Conflict Islands, Papua New Guinea. Eighty miles east of Papua New Guinea rest the Conflict Islands, a 21-island atoll named after a British naval ship that surveyed this remote corner of the Coral Sea in the 1880s. Today, it’s the only freehold archipelago for sale in the world, its name a dramatic misnomer for its tranquil landscape of white sand beaches, swaying palms and electric-blue sea ribboned with colorful coral reefs.