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How many different ways can you have a whopper(tm)?

By ankarbass in ankarbass' Diary
Sat Dec 17, 2005 at 05:45:59 AM EST
Tags: User Diary (all tags) 		User Diary

Burger King says the answer is 256. That's because there are eight items.

1) Beef patty
2) sesame seed bun
3) tomato slices (2)
4) lettuce
5) mayonnaise
6) ketchup
7) pickle slices (4)
8) onion

But, what is clear from this official recipe for a whopper(tm) is that there are two tomato slices and four pickle slices. meaning that there are in fact twelve ingredients and 4096 possible ways to have a whopper. If you observe that the bun has two parts we double this number to 8192.

What is the correct number?

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For the sake of argument we rule out "optional" items like bacon and cheese as this will only complicate things even more.

What about the mayo? You can order heavy mayo or light mayo. Does this add two more possibilities? What is the smallest unit of measure we could reasonably apply to mayo? Ketchup? Do we get charged for extra pickle? Probably not, in which case, extra pickle adds at least one more item to the list perhaps up to four more depending on how we define extra pickle. Extra onion? I'm pretty sure they charge if you want more lettuce and tomato.

But when is a whopper(tm) not a whopper(tm)?

Vegetarians order whoppers(tm) without meat all the time, and people on nutty diets order them without buns, but is it a whopper with neither meat nor bun? Is it still a whopper if we order only meat, or only bun?

Suppose we require at least the bun or the meat then it makes sense that a plain whopper is just bun and meat. But, if someone is a vegitarian is a plain bun even a whopper(tm)? Or do you need at least one more item over the bun for it to be a whopper(tm)

Please provide your analysis below. Each analysis will be graded for completness via the rating system. Grades are final and there will be no opportunities for extra credit. You can however resubmit your proposal as many times as you wish to improve your grade.

3 = A You went above and beyond
2 = B Good job, not the best
1 = C Average solution, works but not much more
0 = F You fail it

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Poll
Whoppers(tm)
o are tastier with dead cow 0%
o are nasty with meat 0%
o are worthless without cheese 9%
o are overpriced 0%
o are way better than a big mac 18%
o never look like the picture 54%
o are called a royale with cheese where I'm from asshole 18%

Votes: 11
Results | Other Polls

Related Links
o ankarbass's Diary

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How many different ways can you have a whopper(tm)? | 26 comments (26 topical, editorial, 0 hidden)
man, you're wasting your time (2.00 / 3) (#1)
by bunk on Sat Dec 17, 2005 at 06:13:45 AM EST

and trying way to hard.  the losers around here only like discussing drugs.


hunger strike + bong hits = super munchies -- horny smurf
You might want to discount some degenerate cases. (2.71 / 7) (#3)
by skyknight on Sat Dec 17, 2005 at 07:31:56 AM EST

For example, is the null whopper really a whopper at all?

It's not much fun at the top. I envy the common people, their hearty meals and Bruce Springsteen and voting. --SIGNOR SPAGHETTI
Overcounting on the tomato and pickle slices (2.80 / 5) (#5)
by PMDBoi on Sat Dec 17, 2005 at 09:25:39 AM EST

It would be incorrect to consider each tomato slice a separate ingredient, since you can't differentiate between them. All other things being equal, a Whopper with just tomato slice #1 is no different from a Whopper with just tomato slice #2: they both just have one tomato slice on them. Instead, if you have an ingredient with a maximum count of k, then there are k + 1 possibilities corresponding to it: 0, 1, 2, ..., k. There are three possible counts of tomato slices on your Whopper: zero slices, one, or two. Similarly, there are five ways you can have pickle slices on your Whopper.

So that adds up to a somewhat less impressive 26 × 3 × 5 = 960 possible Whoppers. If you consider the top and bottom buns distinct, then that brings in a factor of 2, which brings the total up to 1,920 possible Whoppers.

This is only considering the stuff above the horizontal rule in the diary. If you want to find out how many different combinations of extras you can get with a given amount of money, given the prices of all those extras, it's easy to find with a linear homogeneous recurrence relation, but only if you differentiate between different orders of extras (i.e., it would count once for extra pickles on top of extra onions, and once for extra onions on top of extra pickles). Discounting order would require partitions, though, and partition counting is hard.

However, if there's no maximum price, then there are an infinite variety of Whoppers that you can get, since you can order an arbitrary number of pickle slices, right? They're countably infinite, though, and it appears that the set of all Whoppers would be countably infinite as well, since either you count the order of the ingredients, and they're all finite strings on the alphabet of Whopper ingredients, which is finite, or you don't count order, and they're all sub-multisets of the set of ingredients, which is finite.


harder, better, faster, stronger: e2
burger king is right (1.50 / 2) (#10)
by Lemon Juice on Sat Dec 17, 2005 at 12:14:07 PM EST

They are not going to listen to you when you say light on some shit. You could ask them for 5 tomatoes but they won't give it to you.  Have you seen a picture of the bun wrapper? it is normally marked with a line for the special ingredients.

WIPO (none / 1) (#11)
by Enlarged to Show Texture on Sat Dec 17, 2005 at 12:20:15 PM EST

I prefer double-double, animal style


"Those people who think they know everything are a great annoyance to those of us who do." -- Isaac Asimov
WIPO: zero (none / 1) (#14)
by rodoke3 on Sat Dec 17, 2005 at 12:51:05 PM EST

They'll all end up going out the same way they went in, so why bother?

I take umbrage with such statments and am induced to pull out archaic and over pompous words to refute such insipid vitriol. -- kerinsky
Your answer. (none / 0) (#15)
by RandomAction on Sat Dec 17, 2005 at 02:47:48 PM EST

You said: What about the mayo? You can order heavy mayo or light mayo. Does this add two more possibilities? I like your question but there seems to be an assumption here that one has to have mayo. Of course the real option is mayo or no mayo and not more mayo less mayo. However in either situation only one more possibility is added

Not an array of binary options (none / 1) (#16)
by bobpence on Sat Dec 17, 2005 at 03:31:50 PM EST

Rather, each option has its own degree and becomes a factor in the overall number of possibilities.

  1. Beef patty........// factor 1, must have
  2. sesame seed bun...// factor 2, exclude for Atkins or take top and bottom, no unmatched half
  3. tomato slices (2).// factor 3 for 0..2
  4. lettuce...........// factor 3 for {none, a little, normal}
  5. mayonnaise........// factor 4 for {none, light, normal, heavy}, no added charge expected
  6. ketchup...........// factor 4, same as mayo
  7. pickle slices (4).// factor 5 for 0..4
  8. onion.............// factor 3, same as lettuce

So in reality, without paying for bacon or cheese, or paying (we presume) more for extra units of tomato, lettuce, pickle, or onion, there are 1 x 2 x 3 x 3 x 4 x 4 x 5 x 3 = 4320 ways to order a Whopper within the confines of its normal ingredients and still retaining the beef patty to preserve its Whopperness. As a rule of thumb, the busier the restaurant the more likely the person in front of you is trying to have it his way in some way the clerk does not grasp.

Wait, can you ask for how it's cooked?


"Interesting. No wait, the other thing: tedious." - Bender

One. (2.33 / 3) (#20)
by livus on Sat Dec 17, 2005 at 04:49:13 PM EST

Unless you want the burger goons to spit in it.

---
HIREZ substitute.
be concrete asshole, or shut up. - CTS
I guess I skipped school or something to drink on the internet? - lonelyhobo
I'd like to hope that any impression you got about us from internet forums was incorrect. - debillitatus
I consider myself trolled more or less just by visiting the site. HollyHopDrive
How many different ways can you have a whopper(tm)? | 26 comments (26 topical, 0 editorial, 0 hidden)
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