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Apple juice and bottle distribution math puzzle

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You are distributing apple juice. There are 21 bottles in total out of which 7 are full, 7 half empty and 7 empty. The juices has to be distributed among three people.

How will you distribute so that each person gets equal number of bottles and the same quantity of juice?

apple_juice puzzle

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SherlockHolmes Expert Asked on 28th March 2016 in Math Puzzles.
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    • 2 Answer(s)

    Assuming that all bottles are of equal capacity AND that we have adequate means to measure exactly half bottle:

     

    7 full bottles are equivalent to 14 half bottles. Thus, we have  total 21 half-bottles of juice. Hence, an equal distribution among 3 people requires each person getting 7 half-bottles of juice.  From the 7 full bottles. transfer half the quantity to each empty bottle, thereby leaving the 7 earlier-full bottles half-full and 7 earlier-empty ones also half-full, plus 7 which are already half-full. Give each set of 7 to each person. Distribution completed.

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    Viji_Pinarayi Expert Answered on 28th March 2016.
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    Without pouring out juice from the bottles, each can given 3 and half bottles of juice and a total of 7 bottles
    F – full bottle
    H – half bottle
    E – empty bottle

    A – FFF EEE H ( 7 bottles)
    B – FF EE HHH (7 bottles)
    C – FF EE HHH (7 bottles)

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    SreeRoopa Sankararaman Genius Answered on 29th March 2016.
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