Another question is What caused Rainsford to believe Zaroff knew he was hiding in the tree?
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When Rainsford falls off his boat, he swims to the island. It is mentioned that Rainsford has "strong strokes" and doesn't tire easily. Rainsford is your typical escape story protagonist; he is more or less perfect. It is also mentioned that he is a famous hunter known for his prowess in all kinds of deep and hazardous terrain.