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Which coin is fake?

  1. Sep 15, 2008 #1
    You have 10 coins and a balance scale. 1 coin is a fake, but you don't know whether it is lighter or heavier than the rest. You are only allowed to use the scale 3 times. Which coin is fake?

    I don't know the answer to this problem.
  2. jcsd
  3. Sep 15, 2008 #2
    Can you use a graduated cylinder and water? ;-)
  4. Sep 16, 2008 #3


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    Try this:
    90+ %
    --- = balance scale;
    1) 3 coinsA --- 3 coinsB than 2) 3 coinsA or B --- 3 coinsC than you know what group of 3 coins is lighter or heavier 3) spli the group ... 1 coin --- 1 coin and you solve it. But...if all 3 groups (A,B and C) are the same weight, the last coin is the one, but you don´t know if it´s lighter or heavier. :)

    "Some times you don´t have to be exact, you have to be enough."
  5. Sep 16, 2008 #4


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    I´m sorry, that was 100%.
  6. Sep 16, 2008 #5
    If one is lucky, it can be done in 2 trials. 5 v 5, 2 v 2, odd one out.
  7. Sep 16, 2008 #6

    Separate the coins into 3 groups of 3 and a single (A, B, C, and S). Weigh A and B, then B and C (taking note of which is heavier or lighter in both weighings (if both weighings balance, then S is the counterfeit coin). Based on the two weighings you can tell which group of three had the counterfeit coin AND whether it was lighter or heavier than the others. You then weigh two of the three coins in the suspect group (one on each scale). If they balance, then the third coin of the group (not weighed) is the counterfeit. If they do not balance you will know which of the two is counterfeit because you were able to determine whether the counterfeit coin was heavier or lighter from the previous two weighings.
  8. Sep 20, 2008 #7
  9. Sep 20, 2008 #8


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    No, it can't. 5v5 will only tell you that one set is heavier than the other. Since you don't know what the fake coin is, the first weighting tells you nothing.
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