The film Ship of Theseus set me thinking, as, I think, it was intended to. The main conundrum on which the film is based is: does a ship with all its parts replaced remain the same ship? This concept has been beautifully explored in the modern day context by Anand Gandhi in this riveting film.
Wikipedia informs us that Plutarch in late first century had recorded the query about the Ship of Theseus. The ship wherein Theseus and the youth of Athens returned from Crete had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their places, in so much that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same. Heraclitus and Plato had also apparently discussed this paradox prior to Plutarch.