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A train with infinitely many seats, one for each rational number, stops in countably many villages, one for each positive integer, in increasing order, and then finally arrives at the city.

At the first village, two women board the train.

At the second village, one woman leaves the train to go visit her cousin, and two other women board the train.

At the third village, one woman leaves the train to go visit her cousin, and two other women board the train.

At the fourth village, and in fact at every later village, the same thing keeps happening: one woman off to visit her cousin, two new women on board the train. How many women arrive at the city?

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    The answer seems to depend on whether the last stop has women getting on or off the train (ie, infinite being even or odd) which doesn't seem to be a question we can answer. Can someone clarify this at all?2010-08-29
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    @Cam: there is no last stop (before the city).2010-08-29
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    Bonus question: Suppose each woman has a hat, and when she gets off the train she swaps it with a woman getting on. How many hats reach the city? Who's wearing them?2010-08-29
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    See [this question](http://math.stackexchange.com/questions/107/paradox-increasing-sequence-that-goes-to-0)2010-08-29
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    Isn't this just a duplicate of the question linked to above?2010-08-30
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    @Seamus: not quite. The other question specifies which balls are removed.2010-08-31
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    Does that make any difference?2010-08-31

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