23 November 2016
Posted by on
This puzzle is inspired by a combinatorial problem that surfaced in the Feedback section of New Scientist in early 2011. (See issues #2794 and #2798), and was brought to my attention by Hugh Casement. [link]
Here is the puzzle:
When ordering a pizza from the Enigmatic Pizza Company you can specify the toppings on your pizza. There are 34 possible toppings to choose from, and you can have up to 11 toppings on your pizza. But you can have no more than three helpings of any individual topping.
The most basic pizza available would be one with no toppings at all. And a fully loaded veggie pizza might have 3 helpings of cherry tomatoes, 3 helpings of mixed peppers, 3 helpings of jalapeño peppers and 2 helpings of mozzarella cheese, using up all 11 toppings.
What is the total number of different pizza combinations that are available?