athematicians
have
a passion for balls. Colored balls, usually. Or
numbered balls. Imaginary
balls, of course, for they are most useful in a
thought experiments, such
as this one...

At one minute to midnight, a
mathematician placed ten balls,
numbered one through ten, into a vase and removed
the ball marked with
the number one.

At onehalf of a minute to midnight,
the mathematician placed
ten more balls, numbered eleven through twenty, into
the vase and removed
number two.

At onethird of a minute to midnight,
the mathematician placed
ten more balls, numbered twentyone through thirty,
into the vase and removed
number three.

At onefourth of a minute to
midnight,...
At
midnight, how many balls are in
the vase?

