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Brain Teaser #10 (Oh God, it's double-Digits!)

Discussion in 'Other Off Topic Forum' started by PeterS, Jul 7, 2004.

  1. PeterS

    PeterS Three Time F1 World Champ
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    Jan 24, 2003
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    PeterS
    You are given 9 coins. One of the coins is bogus. It is just slightly lighter in weight than the other coins. You must find which coin is fake using only a balance scales. The scales can only be used for comparing the weight of coins on one side of the scales with an equal number of coins on the other side of the scales. What is the least number of times you can use the scales and still be sure of finding which coin is fake?
     
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  3. jimpo1

    jimpo1 Two Time F1 World Champ
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    Jul 30, 2001
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    2 times.

    Now that there are other answers, I'll elaborate.

    3 stacks of 3 coins. Weigh 2 of the stacks. If they balance, the light coin is in the 3rd stack, otherwise you'll know which stack contains the light coin by the scales.

    3 single coins. Weigh 2 of them. If they balance, the light coin is not on the scale, otherwise the scale will tell you which coin is lighter.
     
  4. Forza1

    Forza1 Formula Junior

    Mar 20, 2004
    486
    California
    Twice. I'd explain further, but work prevents me at the moment, so you'll have to wait until 1pm-ish :)



    -DC

    P.S. Argh!
     
  5. matterhorn762

    matterhorn762 Formula Junior

    Apr 19, 2004
    331
    Tennessee
    I agree. 2 times.

    Weight 3 versus 3 at first.

    Take whatever group has the odd weight (the unweighed group if it's even on the scales).

    Then scale one versus one.
     
  6. PeterS

    PeterS Three Time F1 World Champ
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    Jan 24, 2003
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    Correct:

    Two times. First put any 3 coins on one side of the scales and any 3 coins on the other side. If the scales balance, the light coin is one of the remaining three. If one side of the scales rises, the light coin is one on that side of the scales. You now know which group of three coins contains the fake. Choose any two coins from that group and place one on each side of the scales. If the scales balance, the light coin is the remaining one. Otherwise it is the coin of the side of the scales that rises.
     
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