Sums of subsets

Probability Level 5

For a set of numbers T,T, we say that TT has distinct subset sums if all distinct subsets of TT have distinct sums. How many subsets of {1,2,3,4,5,6,7,8}\{1,2,3,4,5,6,7,8\} have distinct subset sums?

Details and assumptions

The empty set (the set of no elements) has a sum of 0 by convention.

As an explicit example, the subset {1,2} \{1, 2 \} satisfies the conditions, since it has 22=42^2 = 4 subsets, whose sums are 0, 1, 2, and 3, which are distinct.

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