What is the Mathematical Formula for...

If there are n items, they can be combined in 2ⁿ-1 ways (if you exclude the null set). The given number does not match this; I suspect they picked it out of thin air.

FWIW, 22,020,098 = 2²⁰ x 3 x 7, so it may mean something.

"I suspect they picked it out of thin air."

I suspect they picked it out of another place.

Ah, thick air!

I'm kind of digging this possibility. Twenty condiments, plus medium-rare/medium/well (3x) and seven different sides (7x). But, wouldn't those be part of the combination calculation mathematically anyway?

Or... Maybe the 3x and 7x are... Platter comes with a starch and you have three options in how you want it (chips, fries, hash browns) and a drink and they have 7 different beverages to choose from? Either way, time for lunch!

Thanks. Had my nose in some old math text books and found it and was coming back here to post when I saw the above replies... I have not been able to come up with their number through any mathematical means that makes sense in regards to burger platter combinations.

The first thing that popped in to my head was that it related to 22,020,096 people served and everyone got their burger served just the way they like it, but your way makes more sense if you actually get to choose what ingredients options you have.

Yes I also work in marketing, can't you tell.

Ya the Waffle House....they actually have 23 ingredients including 18 condiments and the possible combinations total 283,115,520....perhaps they don't offer all the different condiments at your location eh?

http://en.wikipedia.org/wiki/Combination

For 23!/18!5! I get only 33,649 combinations.

No....assuming you start with bread and meat, there is then 41 other ingredients that can be used in any combination... I think...maybe....It doesn't seem that order used would matter...Now I'm hungry, mmmm burger!

The first time you said the 23 ingredients included 18 condiments, not that the 18 condiments were separate....

Now, if I eat one burger per minute, how long will it take to try all combos?

Let's see lettuce, tomato, onion,pickle,cheese,bacon....what's considered a condiment? chopped onions, relish, bacon bits....Oh who cares....time to eat!

No, no, no - it's 2 all beef patties, special sauce, lettuce, cheese, pickles, onions on a sesame seed bun. Why the heck do I remember that dumb ad?

The joke about the "two all beef pattys on the Sesame Street Bus"?

Oooh, that's a nice looking burger!

An advertising agent could, if inclined to make the number large, consider that a sandwich prepared with two pickle slices as a different combination than one prepared with three pickle slices.

Seeded bun cap, plain bun cap, onion roll, red onion or white, extra mayonaise, 1 or 2 or 3 slices of four different cheeses ... the combination possibilites would become quite a large number.

Well for the burger you have rare, medium, medium rare, well done, burnt....the bun can be toasted or not....or perhaps no bun at all, and perhaps raw(steak tartare) you could have the hamburger fat content at 15% or 20% or whatever.....we could go on and on....but the stated number is from them....

Yeah, it was at a Waffle House where I saw the sign. But as for not offering all the condiments, it still doesn't make sense... ^24 gets you 16.8MM and ^25 gets you 33.6MM. But then again it was from a Texas location and although they may have all the condiments, maybe some combinations are considered too progressive and are outlawed. ;-)

Oh we'll, it was an old sign though, maybe they did it before the formula came into force and they used fuzzy math, haha.

Seven types of bread? that seems excessive......but well done.....you, not the burger....not cooked well done, but well done calculating a possible answer....but my figures were from the head office of the Waffle House...not the head waffle house but the head office....I can't eat another bite.....must sleep

Is that the company that claims it can make all these combos of burgers? We don't have a Waffle House out here. We do have In N Out, Fatburger (ooooh, so good), Farmer Boys, Carl's Jr, Burger King, Mc Donalds, Jack in the Box, Del Taco, Wendy's, Five Guys, Primo Burger and Tommy's. I'll take a Fatburger or Farmer Boys any day!

I have heard about Smashburger, but they're not out here.

We do have some of the best Mexican food! I'm from Chicago, where Mexican food was Taco Bell and burning hot hot sauce was Taco Bell Fire Sauce. Now we get those small round soft taco's, huge burritos, handmade tamales, chimichanga's, taquitos, flautas, papusas, etc. And real hot sauce - Habanero all the way!

While ordering sandwiches at "Subway" stall the bearer asked me questions at every step of preparation, I became furious and told him to prepare best way he would like to eat himself. He made nice combination and we all relished it.

Was that his last meal?

No, not at all.

Relished it? Why did you do that? I thought you told him to prepare it the way he would like it? So why did you add relish?

(_{I just know I'm going to get in trouble for that!} )

B'cas he prepared it nicely and we enjoyed it. Some times you have to leave it to professionals.

I apologize. That was a joke best caught by native speakers of English, which changed the usage of "relished" by taking it from action verb in the past tense, to a verb, ignoring the past tense ("ed") ending on it.

That was why I said I knew I'd get in trouble for it. Thank you for not beating me over the joke. Or over the head, either

I think they only have sweet relish at Subway. The bright green relish isn't used.

No need to apologize my friend. We all here to discuss serious subjects along with pulling each others legs. .

22,020,096 = 3*7*220 if that's a clue.

22,020,096 = 3*7*2^20 if that's a clue.

Sorry, for some reason the exponent thing didn't work.

No, but if you could sing a few bars of it that might help.

Good Luck, Old Salt

All this burger talk and I am on the Nutri Systems eating plan now.......I can see that my eating plan is about to change today .....I am craving an In - Out burger 4x4 monster style, with fresh cut fries and a strawberry shake now......

YUMMMMMMM

If order of placement of the ingredients is critical then use the formula for Permutations. If the order of placement is not critical use the formula for Combinations. (Yes, what we call a combination lock is really a permutation lock.)

That will give you the DISCRETE possibilities. If you get to add variations of 1 tbsp of condiment or 2 tbsp of the same condiment, you can run your numbers up for even a small number of ingredients.

Are you counting the (hopefully) inadvertant ingredients such as spit or hair?