Some Thoughts

Today, I extract one of the thorns from my blogging side, so with out further ado…

Have you ever wondered how many possible combinations of Subway sandwiches there are? To answer that question you must first answer the timeless question of “What is a sandwich?” and “What makes a sandwich distinct from another sandwich?” For example, does adding tomatoes to a simple ham and cheese sandwich qualify it to be intrinsically different? If tomatoes do, what about lettuce, that green, virtually tasteless, paper-shredded topping of mostly water? Is there a ranking among the toppings? What about temperature? Surly a sandwich isn’t a Tuna Melt if it hasn’t been heated.

Obviously there are deep philosophical questions here.

I used to work near a Subway store. I probably ate there three to four times a week. Usually just getting the daily specials, or figuring out ways to save some money, like the hidden vegetarian sandwich. I got to know the workers by name and all was bright and happy, until they took away the stamps. But this post isn’t about the demise of a wonderful incentive program, this is about math and numbers.

What would be a close approximation for the number of combinations of sandwiches at your neighborhood Subway?

So not to beat around the bush any longer:

There are 682,518,380,544 combinations at my local Subway store.

In case you are going to write out a check and send it to me that number is: six hundred and eighty-two billion, five hundred and eighteen million, three hundred and eighty thousand, five hundred and forty-four!

The equation used is:

b * c * s * m * t * p = Number of Combinations

Where:
b = breads, c = cheeses, s = sauces, m = meats, t = toppings, p = spices

or more specifically (see Table 1):

b = 6
c = (6 Choose 1) + 1 = 7
s = (12 Choose 3) + 1 = 221
m = (16 Choose 3) + 1 = 561
t = ∑ (13 Choose xi) = 8192, where m = 0, n = 13, assuming capital sigma notation.
p = ∑ (4 Choose xi) = 16, where m = 0, n = 4, assuming capital sigma notation.

Note: The “Choose” function here is a probability function (nCr) that chooses “r” items from “n” choices.
The “+1” on c, s, and m is just taking into account the fact that some one could choose NO cheese, sauce, or meat respectively. “t” and “m” don’t need the “+1” because that is taken into account by setting m = 0, since (X Choose 0) will always equal 1.

So this calculation also places some limits on how big the sandwich can be. No sandwich can have more than 3 types of meat, and 3 types of sauces. A sandwich must have some kind of bread (Sorry Dr. Atkins), and only 1 kind of cheese. A sandwich can go nuts with the toppings and spices though.

A few months ago I switched yet again to a different cell phone provider. I went back to T-Mobile, and was intrigued by their T-Mobile at Home service. You know the one where the phone hooks into your broadband connection and then all subsequent continental U.S. calls are free (after paying them a monthly fee of course).
Anyway, I got the service which works pretty well. The sound quality is normal, and I haven’t experienced any delay in the conversation while talking. Only every now and then does the phone act strange, like refuse to dial, and once in a great while it even crashes in the middle of a conversation. I’ll put up with these little annoyances as long as they don’t happen too frequently, but can’t live without my Mac synchronizing via bluetooth with address book.

Luckily, there is a nice site dedicated to hacking your mobile phone to work with Apple’s iSync:

http://en.isync-hilfe.de/faq-blog.html

It didn’t take long to get it working, and I even made a little graphic for my phone so it looks better in iSync.

It was pretty easy to get set up. I just followed the instructions on the isync-hilfe.de site for the Nokia phone and it worked the first try. iSync will say that the synchronization didn’t work but your phone will know better and everything will come through just fine.

Feel free to use the graphic I made, as long as it not for commercial purposes.