Scales and weights

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I started by trying to figure out the number of weights I needed to get to 40 if I didn't have the constraint of 4.  I found that I could use 1, 2, 4 and 8 to get to 15.  And then to move forward in a similar fashion to get to 40, I needed 16 and 24 also.

I also realized in working with the weights that I could be more efficient with the weights if I used both scales (some to add weight and some to provide alternative weight to make new weights).
But how to I get to 40 with only 4 weights?

So I started back at 1.  It looked like there was some number pattern at work - doubling to get 4 weights to reach 15.
So I tried tripling for 40 and tried 1-3-9-27, and this worked.

I was able to find only 1 solution to get to 40 using 4 weights.

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