Best answer:
The sum of the smallest and largest is -1. If the sum of the total set is 1, then we need to add 2 to it using numbers between -5 and 4.
So we can start with:
-6, 2, 5
And then make a new one where we add one and have -1 as a number:
-6, -1, 3, 5
and then keep expanding:
-6, -2, 4, 5
We can't expand this anymore, but can...
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Best answer:
The sum of the smallest and largest is -1. If the sum of the total set is 1, then we need to add 2 to it using numbers between -5 and 4.
So we can start with:
-6, 2, 5
And then make a new one where we add one and have -1 as a number:
-6, -1, 3, 5
and then keep expanding:
-6, -2, 4, 5
We can't expand this anymore, but can break up the 4:
-6, -2, 1, 3, 5
or we can expand the -2 from the previous:
-6, -3, 1, 4, 5
-6, -4, 2, 4, 5
So, for now, I have 6 answers.
For each one, you can add a 0 to it to make a new set that doesn't change the sum so now we have 12 answers.
There may be others that I missed, but this is really an exercise in brute force vs. mathematics so you can continue to work to see if there are others.