graded out of 30.  median was 29.

1. The Rule of 72

(a) Moore's Law is often expressed as "capacity doubles every year and a
half."  What is Moore's Law expressed as a percentage growth per month?

  4%/month.  because it doubles in 18 months: 72/18.

  minor penalty if they didn't use the rule of 72
  but instead whipped out their calculators?


(b) Suppose that about 25 years from now, you're trying to send your
kids to Princeton and you discover that the tuition has quadrupled from
what it is now.  Approximately what annual rate of tuition increase
would that correspond to?  (Warning to prospective Princeton parents:
college tuition rises faster than inflation.  Start saving.)

  about 6%.  if it quadruples in 25 years, it doubles in about 12 years,
  but it's ok to be a bit more "precise" here.


(c) Princeton's Ben Bernanke, currently chairman of the Federal Reserve,
once said he wants to keep inflation between 1.5% and 2.5% per year.
Assuming he manages to hit the average of these two numbers, when will
inflation have doubled the dollar cost of everything?

  36 years (or 2011+36 if they provide an explicit year).


(d) A NY Times story (11/7/07) says that total power consumption by
Internet servers is doubling about every 6 years.  Suppose that Internet
servers used 10 gigawatts in 2004 and 20 gigawatts in 2010.  How fast is
power consumption growing per month?

  1%.  six years is 72 months


(e) Suppose (improbably) that this power consumption continues to double
at the same rate.  In what year will servers consume 10 terawatts?

  2064.  doubling in 6 years, 10 doublings is 60 years.


(f) An NPR story (10/3/08) states that getting 20% interest for five
years doubles your money.  Is five years too short, too long, or about
right?

  too long.  it's more like 2.5 years


2. Estimation


(a) "π seconds is a nanocentury."  Too high, too low, or just about
right, and why?

  about right.  they have to show some computation.


(b) "Sound travels about one foot in a millisecond."  The speed of sound
at sea level is about 340 meters/second.  Is the quoted speed too high,
too low, or just about right, and why?

  about right.  they have to say why, for example "340 m/sec is 1000 ft/sec
  so 1 ft is 1 msec"


(c) I was at an over-crowded cocktail party recently, and it started me
wondering...  Suppose that 10,000 people come to the same party.  If
they arrange themselves in a square (to make the arithmetic easier),
what would be the approximate dimensions of the square?  State clearly
how much space you estimate that each person will occupy.

  100 x 100 x area of a person.  maybe 2x2 or 3x3 ?  


(d) Approximately what fraction of the football field at the stadium
would they occupy?  (Note for non-football types: the field is 100 yards
long and 50 yards wide; feel free to go metric -- 100 x 50 meters -- if
you prefer.)

  5000 sq meter  / 10000 sq meter = 1/2  if people are 1 meter square, 


(e) Suppose 100 million people showed up at our hypothetical party.
What would be the size of the square for this gathering?

  10000 x 10000 x area


(f) How does the width of the square depend on N, the number of people
in it?

  sqrt(N)


(g) "Video files [...] are typically thousands of time larger than text
files.  A minute of high-definition video is about 50 megabytes, about
10,000 times larger than an 800-word e-mail message."  (NY Times,
9/18/08.)  From these facts, estimate the number of letters in the
average word in an email message.

  50*10^6 / 10000 / 8 is about 6 characters/word.  don't worry about
  spaces, punctuation, etc.


(h) A story on Slashdot on 10/22/09 describes "a new fingernail-size
chip that can hold 1 trillion bytes (a terabyte) of data", which is
claimed to be "up to 20 high-definition DVDs or 250 million pages of
text."  Assuming these numbers are correct, what is the approximate
capacity of a high-definition DVD?

  10^12 / 20 = 50 GB

(i) If the books in question are just ASCII text, is the page-count
estimate much too high, much too low, or approximately right?  (As some
kind of cross-check, Pride and Prejudice is 97,680 words and about 250
pages in at least one edition.)

  10^12 bytes / 250 * 10^6 pages is about 4000 bytes/page.
  pride & prejudice suggests 100K/250 = 400 words/page, so
  that's 10 bytes/word.  so the page count estimate is
  too low by somewhat?  correct arithmetic and
  any sensible conclusion is ok here; it's not a great question.