Distinct sum subsets

Probability Level 3

Consider the set $\{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$ . For each subset, calculate the sum of the elements in the subset. How many distinct sums can we get?

Details and assumptions

The empty subset $\{ \}$ is a valid subset.

The empty sum (sum of no elements) is 0.