TADM2E 3.12

Let's put into the black box whole set $ S=\{x_i\}_{i=1}^n $. If $ bb(S) $ is True, then such a subset exists and we can go on:

1. R:=S
2. for i:=1 to n do
   1. If $ bb(R/\{x_i\}) $ is True then $ R:=R/\{x_i\} $

When this iteration is finished R will be subset of S that adds up to k.

Above solution works even when there are multiple subsets that add up to k.