Question 18
Let $n$ be a natural number. In a cage containing $n$ monkeys there are $n$ climbing poles. To give the monkeys exercise, the keepers put a banana at the top of each pole at feeding time. They also connect the poles by finitely many ropes, with different rope ends attached at different points. When a monkey climbs a pole and encounters a rope, it cannot resist swinging along it before continuing upward. Each monkey starts at a different pole. Show that every monkey gets a banana.