Question

Write 11 numbers in a row so that the sum of any 3 consecutive numbers is negative, while the sum of all the numbers is positive. Is it possible?

Answer 1

Answer: No, it is not possible.

Explanation:

Let the 11 numbers be {a1, a2, ..., a11} such that a1 is the smallest and a11 is the largest. So, a1 < a2 < ... < a11. Furthermore, these numbers are consecutive.

If we add consecutive numbers to get a negative result, then each of the numbers must be negative. So every value in the set {a1, a2, ..., a11} is a negative value which makes it impossible to have a1+a2+...a11 be a positive sum.