A leprechaun places a magic penny under a girl's pillow.
The next night there are 2 magic pennies under her pillow. The
following morning she finds four pennies. Apparently, while
she sleeps each penny turns into two magic pennies. The total
number of pennies seen under the pillow each day is the
grand total; that is, the pennies from each of the
previous days are not being stored away until more pennies
magically appear. How many days would elapse before she has a total
of more than $10 billion?
(Proceed by trial and error.)