Question 1101615
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The smallest sum you can get is by adding all the negative numbers in the set: {{{(-4)+(-3)+(-2)+(-1) = -10}}}<br>
The largest sum you can get is by adding all the positive numbers: {{{1+2+3+4 = 10}}}.<br>
It should be easy to see that you can get an integer sum of any of the integers between those minimum and maximum sums.<br>
So the number of different integer sums you can get is the number of integers between -10 and 10, inclusive; that number is 21 (10 negative, 10 positive , and 0).