# Distinct Sum

How many distinct values are there in the following list of 15 numbers:

$\begin{array}{cccc} 1, & 2, & 3, & 4, \\ 1+2, &1+3, & 1+4, & 2+3, \\ 2+4, &3+4, &1+2+3,& 1+2+4, \\ 1+3+4, & 2+3+4, & 1+2+3+4? & \\ \end{array}$

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