Fish with binary speed

There are nn fish numbered 11 through nn at one end of an aquarium. They all start swimming at the same time to the other end of the aquarium. Once a fish reaches an end of the aquarium, it turns around immediately and continues swimming in the other direction.

Fish 11 swims with speed v1v_1, fish 22 swims with speed v2=2v1v_2 = 2 v_1, fish 33 swims with speed v3=2v2 v_3 = 2 v_2 , and so on.

Will the nn fish all be at the same end of the aquarium at the same time again?

An example aquarium with \(n=3\) fish. An example aquarium with n=3n=3 fish.

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