If three random integers are independently chosen from 1 to n, what is the probability that the first two sum to the third?

Source: Quora

(In reply to

solution: as presented and with a complication by Charlie)

It is pretty obvious that the probability that any one of them is the sum of the other two = 3 * the probability that the 3rd is the sum of the other two. Since at most one of them can be the sum of the other two, the three alternatives are mutually exclusive. I would have just multiplied the first answer by 3, and moved on.