## Billions and Billions of Burgers

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There’s a new restaurant in Manhattan called 4Food which is geared towards Social Networkers, according to this September 16 review on CNNMoney.com:

Customers who step into the restaurant are met by staffers ready to take orders on their iPads, a 240-foot screen featuring live Twitter feeds and Foursquare check-ins, and a menu that offers more than 96 billion customizable burger options.

This paragraph goes on to provide a link to this article in which Stacy Cowley actually explains the mathematics.  It turns out that there are some items where you can only pick 1 [1 bun among 5 choices; 1 scoop of something I don’t normally think of as being on a burger —  mac n cheese and sushi are two of the options — among 18 choices, where one of the choices is “No thanks.”; and finally 1 burger among 8 choices] but for the 4  add-ons like lettuce, the 12 condiments, the 7 cheeses, and the 4 meat slices, you can have as many different kinds as you want.  This means the total number of combinations becomes

$5 \cdot 18 \cdot 8 \cdot 2^{\left( 4+12+7+4\right)}$

which is 96,636,764,160.

The article contains more specific information about each of the choices, and the many many comments include additional information, like that someone in theory should be able to order no bun or no meat, although the comments mostly seem to be arguing whether or not the math is correct (no math mistakes that I see!).  Incidentally, if you allow the option not to have a bun or not to have the patty at all, which seem reasonable options to include, the 5 in the equation changes to a 6 and the 8 to a 9, giving 130,459,631,616 combinations. And that’s a lot of choice.

### One Response to “Billions and Billions of Burgers”

1. Andrew MW Says:

minus 1? Because you can’t have a hamburger made of air alone?