KCC's Quizzes AQQ292 about weighing using 2-plates scale

I hope that the weights can also be placed on a dish with a weighed object.
The weights must have an odd value, so their sum can reach both odd and even numbers. The first two are definitely 1g and 3g. The first higher value above their sum is 5g, so this can be achieved by the combination 9g-3g-1g. And again the first highest unattainable for these 3 weights is the value 1g+3g+9g+1g = 14g, so the next weight value is these 14g and the sum of everything = 27g.

The question is whether we can create all the combinations now. I don't have to examine even numbers and the same goes for the exact weight values.

• 5g +3g+1g= 9g
• 7g +3g = 9g+1g
• 11g +1g = 9g+3g
• 13g = 9g+3g+1g
• 15g +3g+9g = 27g
• 17g +1g+9g = 27g
• 19g +9g = 27g+1g
• .
• .
• 39g = 27g+9g+3g
  
  All combinations are available. Thus we need 4 counterweights: 1g, 3g, 9g, 27g

I hope that the weights can also be placed on a dish with a weighed object.
The weights must have an odd value, so their sum can reach both odd and even numbers. The first two are definitely 1g and 3g. The first higher value above their sum is 5g, so this can be achieved by the combination 9g-3g-1g. And again the first highest unattainable for these 3 weights is the value 1g+3g+9g+1g = 14g, so the next weight value is these 14g and the sum of everything = 27g.

The question is whether we can create all the combinations now. I don't have to examine even numbers and the same goes for the exact weight values.

• 5g +3g+1g= 9g
• 7g +3g = 9g+1g
• 11g +1g = 9g+3g
• 13g = 9g+3g+1g
• 15g +3g+9g = 27g
• 17g +1g+9g = 27g
• 19g +9g = 27g+1g
• .
• .
• 39g = 27g+9g+3g
  
  All combinations are available. Thus we need 4 counterweights: 1g, 3g, 9g, 27g

YES, the minimum set is with 4 elements 1, 3, 9 and 27. Congratulations! But why you said even weights cannot be determined? Look, for example X=20 can be obtained by putting X + 9 + 1 in one plate and 3 + 27 in the other plate !

I wrote it unclearly sorry. Even number need not to be evaluated, the difference is always 1g (either put in on the dish or remove 1g away). 

Ah, understood! Thanks viktor_vojta !