Mr. Burt, The Trailblazer for the Northern California promotion had 39,096 antenna balls in it. Hopefully, you will receive the winners list soon. Thank you for your interest in our promotion. Best Regards, Charles Brooks ConocoPhillips Web Services |

Remember how I wrote that the BBs filled about 59% of a plastic square? This put the ball count at 310/ft³, and the Blazer at about 39,009. In the second week of guessing, I revised my numbers
upward, centering my guesses around 39,009. Here is a table
of all my guesses.

I checked my numbers. I had submitted about 28 guesses every week for the last four weeks, getting as close as 38,912 in the fifth week, 39,009 in the sixth week, 39,089 in the seventh week, and 39,039 in the final week.

In other words I was off by 184 balls in the fifth week, 87 balls in the sixth week, 7 balls in the seventh week, and 57 balls in the final week.

My guesses had really been great!
I was surprised that other people had reached better answers than mine, especially in the seventh week.
Damn, someone had guessed closer than **7** balls?!

Remarkably, they had.

The next day I received an email from Ken H., the winner in the seventh week.

One of his co-workers had told him about my site, and he decided to write me. He turned out to be a mechanical engineer, and his wife owns a Trailblazer, so he got his hands on a box of antenna balls and calculated an answer in much the same way that I had. He entered about 40 times, over four weeks, and had a bit of luck on his side.

A few weeks later, I finally got the winners list in the mail. The other winners from Sacramento were Carrie Douglas and Roger Fong. They won in week 4 and week 5.

Now here is where it gets interesting. I did a search for "Carrie Douglas Sacramento" on Google, trying to determine if the contest was somehow fixed or rigged to only award 76 executive's friends or something. What I found was
a woman named "Carrie Douglas **Fong**", executive director of the Scholarshare investment board here in Sacramento.

Hmm. Carrie Douglas Fong... Roger Fong... both winners from Sacramento, one with two last names. I don't think it is unreasonable to suspect that they cheated!

The contest specified "one prize per person or household". This was a good rule, because once you have gone through the process of measuring the trailblazer and calculating the ball-volumes, you might try to win a bunch of trucks for your family and friends, and that wouldn't really be fair. Of course, if you have two houses and two last names, you could still do it.

According to the winner's report, Carrie Douglas decided to get the Trailblazer, but Roger Fong opted for the $20,000
cash.

I wrote to Charles Brooks at Concoco Phillips and tried to tattletale, but without any real evidence, I'm sure it was less than convincing.

I am very interested to find if they are members of the same household!

I guess I could check voting registrations and property tax statements, but I'm not really interested in making this a life-long pursuit. I've got
sandwich spreads and garden implements to measure, after all!

To be clear about my statements, I don't know if this Carrie Douglas Fong is the same Carrie Douglas that won the truck, and I don't know if they are related, and I don't know if they are married, and I don't know if they live in the same household, and I don't know if I would have won a trailblazer even if they hadn't entered!

Ah well, maybe next time!

-Rob

On June 24th, 2003, Art Medlar sent me a clipping from the MIT Alumni magazine.

In addition to the birth of their first child, Aidan Griffin Fong, on January 16, 2003, 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!

So,
it appears that Carrie is married to I take consolation in the 6,000 entries he submitted. That's 60 times as many as I used (and $2,220 in postage)... and he apparently graduated from MIT. |

Oh, and by the way, a stack of 6,000 entry blanks would only be |

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Last updated June 24th, 2003.