Fourteen ladders stand in a row. At the foot of each ladder is a monkey; at the top is a banana. Festooning the ladders are an arbitrary number of ropes. Each rope connects a rung on one ladder to a rung on another, but no rung receives more than one rope.
At a signal all 14 monkeys begin climbing. If a monkey encounters a rope it climbs along it to the other end and then continues climbing upward. Show that every monkey gets a banana.
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Imagine the process in reverse. If Monkey 1 reaches Banana G and then descends again according to the same rules, it will return to the foot of Ladder 1; its path is uniquely determined. Further, because there’s no occasion for loops or dead ends, each monkey will eventually reach the top of some ladder. If every monkey reaches a goal, and no two monkeys reach the same goal, then every monkey gets a banana. The solution generalizes to any number of ladders.
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