The set (-1, 0, 1, 2, 3, 4, 5) also gives a sum of 14 but has a different number of terms.

Since it does not specify a starting point for the set, we can't assume that the set should start with 1.

Unless the problem statement says that S is a set of consecutive positive integers, one cannot restrict the set to integers greater than 1.

The second issue in this problem is how to make sure that you can spot the other set that Bill pointed out in his post: {-1, 0, 1, 2, 3, 4, 5}. Some of us might be able to see that example, but some of us will need some structure so we can spot it.

If k is the median of a set of consecutive integers(or a uniformly spaced sequence) and n is the number of consecutive integers in the set, then the Sum = Median*Number of Terms, or in this case n*k = 14, if we set n to be 7(factor of 14), then the median k=2, this is a set of 7 consecutive integers with 2 as the median, or -1, 0, 1, 2, 3, 4, 5, placing three numbers on both sides of the median. The original set you proposed: (2, 3, 4, 5} results if n=4, and the median is then 3.5.

Dabral