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Monkey and beans riddle for kids

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There is a bean bag containing 99 white beans and 100 black beans. A monkey will take two beans from the bag. If they are the same he throws the two beans away while if they are different color he puts the beans back.

What color will the last bean be?

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SherlockHolmes Expert Asked on 5th July 2017 in Easy puzzles.
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    • 1 Answer(s)

    Last bean left will be WHITE.

    This is because the monkey always picks two beans at a time and either throws OR keeps both. So, with every pick-up, either two whites OR two backs will be removed (unless the pick is a black-white pair, which is as good as no pick, because they are put back). So, the only possibility of remaining till the end is only if the number is odd, which is white.

    e.g. Assume that there are only 10 black and 9 white beans.

    P1: Black + White => No result
    P2: Black + Black => Remaining Blacks = 8
    P3: White + White => Remaining Whites = 8

    (Note: P2 & P3 may be in reverse order also, makes no difference)

    Now, if P2 and P3 are repeated (in any order) four times, the entire set of blacks will be exhausted, whereas one white will remain. (Even if P3 was repeated 4 times in succession, one white will remain which will never be thrown out because it has is no pair to be thrown out with.

     

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    Viji_Pinarayi Expert Answered on 1st August 2017.
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