How to weigh any weight from 1 to 40 using four weights whose sum is 40KG?

Question

A merchant has a 40 kg weight which he used in his shop. Once, it fell from his hands and was broken into 4 pieces. But surprisingly, now he can weigh any weight between 1 kg to 40 kg with the combination of these 4 pieces.

So question is, what are weights of those 4 pieces..?

Answer 1

1+3+9+27=40
9-3+1=5
9-3=6
9+1-3=7
9-1=8
9+3-1=11
27-9-3-1=14
etc
etc

Comments

but how do u know the weights are  1, 3 , 9 , 27, ...any logic

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How will you solve the problem

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What is the step for this prob?

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a+b+c+d = 40 (given)
39 = a + b + c + d (Nope...it's above)
or
39 = a + b + c - d = 39 (Nope, then a+b+c >= 40 )
so
39 = a + b + c
Thus:
d = 1