Dear Ken Selby, Chairman, Mazzio’s Italian Eatery:
Tonight, my family and I ate pizzas from Mazzio’s. They were very tasty. ‘Delicious’ is not too strong a word (and I say this as one not prone to hyperbole). But affixed to the pizza boxes was an advertisement for your new “Mia Pasta” campaign, the text of which contained a deceptive falsehood.
Start with one of three pastas, then choose one of six sauces and one of four meats, plus three of eleven veggies.
With so many options, your possibilites are endless!
(emphasis in original)
Endless? That would seem to be a surefire enticement to purchase your meal. “I can’t go wrong,” the prospective diner would think, “since my possibilities are endless!” But I’m afraid your claim of infinity is demonstrably false. Taking the choices (as you have described them yourself), we may calculate the possible allowed combinations thusly:
3 x 6 x 4 x 11! / (3! x (11-3)!)
The unassailable science of mathematics yields a total number of only 11,880 “Mia Pasta” possibilities, and 11,880, being a finite number, is manifestly not infinite. QED.
You may wish to claim a right of poetic (or some such) license, and assert that 11,880, while not technically infinite, is such a high number that it is virtually infinite. Such a claim could be readily dismissed by imagining, say, an $11,880 federal budget, or an ocean filled with 11,880 gallons of water. Far from being infinite, or even virtually so, 11,880 is a triflingly small number. A pittance. But the unwary pastaphagous patrons of your establishment are nowhere advised that their choices are subject to such a severe limit, nor indeed any limit!
Fortunately, redressing this problem presents no difficulty. Here are some suggestions for the reworded advertising copy:
- “With so many options, your possibilities are more than if there were fewer options!”
- “With so many options, your possibilities are 3 x 6 x 4 x 11! / (3! x (11-3)!)”
- “With so many options, your possibilities are exactly 11,880.”
- “With so many options, your possibilities are exactly 11,880! Note the exclamation point following 11,880 in the foregoing sentence is for emphasis, and not for factorialization!”
- “With so many options, your possibilities are endless, or 11,880, whichever is lower!”
- “With so many options, your possibilities are actually 106,920, since we forgot to mention we offer nine different beverages!”
I look forward to seeing your corrected flyers, and many more delicious Mazzio’s meals in the future.
Best regards:
Sean Gleeson
sean@gleeson.us
http://sean.gleeson.us/
UPDATE: The error has been corrected! Please read Mazzio’s makes good!
I prefer the Waffle House. They are far more exact in their advertising. See ‘844,739 Ways To Eat A Hamburger’ at WaffleHouseDotCom.
It was good pizza though, even finite.
Phoebe, notwithstanding my professed esteem for Waffle House, I cannot concur with your commendation for exactness. Unlike Mazzio’s, Waffle House did not submit their data for review. We have no way of knowing how they calculated the ways to eat a hamburger at 844,739.
Nonetheless, we can definitely prove Waffle House’s number is wrong. Since the different “ways” certainly involve at least one binary choice (with or without catsup, e.g.), the total number of ways must be a multiple of two.
I do like the song, though it’s a pity the online juke box omits the chorus, which is the best part.
Disproving the Waffle House number even further, we may split 844,739 into its prime factors. These, shockingly, are 7 x 120,677. And so Waffle House’s figure can only be true if hamburger eaters are presented with only two independent choices, one of which has seven mutually exclusive outcomes, and the other has 120,677 mutually exclusive outcomes!
It is difficult, but not impossible, to imagine a choice of seven options. A choice of zero through six pickle slices, perhaps. But making a choice of 120,677 mutually exclusive options in a hamburger is beyond belief. Even dictating the number of sesame seeds on the bun wouldn’t give you a thousandth as many options. (The average sesame bun has 178 sesame seeds.)
In the absence of any exculpatory data from Waffle House, we are forced to render a default judgment against them: the number is wrong. Perhaps it’s time for another open letter.
Gosh.
Friday
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If you prime factorialized 844,739, you must be some sorta idiot savant.
(I’d rather believe this exciting possibility than the more mundane explanation that you googled to find a prime factorializing web-site.)
A second open letter does seem warranted.
Doc, you mean to tell me there are websites that do that? Jeez, had I known, I coulda saved 1.38 pencils.
It’s not about Flash!
When I saw Sean’s headline, "An Open Letter to Mazzio’s," in my RSS bookmarks, I thought "He’s taking them to task for their horrendiferous flash-only, too-bad-if-you’re-blind, we-like-the-…
No… they wouldn’t lie to me, would they?
Sean Gleeson spots a glaring mathematical error (or is it really that glaring?) in a Mazzio’…
Sean, you have entirely toooooo much time on your hands!
(read that, please explain what the ! means in your calculations)
I can answer that. That’s the mathematical symbol for factorialization, and it’s shorthand for the number multiplied times all the positive whole numbers that came before it. For instance, five factorial, or 5! is 5 x 4 x 3 x 2 x 1 or 120. Factorials have uses beyond figuring out pasta combinations, but really, to what better use could they be put?
When reading an expression containing a factorial in it, 5! is pronounced “Five factorial” or, alternately, “Five bang” or “Five shriek” (although I have never heard “shriek” outside of extremely geeky circles)
It is not, I am sad to say, pronounced “FIVE!”, although I always say it that way in my head.
Well, then, are golfers really shouting “24″?
Sorry, got distracted. Really this is all just a cultural misunderstanding. Pasta, as we all know, was invented in China, and in Chinese, the number 10,000 was symbolically used to mean infinity. Consequently, in its appropriate cultural context, by using a number greater than 10,000, the Mazzio’s ad is entirely correct.
Endless Possibilities
Are you the sort of person who examines advertisements for mathematical accuracy? Would you whip out a calculator after reading: Start with one of three pastas, then choose one of six sauces and one of four meats, plus three of…
Wataburger makes a similar claim which intrigues me.