The sum of eleven different integers is zero. What is the least number of these integers that MUST be positive?

Question

I tried this question, but when I added negative numbers, it obviously comes out as a negative number. Please help. Thank you!

Answer 1

The least number that must be positive is one integer.  We can have 10 different integers, all negative, and one positive integer that equals the absolute value of the sum of the other 10.  For example:

 

-2-3-7-9-22-30-31-52-84-101+341=0