Now everybody’s got me thinking about just what steps the Prince would have had to follow to track Fezzik, Inigo, and Vizzini to get back Buttercup.
Beginning with the premise that the Prince knew where Buttercup went riding and told Vizzini to wait there doesn’t count — at no point can the Prince make any deduction in front of his guards that comes from the knowledge that he himself sent Vizzini or arranged the whole thing. However, we can grant the Prince the uncanny ability to track people from the tiniest clues — and the discretion to ignore clues if they give away his own complicity.
So — Vizzini captures the Princess, takes her to the boat launch, puts the fabric from the uniform of an army officer of Guilder on the saddle of a horse, and slaps the horse to send it off for later discovery.
The Princess’s horse likely returns to its stable, or heads in the direction of it. If the Prince were playing it safe, that would be the moment he’d allow himself to know Buttercup had been taken. He can’t leap to the conclusion of kidnap too soon.
Humperdinck can either follow Buttercup’s horse’s prints out from the stable, which is the colder trail, or follow the incoming hoofprints back to where the horse came from most recently. He’s allowed to suspect, because of the fabric on the horse, that the kidnappers are taking her in the direction of Guilder. (He could announce suspicions, for the benefit of the guards, that it was only a ruse; but I don’t see what that achieves for him.)
He knows the incoming horse trail is more recent, but not if it’s shorter. He might track them both — Count Rugan suggests they have the ability (“shall we track them both?”).
Assuming they track both, they find where Buttercup was captured by three men on foot: one medium-sized, one short, one very big. The tracks lead to the boat launch, meeting up with the track of the horse.
The Prince could probably see that the horse was startled away, dashing away quickly in response to something, but he’d probably keep that to himself. Knowing the horse was driven away deliberately leads too strongly to the conclusion that the horse was meant to be discovered, and that the Guilder thing might be a ruse.
So now he’s got footprint samples in mind for the tracks of his three perpetrators: he probably recognizes Vizzini’s tracks — that is, unless he hired Vizzini in a letter and not face-to-face — but may not recognize Inigo’s and Fezzik’s. Vizzini hired them personally.
As the tracks do not lead away from the boat launch, he can assume they took a boat. He probably follows the Guilder lead and makes in that direction personally, and sending off some other boats in other directions to inquire about a traveling party of a giant, a man, a woman, and a short guy.
How does the Prince get from the Boat Launch to the Cliffs of Insanity? At what point does the Prince privately know that some outside agent is interfering with Vizzini’s plan? Does Humperdinck suspect this before he finds Vizzini dead? How does he know that Westley’s prints at the Cliffs aren’t part of the plan?