"I know something you don't know."
"Oh. What is that?"
"I'm not left handed either!"
Love this fight!
Moving my reply here to avoid derailing the Avatar vs. debate.
Yeah, it says something that 35 years after it was made memes from this movie are
still going strong, whether "I am not left-handed" or "My name is Inigo Montoya, you killed my father, prepare to die."
I wish more movies today would have fights like this one instead of the frenetic mass of CG we get anymore. Then again, even when it was made, this was THE definitive swordfight and its contemporaries couldn't compete either. I expect that in another 35 years this fight is
still going to be legendary. The hand-changing is also a
very good piece of cinematography, it's typical to draw out such a fight by having one person have an advantage, then the other, and so forth to draw things out. The hand-changes are an
excellent way to do so without it seeming forced or unnatural.
The book actually has a bit more context, Inigo goes into more detail about his father, and the reason his father refused the six-fingered man wasn't about money. It was because his father considered the custom sword a piece of True Art, and the six-fingered man disrespected it. Inigo's father considered himself a craftsman and spent his entire life trying to go beyond mere Craft to Art, and the sword was what he considered the masterpiece that took him from Blacksmith to True Artist. Then the six-fingered man said "Well, I guess it's okay" and only offered a pittance for it which enraged the father. Wesley is contrasted to him in that he immediately recognizes that the sword is amazingly well-made and a piece of True Art.
Additionally in the book, showing his skills as a tracker Prince Humperdink recreates the duel by analyzing the footprints. However he's stymied when they change hands, he can see that their poses switch from left-handed to right-handed but he doesn't see any blood that would indicate an injury to an arm that would make them switch, and can't comprehend that a person would choose to deliberately handicap themselves in a fight. It's a very subtly, very nice foreshadowing of the kind of man Humperdink is and that he doesn't appreciate anything that doesn't give himself maximum immediate advantage.
Fun fact: The supposed fencing schools Inigo and Wesley claim to have studied as they duel are actually notable chess grandmasters.