You are one of 20 prisoners on death row with the execution date set for tomorrow. Your king is a ruthless man who likes to toy with his people's miseries. He comes to your cell today and tells you:
“I’m gonna give you prisoners a chance to go free tomorrow. You will all stand in a row (queue) before the executioner and we will put a hat on your head, either a red or a black one. Of course you will not be able to see the color of your own hat; you will only be able to see the prisoners in front of you with their hats on; you will not be allowed to look back or communicate together in any way (talking, touching.....).
The prisoner in the back will be able to see the 19 prisoners in front of him. The one in front of him will be able to see 18…
Starting with the last person in the row, the one who can see everybody in front of him, he will be asked a simple question: WHAT IS THE COLOR OF YOUR HAT?
He will be only allowed to answer “BLACK” or “RED”. If he says anything else you will ALL be executed immediately.
If he guesses the right color of the hat on his head he is set free, otherwise he is put to death. And we move on to the one in front of him and ask him the same question and so on…
Well, good luck tomorrow, HA HA HA HA HA HA!”
Now since you all can communicate freely during the night, can you find a way to guarantee the freedom of some prisoners tomorrow? How many?
7 comments:
The first guy states the color of the hat on the guy in front of him. The next guy will then know what color his hat is. Since everybody knows the system it will assure that everybody except the first guy will get it right. 19 will be spared. The first guy will have to get lucky to make it 20.
Dad
Right-O, Charley. 19 with a 50/50 chance for the 20th. That's one dumb King.
I thought that at first too, but only every other one would be spared that way. Think about it- if guy #20 tells guy #19 his hat is red, but guy #17 has on a black hat, then what is guy #18 going to say? Red because that is the color of his hat and he will be spared, or black to tell his friend? Only about 15 at most would be able to live this way if every other said the color of the guy in front of him and the other ones said the color they were told. They other half would have to guess at their own and have a 50/50 chance of getting it right.
I realized that when I was explaning the riddle to Gail last night. Opps! Sorry #18.
Dad
Come on Jake. Solve this one for us.
Gail
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