An old chestnut goes as follows:

I have an infinitely large bin, initially empty, and an infinite supply of balls. At 1/n hours before 12:00, for n = 1, 2, 3, ..., I put 10 balls in a bin, then take one ball out of the bin. At 12:00, how many balls are in the bin?

A closely related problem is this one:
I do the same as the above, but I take that action in each of 2 bins and the balls are numbered 1 to infinity. At 1 hour before 12:00, I put 10 balls numbered 1 to 10 in each bin, and I remove number 1 from the first bin and remove number 10 from the second bin. I continue in the same fashion: At 1/n hours before 12:00, I put balls numbered 10n-9 to 10n in each bin, but I take out ball n from the first bin and ball 10n from the second bin. At the end, which balls are in each bin? What is the total number of balls in each bin? How is this possible?


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