# 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?

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.

how will you weight 2, 5,6,7,8??

according to me ans should be 7……1,2,4,8,16,32 and 64

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!!

How to weigh 15,16.. ?

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

Great! How did you formulate this?

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

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)

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.

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