Treebeard's Stumper 22 October 1999

Too Many Ancestors

I have two parents, and so do they. That gives me four grandparents and eight great-grandparents. Details get fuzzy after that, but I'm sure my family tree keeps doubling every generation: 16, 32, 64, 128, 256, and so on. After 10 generations, I'm back to the founding of our country with 1,024 of my ancestors on the loose. After 20 generations, I have over a million ancestors. After 30 generations, I have a billion ancestors. But that's far more than the (then) population of the world! That's impossible! How does my family tree narrow down?

Answer

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