I ate at **Romano’s Macaroni Grill** for the first time last week. I was particularly intruiged by their “Create your own pasta” dish. (I accidentally called it “Make your own pasta” when I ordered, our waitress instantly corrected me. Lordy.) To create your own pasta, you are a given a menu. You pick any of six noodles, eight sauces, up to three vegetables out ten, five meats, and a couple of salads (numbers are from memory). That’s a good amount of variety. And in fact the meal was delightful and I will return. So why am I blogging? Because of the catchphrase on the menu. “The possibilities are endless”. No, they’re not. The possibilities are not endless, they are finite, countable, and easily calculated.

6 noodles X

8 sauces X

120 vegetable combinations X

5 meats X

3 salads (none, A, or B) =

86,400 combinations*. Very finite.

But Romano’s is not the only offender. Let’s talk about **Waffle House. ** They claim prominently on their menu how many ways there are to prepare a burger. On their website, they claim at least 70,778,880 different ways.

This was deconstructed nicely in this article. Here’s how you do math for something like this. How many possible toppings are there? Eight. Each one can either be there or not — two ways for each topping. So you take two, and multiply it by itself eight times. This equals 256. How do you get from 256 to 70 million? You can’t. You can get weasely to get closer. For instance, you could either have a bun top, bun bottom, or not. That’s another factor of 4. You could get the burger rare, medium rare, medium, medium well, well done. That’s a factor of 5. That gets you to 5,120. We are almost halfway to supporting their claim (because 5,120 squared is almost 70 million.) But we’ve used everything we got.

Here’s one way to explain the discrepancy. Consider the clientele and employee base at Waffle House. Do they strike you as particulary sophisticated when it comes to mathematics? I’d guess over half the people who eat there need a tip calculator to figure out what 15% of $10.00 is. The workers are no better. It’s the bottom of the barrel, no getting around it. The management doesn’t look like they’re taking Number Theory courses at night either. So based on this limited sample, we conclude that everyone associated with Waffle House is a drooling idiot of some kind. I conclude that their advertising claim is false, but is merely due to stupidity rather than malice.

*Interestingly, this number is the exact number of seconds in a day. I often need to use this at work to convert dates to datetimes and back. From now on, all my code will call it the “Romano” factor.

I realized after posting this that my math was off for Romano’s. For the vegetables, it is not 120. The 120 was deduced by calculating the number of ways to choose three out of a universe of 10. (10!/7!*3!)=(10*9*8/6)=(720/6)=120. However, I neglected that you do not have to get exactly three vegetables. You can get none, one, two, or three. There are several ways to calculate the right answer, and the answer works out to 176. Amazingly, Google can do this for you.

However, I like the coincidence of the datetime converter, and since I’m not sure any of my other numbers are right, I’m leaving as is for now.

Consarn it! Perhaps you can also ask for double mushrooms or something like that. In that case, you would say you have 3 independent choices, each from a group of 11 (10 vegetables, or nothing). However, you would need to divide by 6, to show that mushroom-mushroom-pepper is the same as pepper-mushroom-mushroom. So it’s 11*11*11/6 = 222. That’s simplistic, but ballpark correct. We’re at 159,840 possible pasta choices, but I’m no longer pretending that’s exact.

Clearly, I will need to return, ask some poor waitress for all the rules and assumptions about what can be ordered, and then steal a menu.

Just because all pasta combinations are possible doesn’t mean they should be allowed. For instance, take a nice chunky bolognese, then put it over angel hair pasta: instant culinary disaster, especially after you add all of your three vegetables and meats to it.