smc

Notice that if the consecutive positive integers have a sum of $15$, then their average (which could be a fraction) must be a divisor of $15$. If the number of integers in the list is odd, then the average must be either $1,3,$ or $5$, and $1$ is clearly not possible. The other two possibilities both work: $1+2+3+4+5=15$ $4+5+6=15$ If the number of integers in the list is even, then the average will have a $\frac{1}{2}$. The only possibility is $\frac{15}{2}$, from which we get: * $15=7+8$ Thus, the correct answer is $\boxed{3}.$ Question: (RealityWrites) Is it possible that the answer is $4$, because $0+1+2+3+4+5$ should technically count, right? Answer: (IMGROOT2) It isn't possible because the question asks for positive integers, and this means that negative integers or zero aren't allowed. Note to readers: make sure to always read the problem VERY carefully before attempting; it could mean the difference of making the cutoff.