“You are very near your goal. The quickest way is past me.”
“So…so will you move, please?” said Harry, knowing what the answer was going to be.
“No,” she said, continuing to pace. “Not unless you can answer my riddle. Answer on your first guess - I let you pass. Answer wrongly - I attack. Remain silent - I will let you walk away from me unscathed.”
According to the context, "Answer on your first guess" probably means to manage to get the answer correctly on your first guess. But I'm curious why it hasn't been written as "Answer correctly on your first guess"? How should we understand "Answer on your first guess" here?