Pizza’s Many Faces

by Paul Rangel

Submitted : Fall 2011

The project, although is seems insignificant, is about the different combinations that can be offered from a single pizza parlor, Little Caesars, due to the amount of ingredients, toppings and crusts that are offered. In reality, it is not just a combination, it is also a permutation of the 4 different crusts, 3 types of ingredients that sustain the toppings and the 15 different topping offered by Little Caesars. At first, the numbers were multiplied together to deliver the different combinations of one topping, one crust and one ingredient which was 180 different types of pizzas. But this seemed wrong as there are many different equations offered by the mathematical community on combinations and permutations. The trouble was which one to use, but that was resolved once the math advisor was consulted on the subject. The crusts and ingredients would not be factorials as you could only choose one, but the amount of toppings were not limited. If one wanted to they could add all 14 toppings to the pizza.

Using the equation for permutations, it was calculated that a simple equation lead to millions of options of pizzas to choose from, if not more. But there was an error, doubling on toppings were not permitted except for cheese, which working as an ingredient as well had to be placed as a topping. Another factor to consider was a cheese pizza, which is basically a pizza with no toppings at all. So a topping of none had to be added to the toppings list to suggest no toppings, just a crust and ingredient. So going over the equation again, a factorial had to be added in order to figure out what different variations could be offered. The results were staggering when using factorials for the toppings, with a culmination of over 15 trillion types of pizzas that could be ordered! Now, this computation is for adding all toppings or none at all on a pizza. This did not include the specials that they had or the sides they offered along with them.

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