Problema Solution

Pizza comes in 3 kinds of crusts with any combination of different toppings. The ad says there are almost 200 different ways to order a pizza. What is the smallest number of toppings?

Answer provided by our tutors

1) There are 3 ways to choose the type of crust (assuming that we choose exactly one of the three types of crust for the pizza). Also, for each available topping, we have 2 choices: either include or exclude that topping.


So if n is the number of toppings, then by the Fundamental Counting Principle,

number of ways to order the pizza = 3(2^n).

(No, the number of ways is not just 3n, since one can choose no toppings and can also choose more than one topping.)


Since there are "almost" 200 ways to order the pizza, 3(2^n) is "almost" 200.

Thus, 2^n is "almost" 66 2/3. Note that 2^6 = 64 and 2^7 = 128, so 6 toppings is the most reasonable answer. (For 6 toppings, there are 192 possible ways to order the pizza, which is "almost" 200.)