If I was trapped on an island the three things I would bring with me would be a fishing rod, a solar-powered electric stove (I’m sure that is a thing somewhere in the world), and a nice tent. Even though the major issue here would be the lack of drinking water, at least I will be eating full meals (if I can catch anything) and living comfortably in my tent before I collapse from dehydration. However, if my goal was to survive, I would simply bring a speed boat, radio, and a flare gun to leave the island and get help.
