The solution seems to lead to a drawn position - at least the computer only managed to draw against me! This is hardly "gaining the maximum advantage in the shortest number of moves". And 1 g8=Q, which was my try, also seems to lead to a draw. What am I missing?
Yet again, this is a failure of GK to do a proper analysis. I've seen at least a dozen problems that were theoretical draws that they claimed one side or the other had an advantage.