# Fish with binary speed

There are $n$ fish numbered $1$ through $n$ 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 $1$ swims with speed $v_1$, fish $2$ swims with speed $v_2 = 2 v_1$, fish $3$ swims with speed $v_3 = 2 v_2$, and so on.

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

An example aquarium with $n=3$ fish.

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