How to choose a set of numbers such that sum of any combination of numbers in that set yields a unique result? I don't remember whether it was VLC or Utorrent exactly but there was a settings page wherein you could choose:
Option A (3)
Option B (5)
Option C (7)
The way you would choose these options was by adding the corresponding numbers and typing it down. If you type 12 for example, it would know you have chosen B and C. Similarly 15 implies all three options.
I tried to make my own version of this by taking first 6 primes
A = 3
B = 5
C = 7
D = 11
E = 13
F = 15
But there was a discrepancy when the result was 18. It could either mean C + D or it could mean B + E.
How to choose a set of numbers such that sum of any combination of numbers in that set yields a unique result?

The usual way to do this is to use powers of two. Then each summand corresponds to a set bit in the binary representation of the sum, so you can readily and uniquely reconstruct which summands were used from that binary representation.
