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May 21-June 6th, 2011. Peru, on a 100 year anniversary of Machu Picchu's first publication in the National Geographic, a 10 day expedition sets out to trace the explorer Hiram Bingham's path to Inca's most sacred city. Here, at the busy Hydroelectrica train station locals depend on the sporadic trains leaving for Aquas Callientes. Piotr Redlinski for The New York Times.