In "The Most Dangerous Game," where does Rainsford finally meet Zaroff?

In Richard Connel's short story "The Most Dangerous Game" a big game hunter named Sanger Rainsford accidentally falls off a yacht heading for South America and swims to a nearby island. On the island he discovers a "palatial chateau" in the middle of the jungle. There he meets General Zaroff for the first time. Zaroff is a Cossack who fled Russia after the civil war. It turns out that, because he has grown bored with...

In Richard Connel's short story "The Most Dangerous Game" a big game hunter named Sanger Rainsford accidentally falls off a yacht heading for South America and swims to a nearby island. On the island he discovers a "palatial chateau" in the middle of the jungle. There he meets General Zaroff for the first time. Zaroff is a Cossack who fled Russia after the civil war. It turns out that, because he has grown bored with hunting animals, Zaroff now hunts men.

When Rainsford refuses to hunt with Zaroff, the general provides Rainsford with a three day head start, a pair of moccasins and a hunting knife. Then Zaroff sets out to hunt Rainsford. Although Rainsford wounds Zaroff and kills the general's servant and best dog, he eventually has to jump into the ocean to escape.

After eluding the general, Rainsford swims across a cove to Zaroff's chateau and hides in the bedroom. Rainsford confronts the general and they duel. The final lines of the story reveal that Rainsford has won:

He had never slept in a better bed, Rainsford decided.