all of them see a red x
R	G	R	Cause all of them see a red x

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Last Modified 12/10/08 5:40 PM