Minimum Number of Weigths

A wholesale merchant came to me one day and posed this problem. Every day in his business he has to weigh amounts from one pound to one hundred and twenty-one pounds, to the nearest pound. To do this, what is the minimum number of weights he needs and how heavy should each weight be?

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JamesBond Pundit Asked on 26th July 2015 in Microsoft Interview Puzzles.
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    The minimum number of weights required is five and these should weight 1, 3, 9, 27 and 81
    pounds.

    [MODIFICATION]
    Explanation As per “BhaiBhai” comment-

    For 2 Kg –
    On one pan put 3 kg and on the other one put 1 kg

    Likewise for 5 kg – 
    9 kg on one pan and 1+3 kg on another pan

    For 6 kg – 9 on one and 3 on another
    for 7 kg   –  1 and 9 on one and 3 on another
    for 8 kg   – 9 on one pan and 1 on another.

    John123 Expert Answered on 26th July 2015.

    how will you weight 2, 5,6,7,8??
    according to me ans should be 7……1,2,4,8,16,32 and 64

    on 4th September 2015.

    Hey Friend,
    For 2 Kg on one pan put 3 kg and on the other one put 1 kg
    Likewise for 5 kg , 9 kg on one pan and 1+3 kg on another pan
    for 6 kg,9 on one and 3 on another
    for 7 kg, 1 and 9 on one and 3 on another
    for 8 kg , 9 on one pan and 1 on another.
    Think before you comment!!

    on 5th September 2015.

    How to weigh 15,16.. ?

    on 16th September 2015.

    For 15 kg – Put 27 kg on one and 9 kg +1 kg on other
    For 16 kg – Put 27 kg on one and 9 kg   on other

    on 16th October 2015.

    Great! How did you formulate this?

    on 21st January 2016.

    I am unable to get the exact answer.Can any one tell  me the way of doing it??

    on 16th March 2016.

    it is something like
    for 121= it lies between 3^1-3^4 so we consider 1,3^1,3^2,3^3,3^4.
    similarly for 250 we will consider numbers from 3^1-3-5 i.e(1,3,9,27,81,243)

    on 14th June 2016.

    question says ‘to the nearest pound’, so shouldn’t  we have 0.5 pound weight too? that way if something weighs 2.25 pound we will be able to measure it as 2 pounds. otherwise it will be heavier than 2 and lighter than 3 pounds and we wont be able to tell the nearest pound.

    on 27th October 2016.
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