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Math Help - Problem: the black and white pebbles

  1. #1
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    Problem: the black and white pebbles

    A man who works as a slave for a wealthy merchant borrows some money from the merchant. The merchant gives him 90 days in which to return the money, after which, the man must give up his only daughter's hand in marriage to the merchant.

    90 days pass. The slave fails to pay the merchant back. The slave's daughter is called. She is very frightened when she hears of what is to happen which makes the merchant rethink. There are many black and white pebbles scattered over the courtyard in which the three of them are standing. The merchant says to the girl that he will pick two pebbles in his hand: one black and one white. The merchant will then ask the girl to choose a pebble. If she chooses a white pebble, she is set free. If she chooses a black pebble, she must marry the merchant. The girl agrees.

    The merchant picks up two pebbles, however, he sneakily picks up two black pebbles and places them into a pouch. The girl's father does not notice but the girl does and immediately sees that no matter which way she chooses, she will have to end up marrying the merchant. She cannot say anything for fear of more trouble.


    However, there is a way out of it. The girl can do something very logical that will end up with her being set free.
    What is it?
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  2. #2
    Senior Member TheAbstractionist's Avatar
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    Quote Originally Posted by blueirony View Post
    A man who works as a slave for a wealthy merchant borrows some money from the merchant. The merchant gives him 90 days in which to return the money, after which, the man must give up his only daughter's hand in marriage to the merchant.

    90 days pass. The slave fails to pay the merchant back. The slave's daughter is called. She is very frightened when she hears of what is to happen which makes the merchant rethink. There are many black and white pebbles scattered over the courtyard in which the three of them are standing. The merchant says to the girl that he will pick two pebbles in his hand: one black and one white. The merchant will then ask the girl to choose a pebble. If she chooses a white pebble, she is set free. If she chooses a black pebble, she must marry the merchant. The girl agrees.

    The merchant picks up two pebbles, however, he sneakily picks up two black pebbles and places them into a pouch. The girl's father does not notice but the girl does and immediately sees that no matter which way she chooses, she will have to end up marrying the merchant. She cannot say anything for fear of more trouble.


    However, there is a way out of it. The girl can do something very logical that will end up with her being set free.
    What is it?
    Hi blueirony.

    Spoiler:
    The girl chooses a random hand, but as the merchant is about open that hand she quickly knocks out the pebble before anybody could see which colour the pebble was. In order to “determine” the colour of that pebble, the merchant must open his other hand; since it’s a black pebble, the girl can claim that the other pebble must be white. The merchant will have to agree, otherwise he would have to confess to his cheating tactic.
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  3. #3
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    TheAbstractionist - you are absolutely correct!
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