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Usenet Newsgroups : rec.puzzles Hall of Fame

The rec.puzzles Hall of Fame is a compilation of over 500 of the most popular puzzles that have been posted and discussed in the rec.puzzles newsgroup. In most cases a detailed solution has been provided.

Many of these puzzles also appear in Braingle's own collection.

Hall of Fame
Categories : logic : supertasks.p

You have an empty urn, and an infinite number of labeled balls.  Each
has a number written on it corresponding to when it will go in.  At a
minute to the hour, you take the first ten balls and put them in the
urn, and remove the last ball.  At the next half interval, you put in
the next ten balls, and remove ball number 20.  At the next half
interval, you put in ten more balls and remove ball 30.  This continues
for the whole minute.... how many balls are in the urn at this point?

You have the same urn, and the same set of balls.  This time, you put
in 10 balls and remove ball number 1.  Then you put in another ten
balls and remove ball number 2.  Then you put in another ten balls and
remove ball number 3.  After the minute is over, how many balls are
left in the urn now? (zero)

Are the above answers correct, and why or why not?


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