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Originally Posted by Sam5
Hmm, I don’t get it. Maybe I’m just too stupid to understand the puzzle, but it seems to me that based on the basic premise of the story, every generation would be just as much “near the end”, if we think that “this” generation is “near the end.” Or to put it another way, every generation would have just as much a chance of being “near the end” as any other.
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It's not that you're stupid. It's that you have good intuition.

It's pretty clear that the conclusion can not be correct. The reason is that the premise of the puzzle is flawed, so the conclusion is flawed. You've stated in words what I've stated mathematically above.