The math behind 96 billion burger choices
September 16th, 2010
02:45 PM ET
Share this on:

Today, CNN Money's Laurie Segall reports on 4food, a new New York City restaurant that's fueling its customer base with the use of social media. The restaurateurs claim to offer 96 billion burger combos available as orders. Stacy Cowley crunches the numbers.

New Manhattan burger joint 4food lets eaters customize their creations with an extensive ingredient menu, and news reports have put the range of options at anywhere from "more than a million" to "140 million" burger combinations.

"There can't possibly be 140 million combinations," I said to my statistician spouse.

"Let's find out," he said, firing up Excel.

Here, based on the menu on 4food's website, are the parameters we started with, and our assumptions:

5 buns [breakfast bagel, brioche, multigrain, pressed rice, pumpernickle]: Have to have 1

4 add-ons [lettuce, NY pickle, tomato, onion]: Can have 0-4

12 condiments [mustard, guacamole, bbq, horseradish, hummus, jerk sauce, tartar sauce, mayonnaise, ketchup, salsa verde, sweet chili, tzatziki]: Can have 0-12, should have 0-3

7 cheese [blue, goat, fontina, gruyere, manchego, mozzarella, cheddar]: Can have 0-7, should have 0-2

4 slices [avocado, pancetta, mushroom, sopresatta]: Can have 0-4

17 scoops [avocado & chili mango, baked beans, grits, hominy, fruit & nut, edamame, egg, mac & cheese, mofo, mushroom & onion, peppers, chorizo & potato hash, brussels sprouts, spinach, veggie chili, veggie sushi, winter slaw]: Can have 0-1

8 patties [beef, breakfast pork, egg, lamb, pork, salmon, turkey, veggie]: Can have 1

Using that, we ran two formulas. The first calculated how many choices you'd have if you stuck with "should have" - no more than two cheese slices, three condiments, etc. That gave us this:

5 * (2^4) * (12C3 + 12C2 + 12C1 + 12C0) * (7C2 + 7C1 +7C0) * (2^4) * 18 * 8 = 1,598,238,720

... which is 1.6 billion combos.

But if you take off all sane restraints - want 12 toppings and 7 cheese slices? Sure! - and allow all theoretically possible combos, you get this:

5 * (2^4) * (2^12) * (2^7) * (2^4) * 18 * 8 = 96,639,764,160

... which results in more than 96 billion combos. Jam that on your leaderboard.

Read CNN Money's 4food report

Posted by:
Filed under: Bite • Casual • Restaurants

soundoff (152 Responses)
  1. smartphone quad core

    At least some bloggers can still write. Thank you for this piece of writing!!!

    November 12, 2011 at 6:35 am |

    This post could not be more right on..

    October 29, 2011 at 5:55 am |

    Very well executed article..

    October 20, 2011 at 2:07 am |
  4. David

    Where is the BACON ?!?

    September 23, 2010 at 12:32 am |
  5. David

    Where is he bacon ?!?

    September 23, 2010 at 12:31 am |
  6. GEdwards

    Hopefully liveobxhwy12 comes back to learn the simple difference between the number of COMBINATIONS that can be chosen/ordered, and the fact that no two burgers will be EXACTLY the same. (I particularly liked TSmoov's knocking off the sesame seed point.)
    Heck, using liveobxhwy12's reasoning – or lack thereof – even the hamburger at McDonald's approaches an infinite number of variations. But it has only has 8 or so combinations (w/ and w/o mustard, catsup, pickle, ??). 1*1*2^3. (Note: if you have McD's put cheese on it, it's a different menu item.)

    September 20, 2010 at 5:38 pm |
  7. TSmoov

    @ liveobxhwy12: You’re too funny. The combinations are defined by the number of ingredients not the manner in which you alter a single ingredient – this is definitional to the chosen manner in which the owner would like to count his burger combinations. Choosing to scratch the cheese, or fold the cheese, or toss a tiny piece of cheese aside, or knocking a sesame seed off a bun, or squeezing the juice out of a pickle, etc; WILL NOT create another defined combination. If a box of crayons has 64 colors then the count of colors is 64. It does not become infinity simple because you can create more colors (I’d be willing to bet, BTW, the coloring in coloring books is more your forte than either mathematics, statistics, or even cuisine). At least be consistent for your fellow humans’ sake and the next time your are personally counted for any purpose please answer “Infinity” rather than “one” since there are an infinite amount of ways in which you can vary your appearance and thereby should be considered and infinite set of humans.

    September 20, 2010 at 2:22 pm |
  8. TSmoov

    I've been reading most of these posts and have been getting a good laugh at the funny comments. Especially funny is this liveobxhwy12 person. However, the humor with them is that they can't comprehend the situation here. @ liveobxhwy12: This article is simply about having a bit of “fun” by verifying one single stores apparent boasting that, with the ample ingredients that they specifically and generously offer, they can offer a specified and, YES, FINITE amount of combinations of burgers (BTW, regarding another posters suggestion: The store obviously won’t allow infinite slices of cheese in order to get an infinite amount of combinations. Also, an infinite cheese slice count does not itself exist). It is really just one “fun” article about one single “fun” store owner being goofy in the manner in which they chose to communicate “hey we have lots of burger choices”.

    September 20, 2010 at 2:21 pm |
1 2
| Part of

Get every new post delivered to your Inbox.

Join 9,973 other followers