A good math question?

Question

I think I have the answer but just to check need help?
The question is:
If a person had a 40 lbs counter weight for an old style weighing balance, and they accidentally dropped it and the weight broke in to 4 pieces. This was better because it allowed the person now to weight anything from 1 to 40 lbs weight. What were the weights of the four pieces?

Answer 1

The answer is 1, 3, 9 and 27.
The trick is to place balancing weight in both sides.

How to get answer in general...
Start with 1, you need it.
Now x-1, x, x+1 should be next numbers. So
x-1 = 2 or x=3 or x+1 =4.
=> x=3 consistent.

So you get 1 and 3. Now
x-4,x-3,x-2,x-1, x, x+1, x+2, x+3, x+4
Must be next numbers.
So x-4=5, x-3=6, x-2=7,x-1=8, etc...
Everything giving x=9

So you have 1,3, and 9. Giving all the way upto 13.
Let us speed up our calculations. Take only the first one
ie
14 = x-13
=> x= 27
Gives upto 40.

So we are done.

If you want the next number in series..
x-40 = 41 i.e. x=41+40 = 81
Giving upto 81+40 = 121

So if we break 121 lbs weight you should get 1,3,9,27,81

It goes on....

Answer 2

40 pieces

Answer 3

1, 3, 9, and 27.