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12 rubies weighing problem/riddle

  1. Feb 8, 2012 #1
    i searched for this one if it is posted before, apparently not, but if it is, sorry for that.

    a merchant has 12 identical rubies with equal masses that he wants to put on display, however, he knows that one of these rubies is special in the sense that its either heavier or lighter than the rest. he wants to know which one of them is the special one AND if it is heavier or lighter. however, he has a balance scale that he can use only 3 times. how would he identify the special ruby and know if its heavier or lighter.

    the scale can only tell which side is heavier, the merchant cant measure the angle at which its sloped.
    the rubies are of identical shapes, but they can be labeled.
    the merchant doesnt have any other tools but the balance scale.
  2. jcsd
  3. Feb 13, 2012 #2
    Fun stuff, this is.

    Merchant weighs six rubies against six rubies. (2 weigh-ins remaining)
    He takes the heavier six and divides them, three against three. He weighs these against each other. (1 weigh-in remaining)
    The heavier three are split again. This time just one to one. (no weigh-ins remaining)
    If the balance is not equal, the heavier one is obvious. If the balance is equal, then, by elimination, the last, unweighted ruby is the heaviest.

    However, this only works if you know that the odd ruby is also the heaviest. I was just thinking about it and if, in the previous step, the balance is not equal and you don't know if the ruby is supposed to be heavier or lighter then you can't determine which the odd ruby is. I'd be very interested in hearing the solution if this is the case.
    Last edited: Feb 13, 2012
  4. Feb 13, 2012 #3

    first move: 1234 x 5678

    If 1234 lighter:

    Second move 125 x 369

    if 125 lighter

    Third move 1 x 2

    If 1 lighter: solution 1 lighter

    If 1 heavier: solution 2 lighter

    if equal: solution 6 heavier.

    Second move: if 125 heavier
    Third move: 5 x 12
    5 heavier
    equal 3 lighter

    Second move: if 125 equal
    Third move:7 * 8

    If 7 heavier : 7
    if 8 heavier : 8
    if equal: 4 lighter

    First move if 1234 heavier, same sequence but heavy light reversed.

    First move if 1234 equal;
    second move 9-10 x 11 - 1

    9-10 heavier (lighter)

    9 x 10

    9 heavier (lighter)
    10 heavier (lighter)
    equal: 11 lighter (heavier)

    Second move 9-10 equal

    Third move 12 x 1
    12 lighter of heavier
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