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***** Growth Puzzles ****************
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1. "I want to rent this room for the month of July," he said.  The clerk
wheezed.  He peered through the narrow slits of his bloodshot eyes,
glaring through the murk of the humid dusty darkness of the fleabag
lobby, and said, "for you-- a deal."  "How much?" said the big guy,
sweat trickling down his face, staining the collar of his dingy shirt
which didn't appear to have been washed in weeks.  Noticing the telltale
bulge of a revolver under the stranger's dirt-stained jacket, the clerk
replied, "First day-- one cent.  Second day-- two cents.  Third day--
four.  Every day it doubles."  The stranger's face drew into a knot as
he scrutinized the greasy poker faced clerk.  He said, "That's nothin'.
What's the hitch?"

	a)	How much would the stranger pay on July 31st?
	b)	What would the bill be for the month of July?

2. You get a letter in the mail that says, "Send a dollar to each of the
five people on this list.  Add your name to the bottom, take the top
name off, and send a copy of the new list plus these instructions to
five new people.  P.S.  If you break the chain you will have to watch
Brady Bunch reruns every day for the rest of your life."

	a)	Assuming nobody broke the chain, and every letter was
passed on in one day, how much money would you have after 10 days?  20
days?  One hundred days?

	b)	Assuming no person ever received the letter twice, and
each letter was passed on in one day (and nobody broke the chain) how
long would it take for everyone on the planet to get a letter?