Fermi Problems

I was thinking of a good way to celebrate two New York Times articles that are hot off the presses right now. The first the Fed’s $85 billion dollar bailout of AIG, and the second is an article on the habit of making absurd estimations known as Fermi Problems. So I decided I would estimate the number of semi trailers it would take to send AIG the money in 20 dollar bills. Hey, it beats doing my Mechanics homework. (Full disclosure: I allowed 1 use of Google per problem which is technically against the rules, and before posting this I checked my answers with a calculator so I wasn’t embarrassed.) Estimates after the jump.

Like most of the banks in America I have no cash on hand. So the thing I looked up was the volume of a dollar bill. According to Wikipedia it’s 6.41″ by 2.61″ by .0043″ The 43 thousandths thing was bothering me so to simplify I decided to calculate the volume of 1000 x $20 bills, or the volume of $20,000. Multiplying the last dimension by 1000, and then converting all the dimensions to feet with some estimation, I got the thousand 20 dollar bills as ~ .5′ by .2′ by .33′ or .033 cubic feet. This number is probably a little small but it’s right to an order of magnitude. Now estimating a semi at 8 feet wide and 8 feet tall and 45 feet long, we get the semi isĀ  ~ 3000 cubic feet. The volume of the truck divided by the volume of the money times the value of the money (3×10^3/3×10^-2 * 2 x 10^4) is 2×10^9 dollars per semi or 2 billion dollars per semi. So to send all the money you would need a total of 43 semis.

Now, I was a little curious about how much the gas would cost. Since I’m not an East Coaster, I chose to Google the distance from the White House to Wall Street. It’s ~200 miles. Estimating 10 miles per gallon you get 20 gallons of gas needed per truck. Times 20 by 43 semis and there is 860 gallons of gas. Estimating the cost of gas at $5 dollars (it’s diesel) it ends up beingĀ $4300.

I’m just trying to put things into perspective. It makes me wonder how we are sending all that money over to Iraq. I also find it to be interesting that the Iraqi government announced it had a 79 billion dollar surplus last month. Hmm. This is my first time doing Fermi problems and they are surprising fun to do. Add your own ideas, estimates, and/or corrections in the comments.

Comments (7) left to “Fermi Problems”

  1. Patrick wrote:

    Just so people on the site know, I want to start doing science-related blogging. This is just a test if Shambot is the best place for this type of stuff, and if I can even make science-related posts interesting.

  2. Patrick wrote:

    Also, looking online, it turns out that diesel cost 5 dollars last month, now it’s only about 4 dollars. So i guess it would cost closer to $3440 to send the money.

  3. Bill wrote:

    I think we need more mathematics related posts here.

    Also, I like when people post news articles! I mean, I read BBC news sometimes and surf around, but I like to hear opinions and things.

    The article about estimation was pretty interesting. Do you sit around with friends and approximate?

  4. Emma wrote:

    I could never ever do something like what you just did, and I find it FASCINATING.

    more, plz.

  5. Ben wrote:

    Man, I always thought that I overestimated the volume of money, like in movies when they have $10,000 in $100 bills filling a briefcase. I guess $20s make it 5 times as voluminous, though. Aaaand $85 billion is a LOT of money…

    I like posts like this! You should definitely do more!

  6. Patrick wrote:

    Yeah I am pretty sure you could realistically fit 100,000 dollars in a briefcase. Using a calculator this time; this (http://www.amazon.com/Samsonite-Aluminum-Computer-Attache-Silver/dp/B00008S83F/ref=pd_bbs_7?ie=UTF8&s=office-products&qid=1221667512&sr=8-7) briefcase could fit around 1.3 million dollars in hundreds. But even then, you would need around 65,000 suitcases to hold 85 billion dollars we would be sending to AIG.

    It all reminds me of a quote from Richard Feynman:
    “There are 10^11 stars in the galaxy. That used to be a huge number. But it’s only a hundred billion. It’s less than the national deficit! We used to call them astronomical numbers. Now we should call them economical numbers.” And he said that nearly 40 years BEFORE the Bush administration!

  7. Angie wrote:

    Not only do I find the math problems fascinating, I also have a long history to working weird problems like this out visually. I think it’d be cool for our more visually inclined shamboties to provide visual descriptions of the cool math problems that we’re all (and by all I mean Patrick) going to be posting now! :)