Sandrew’s birthday chocolate distribution puzzle

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Today is Sandrew’s birthday for which he is distributing chocolates. There are 100 chocolates in his chocolate box. The box was passed down along a row of friends.

The first friend took one chocolate. Each friend down the row took more chocolates than the friend before, until the box gets empty.

What is the largest number of friends that could have been in the row?

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13

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on 6th November 2015.

13

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on 13th November 2015.
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  • 3 Answer(s)

    13

    jayeshram7 Curious Answered on 6th November 2015.

    How?

    on 6th November 2015.
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    The longest line of friends that can have chocolate is 13, with the last person taking all the remaining chocolates.
    There are not enough chocolates for a fourteenth person, because they would have to take 14 chocolates (after the previous person had taken 13) and there would be only 9 left.

    SherlockHolmes Expert Answered on 7th November 2015.
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    The next person can take a chocolate by a minimum of one more chocolate to get the max no. of friends in line. This means that sum of 1,2,3,….. should equal 100. Thus n(n+1) div by 2 = 100. On solving, n would lie between 13 and 14.

    So the answer in whole no. will be 13.

    Ayushi Curious Answered on 15th November 2015.
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