Need help in understanding USACO GOLD Angry Cow's solution

PROBLEM: USACO ANGRY COWS | SOLUTION
In above mentioned problem’s solutions, it is assumed that the blast in optimal case will start from one of the locations provided in the input. Can anyone explain why it is the case, and why blast originating from location other than the ones provided in input will not yield a better result?

This is incorrect; the solutions do not assume this. Though it’s worth nothing that not all of the solutions are correct …

I heard the the solution for Build Gates is also wrong :frowning: