pizza facts and factorials

After all these years, I don't know why I'm still obsessing about this...

Back in the early nineties there was a little caesar's commercial on tv (I found it on youtube - http://www.youtube.com/watch?v=cmlRAstCCro). In the commercial there's a pizza special - 2 pizzas, 5 toppings each. The little boy in the commercial says "wow, the possibilities are endless". The dad says "what do you mean, 5 + 5 are 10". And the little boy says "actually, it's 1,480,576 possibilities".

So, for fun, I decided to try to calculate the number. I decided it would be a factorial:


n•(n - 1)•(n - 2)•(n - 3)....•1

For 5:
5•4•3•2•1 = 120

Not even close.

So I wrote the number and the problem on the white board in my office to work on when I needed a break. That proved to be a disaster since I was working with a bunch of mathematicians. Everyone became obsessed with the problem and we would spend hours arguing about it.

One of the mathematicians said that, since you could get all the same toppings on one pizza, the problem was 30! (5 toppings + 5 of the same topping * 5 - though this was debated as being wrong). That answer:

30! Factorial -    265,252,859,812,191,058,636,308,480,000,000

We then began calling little caesars pizza places to find out how many toppings they had to select from. The average was 10 so we did 10! -  3,628,800.

After more arguing, calculating, and one guy writing a computer program, we gave up on finding the answer. So I went to the library (this was back before companies were on the internet - wow, that makes me feel old) and looked up the address for little caesar's corporate headquarters. I sent a letter to the president asking how the number used in the commercial was calculated. I suggested in my letter that they must have hired someone to calculate the number, rather than making something up, because it wouldn't have been that expensive to hire a mathematician. And I also had a rambling paragraph about the sorry state of math in the US.


In response I received a form letter, and $30 worth of coupons for free little caesar's pizzas. I gave the coupons away and have, to this day, never eaten little caesar's pizza because I was so pissed about the commercial. 


Last year I finally took the commercial number off the back of my calculator, where I had taped it in case I had a sudden insight into where it might have come from.