Posers and Puzzles

Posers and Puzzles

  1. Joined
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    10 Apr '05 06:47
    Suppose a lunatic king is bored and wants to play a game with the 1000 peasants he lords over. He gets all the peasants together and tells them the following rules of the game:

    1. All 1000 of the peasants will be lined up into a single row.
    2. The king will then place either a red or blue hat onto each peasant's head in a random fashion (according to the king's whim).
    3. Each peasant will not be able to see the color of their hat or the hats behind them, but will be able to see the hats in front of them. Additionally, the peasants will be able to hear words spoken in front or behind them.
    4. Starting with the peasant in the back of the row, the king will ask each peasant in turn "What is the color of your hat?" The peasant must then answer either "blue" or "red" and nothing more. If the peasant answers incorrectly, he will be killed without a sound. If he answers correctly, his life will be spared, but he must remain silent for the rest of the game. The king will then proceed up the row, asking each peasant the same question.
    5. Before the game begins, the peasants will be allowed to confer with each other.

    If the peasants are smart, how many peasants will survive the game for certain?
  2. Standard memberAlcra
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    10 Apr '05 07:05
    Originally posted by davegage
    Suppose a lunatic king is bored and wants to play a game with the 1000 peasants he lords over. He gets all the peasants together and tells them the following rules of the game:

    1. All 1000 of the peasants will be lined up into a single row.
    2. The king will then place either a red or blue hat onto each peasant's head in a random fashion (according to ...[text shortened]... h each other.

    If the peasants are smart, how many peasants will survive the game for certain?
    999

    Each peasent when asked will say his hat is the colour of the next person's hat. That way, only the first peasent will take a chance, the rest will KNOW their hat colour.

  3. SubscriberAThousandYoung
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    10 Apr '05 07:091 edit
    Originally posted by davegage
    Suppose a lunatic king is bored and wants to play a game with the 1000 peasants he lords over. He gets all the peasants together and tells them the following rules of the game:

    1. All 1000 of the peasants will be lined up into a single ...[text shortened]... ts are smart, how many peasants will survive the game for certain?
    I guess 500 would survive for certain?

    The first peasant will see 999 peasants. Let's assume he counts up everyone's hats. Whichever color is more prevalent, the peasant will say that color (or he could say the other color - as long as all the peasants know which he is going to do).

    Now all the rest of the peasants will say the more prevalent color, and at least 500 of the 999 will survive.
  4. SubscriberAThousandYoung
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    10 Apr '05 07:101 edit
    Originally posted by Alcra
    999

    Each peasent when asked will say his hat is the colour of the next person's hat. That way, only the first peasent will take a chance, the rest will KNOW their hat colour.

    Suppose the first peasant says 'blue'. You are the second peasant, and you see the third one has a red hat. Are you going to say 'red' and die so the next guy knows what kind of hat he has?

    Your strategy doesn't work.
  5. Joined
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    10 Apr '05 07:25
    Originally posted by Alcra
    999

    Each peasent when asked will say his hat is the colour of the next person's hat. That way, only the first peasent will take a chance, the rest will KNOW their hat colour.

    As a thousandandyoung pointed out, this strategy won't work.
  6. Joined
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    10 Apr '05 07:26
    Originally posted by AThousandYoung
    I guess 500 would survive for certain?

    The first peasant will see 999 peasants. Let's assume he counts up everyone's hats. Whichever color is more prevalent, the peasant will say that color (or he could say the other color - as long as all the peasants know which he is going to do).

    Now all the rest of the peasants will say the more prevalent color, and at least 500 of the 999 will survive.
    this strategy will save 500 for certain, but the peasants can do better than that.
  7. Standard membertheangrystudent
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    10 Apr '05 07:32
    Originally posted by davegage
    Suppose a lunatic king is bored and wants to play a game with the 1000 peasants he lords over. He gets all the peasants together and tells them the following rules of the game:

    1. All 1000 of the peasants will be lined up into a single row.
    2. The king will then place either a red or blue hat onto each peasant's head in a random fashion (according to ...[text shortened]... h each other.

    If the peasants are smart, how many peasants will survive the game for certain?
    I say at least 999 should be able to live through the experience.

    A simple but effecitve strategy would be for the person stating the color of their hat to yell their response if it is the same color as the hat next in line, and to speak normally if the color they are saying is the opposite of the color of the hat in front of them.

    Hence the person in front of the one being asked would know the color of their hat before the the king asks them the question.

    So all but the first person would get a free pass.
  8. Joined
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    10 Apr '05 07:39
    Originally posted by theangrystudent
    I say at least 999 should be able to live through the experience.

    A simple but effecitve strategy would be for the person stating the color of their hat to yell their response if it is the same color as the hat next in line, and to speak normally if the color they are saying is the opposite of the color of the hat in front of them.

    Hence the ...[text shortened]... efore the the king asks them the question.

    So all but the first person would get a free pass.
    yes -- very good.

    so i guess it would take a bare minimum of 1000 games for the king to kill off all the peasants using this strategy...
  9. Standard memberflexmore
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    10 Apr '05 07:41
    Originally posted by davegage
    Suppose a lunatic king is bored and wants to play a game with the 1000 peasants he lords over. He gets all the peasants together and tells them the following rules of the game:

    1. All 1000 of the peasants will be lined up into a single row.
    2. The king will then place either a red or blue hat onto each peasant's head in a random fashion (according to ...[text shortened]... h each other.

    If the peasants are smart, how many peasants will survive the game for certain?
    1000 peasants wil survive - but that king will not.
  10. Joined
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    10 Apr '05 10:11
    999 will live. the first one can look ahead and tell everyone the color of their hats, or he can tell the guy in front of him, then he can tell the guy in front of him and so on.
  11. Standard memberTheMaster37
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    10 Apr '05 11:28
    The peasant are allowed to confer before the King starts? Every peasant asks what color his hat is to another peasant. This way He KNOWS his own hat color. All 1000 live.

    If that's not allowed then it's all based on luck since the peasant cannot know the total amount of red/blue hat, thus cannot reason their way to the solution.
  12. Standard memberBowmann
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    10 Apr '05 17:05
    Does the King wear a hat?
  13. Standard membertheangrystudent
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    10 Apr '05 18:11
    Originally posted by TheMaster37
    The peasant are allowed to confer before the King starts? Every peasant asks what color his hat is to another peasant. This way He KNOWS his own hat color. All 1000 live.

    If that's not allowed then it's all based on luck since the peasant cannot know the total amount of red/blue hat, thus cannot reason their way to the solution.
    You need to understand the question a little better.

    The king first explains the game to the peasants. The peasants then have a little time to come up with some sort of strategy on how they are going to play the game. After that the king lines up the peasants in a strait line by placing one peasent in front of the one he just placed. The king then goes to the back of the line and begins placing colored hats on all the people. Then the king goes once more to the back of the line and askes the person what color his hat is.

    For a simple solution to the problem, look for my post above.
  14. Standard memberskeeter
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    10 Apr '05 18:32
    All birds will survive. After the hats are placed the pheasants pair off in the line so that in each pair both pheasants are facing each other. They then ask each other the colour of their hat.

    OR the last bird in the line who can see all the other birds hats runs down the line touching the birds in turn and calling the hat colour. When he gets to the front the bird behind him calls out his colour.

    skeeter
  15. Standard memberBowmann
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    10 Apr '05 19:321 edit
    Originally posted by skeeter
    All birds will survive. After the hats are placed the pheasants pair off in the line so that in each pair both pheasants are facing each other. They then ask each other the colour of their hat.

    [b]OR
    the last bird in the line who ca ...[text shortened]... to the front the bird behind him calls out his colour.

    skeeter[/b]
    I'm not a pheasant plucker, I'm a pheasant plucker's son
    I'm only plucking pheasants 'till the pheasant plucker comes.

    Me husband is a keeper, he's a very busy man
    I try to understand him and I help him all I can,
    But sometimes in an evening I feel a trifle dim
    All alone, I'm plucking pheasants, when I'd rather pluck with him.

    I'm not a pheasant plucker, I'm a pheasant plucker's mate
    I'm only plucking pheasants 'cos the pheasant plucker's late!

    I'm not good at plucking pheasants, at pheasant plucking I get stuck
    Though some pheasants find it pleasant I'd rather pluck a duck.
    Oh plucking geese is gorgeous, I can pluck a goose with ease
    But pheasant plucking's torture because they haven't any grease.

    I'm not a pheasant plucker, he has gone out on the tiles
    He only plucked one pheasant and I'm sitting here with piles!

    You have to pluck them fresh, if it’s fresh they’re not unpleasant,
    I knew a man in Dunstable who could pluck a frozen pheasant.
    They say the village constable had pheasant plucking sessions
    With the vicar on a Sunday ‘tween the first and second lessons.

    I'm not a pheasant plucker, I'm a pheasant plucker's mum
    I'm only plucking pheasants 'till the pheasant plucker's come.

    My good friend Godfrey is most adept, he's really got the knack
    He likes to have a pheasant plucked before he hits the sack.
    I like to give a helping hand, I gather up the feathers,
    It's really all our pheasant plucking keeps us pair together.

    I'm not a pheasant plucker, I'm a pheasant plucker's friend
    I'm only plucking pheasants as a means unto an end!

    My husband's in the forest always banging with his gun
    If he could hear me half the time I'm sure that he would run,
    For there's fluff in all my crannies, there's feathers up my nose
    And I'm itching in the kitchen from my head down to my toes.

    I'm not a pheasant plucker, I'm a pheasant plucker's wife
    And when we pluck together it's a pheasant plucking life!

    (For skeet)
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