Scientia omnia vincit

From the MIT Class of 1987 class news. (Thanks again to Dave Russ.)

Carrie and Ryan Fong* thought that many like-minded MIT classmates might
get a kick out of the following story pertaining to a number of contests
they entered late last year. I know I did:

76 (gas stations) had a promotion for customers to try to guess the number
of 76 antenna balls that would fit into a Chevy Trailblazer. The contest ran
for 8 weeks with the person with the closest guess (without going over) in
each of the 8 weeks winning a new Trailblazer. I didn't find out about the
contest until it was well into the 3rd week. The primary rules of the
contest were that you could enter as many times as you would like, but that
only one winner per household would be allowed. Each entry had to be on an
official form obtainable only from 76 stations, and filled out by hand. The
winner each week was not announced until all 8 weeks had passed (that would
be too easy if they didn't have that rule).

I rented out a Chevy Trailblazer and filled it with packing peanuts to help
determine the interior volume. Using a little math & science related to
sphere packing densities, I estimated the number of antenna balls that might
fit into the space. While there is math for sphere packing in an ordered
manner, and even experimental results for random packing of spheres, there
are factors unique to this contest that had to be considered, including how
the spheres contact the irregularly-shaped container (vehicle walls), as
well as the effects of surface friction and mass of the antenna balls. After
making some educated guesses about the ranges of variation that were
probable, I came up with a distribution of guesses.

Meanwhile, I gathered up in excess of 6,000 entry blanks from 76 stations
throughout the area (picture a stack of entry blanks almost 3 feet tall),
and with the assistance of friends and family (none living in the same
household), proceeded to complete and submit the entries We submitted
approximately 1200 entries a week for the final 5 weeks of the contest, with
slight shifts in the guess distribution to more thoroughly cover the guess
range.

Because of the relatively tight range of my required guess distribution, we
actually hit most numbers very close to the central guess twice. In deciding
how to distribute the guesses, I had to decide how confident I was of my
calculations (tighten the distribution), and whether I wanted to maximize my
chances of winning at least one vehicle (spread out the distribution), or of
winning multiple vehicle (tighten the distribution). Well, I'm happy to say
that we won 4 out of the last 5 Trailblazers - we had the correct number
one week and were low by 1, 2 & 4 on the other weeks that we won. The week
we lost, we were actually low by 5 antenna balls. I was bummed to have
missed my clean sweep, but I spoke with a couple of other MIT classmates and
discovered that the same contest was going on in another state. I was able
to provide one classmate with my guess distributions in time for him to win
the last Trailblazer in his region!