You arrive to the island of New Three Land where King Threeodore has a peculiar problem: He likes to take a tour from his castle through the country by only taking alternating left and right turns at intersections. Due to the consitution (the Charters of Threedom) all intersections must have exactly three roads leading in/out and dead ends are forbidden. These tours have always lead him back to the castle and he is worried that changing his place of residency may mean an end to this tradition.
Can you assure King Theeodore that no matter where he starts, a left/right tour will return him to the same spot?