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Prisoner Question

June 15, 2008

“Our expedition on Planet X had enraged the aliens residing there. The planet authority imprisoned 21 of us in a laser cabin, there’s no means of escaping.

A few days later the king sent his messenger:

“In order to prevent intergalactic conflict, our ruler decided to show some mercy to the earthlings. Tomorrow you shall line in a row, and each of you will be given either a red, blue or green hat. The distribution of color can be of any proportion.(That is, I can give you all red/all blue hat if I want. I can also use some random sequences.)”

“However, you will only know the color of the hat of everyone in front of you. Our king shall begin asking from the last person in the row. Only those who are certain of the color of their own hat will be granted freedom. (We have psychic sensor, don’t try to guess) And of course, all execution/release will be performed secretly.”

“In addition, you are only allowed to reply either red, blue, or green, in a monotonous tone.”

We were given a night to discuss among ourselves. Obviously there’s no way everyone can be freed.

The last person would die for certain. But what is the least amount of people who need to be sacrificed in order to free everyone else?

Blogger’s hint: The last person is the key. Red, blue and green will represent a unique meaning. By the way, to save 50% of them is easy—everyone will have to say the color of the person in front of them. But to save more than that? Or, even better, just sacrifice one person?

If this question is too hard for you, you may edit the question such as there’s only 2 possible hat color. (And only 2 possible reply, of course.)

5 Comments leave one →
  1. June 16, 2008 1:36 am

    sorry, I’m able to online just now, sent me your articel.

  2. Wencin permalink
    June 17, 2008 10:16 pm

    Hi, fust read your article about the hats riddle. Interesting one…I think I’ve got a strategy that can save at least 20 of them.

  3. June 18, 2008 10:20 pm

    To Wencin: lol There is a way to save all of them except one. By the way, what is your stratergy?

    I will post the solution this weekend. Stay tune. πŸ™‚

    To Ng Xin Zhao:
    πŸ™‚ Sure, I will send the notes this weekend. Is that ok for you?

  4. Yong Kai permalink
    July 2, 2008 3:43 pm

    hey, I would like to ask if the King mentions the numbers of the colors? Must it be 2 blue, 2 green, and 1 red? Can it be 3 Blue but 1 red and i Green

  5. July 3, 2008 8:12 pm

    The color can be of any proportion. That means, if he wants, all the hats can be all of the same color.

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