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The number of new starships

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If you were planning a viral colonization of the galaxy and star ships made a stop about every 900 years on an Earth-like planet, retired the original star ship, established a civilization and 100 years later launched 2 new identical star ships that continued on similar 900 year missions, how many star systems would have been colonized over a 20,000 year period starting with the 1 starship from Earth?

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The number of new starships are figured.

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The number of new starships sent will double every 1000 years, so that there will be 2^19 ...

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