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  1. #1
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    Post Puzzle #469 - The Fake Diamonds - Take Two

    Puzzle #469 - The Fake Diamonds - Take Two



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  2. #2
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    Post Puzzle #469 - The Fake Diamonds - Take Two

    Let the 6 diamonds be (Ba, Bb), (Pa, Pb) and (Wa, Wb) for blue, pink & white respectively. Specifically each set will have one real and other as fake. We can separate the fakes from real in a maximum of 2 weighing.

    WEIGHING 01 - Weigh Wa+Pa vs. Wb+Ba. This will give rise to either of the following cases:

    Case 01 - Balanced Scale, which means each side contains one fake diamond since we already know either of Wa or Wb is fake. Hence either of Pa or Ba is fake too. So now do the 2nd weighing.
    WEIGHING 02 - Weigh Pa vs Pb. Whichever is heavier is the real stone. If Pa is heavier, than Pa is real and from above weighing Wa is fake --> Wb is real --> Ba is fake --> Bb is real. Hence the sets for real & fake are (Pa, Wb, Bb) & (Pb, Wa, Ba) respectively. Similar can be done is Pb is heavier, and then the sets for real and fake are (Pb, Wa, Ba) & (Pa, Wb, Bb) respectively.


    Case 02 - The two sides are not balanced. Whichever side is heavier, we can definitely say that the White diamond on that side is the real one, and the one on the other side is fake. If side containing Wb is heavier, then Wb is real --> Wa is fake or vice versa. Now do the 2nd weighing as follows (analysis done using Wb heavier than Wa):
    WEIGHING 02 - Weigh Ba vs, Pb. Three cases will arise:
    Case A - Balanced Scales, which means Ba and Pa are of different weights. This means that Ba is real --> Pb is real and others are fake.
    Case B - Ba is heavier than Pb --> Ba is real --> Bb is fake --> Pb is fake --> Pa is real.
    Case C - Ba is lighter than Pb --> Pb & Bb are real --> Pa & Ba are fake.

    Hence we know fake vs real in all the possible cases.

  3. #3
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    Post Puzzle #469 - The Fake Diamonds - Take Two

    First weighing
    *weigh 1 of each color on one side and rest 3 in other pan....
    *Case1 - first pan has all real and second one all fake ----> simple case we got the solution
    *Case 2 - One pan has 2 fake 1 real and other one has 1 fake and 2 real....
    *there is no other case

    **Second weighing -- pick the diamonds from lighter pan
    ** weigh any 2 diamonds - if equal then both are fake and pick the diamond from the second pan ( of first weighing )which has color other than the fake ones identified.
    **if unequal then pick the lighter one and the one not weighed and pick the diamond from the second pan ( of first weighing )which has color other than the fake ones identified.

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