Distinct sum subsets

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.

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