# Problem 106: Special subset sums: meta-testing
Let S(A) represent the sum of elements in set A of size n. We shall call
it a special sum set if for any two non-empty disjoint subsets, B and C,
the following properties are true: S(B) ≠ S(C); that is, sums of subsets
cannot be equal. If B contains more elements than C then S(B) > S(C).
For this problem we shall assume that a given set contains n strictly
increasing elements and it already satisfies the second rule.
Surprisingly, out of the 25 possible subset pairs that can be obtained
from a set for which n = 4, only 1 of these pairs need to be tested for
equality (first rule). Similarly, when n = 7, only 70 out of the 966
subset pairs need to be tested. For n = 12, how many of the 261625
subset pairs that can be obtained need to be tested for equality? NOTE:
This problem is related to Problem 103 and Problem 105.