Birthday Pizza!

Level 2

Answer this problem first.

The next day, you buy 3 pizzas for Nathan’s birthday! Everyone’s satisfaction is a must for the party. The following are the conditions so that we will be satisfied:

  1. Ian will be satisfied if every pizza has exactly 3 toppings.
  2. Samuel will be satisfied if the pizzas contain ALL KINDS of toppings.
  3. Nathan will be satisfied if there are at least 2 pizzas with hotdog crust.
  4. I will be satisfied if all the pizzas have additional cheese.
  5. Brent will be satisfied if at most 1 topping is present in every pizza.(e.g. he won’t be satisfied with both ham and pineapple on every pizza.)
  6. Our new friend, Gabriel, will be satisfied if all the pizzas with hotdog crust have pepperoni.

The additional toppings cost:

  1. Hotdog crust-$2.5
  2. Pineapple-$0.5
  3. Additional Cheese-$0.75
  4. Ham-$1.25
  5. Pepperoni-$2

Find the least amount of money we should spend.

This problem is part of Pizza Math!


The answer is 13.

Jerome Te by Jerome Te , 22, Philippines

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2 solutions

Jerome Te
Dec 18, 2018
  1. Let (a, b, c) represent the toppings on each pizza(or some other letters). There should be exactly three elements in each set. (From Ian)
  2. So from me, (Cheese, b, c), (Cheese, d, e), (Cheese, f, g).
  3. From Brent and Nathan(and the facts we know), there should be exactly two pizzas with hotdog crust. (Cheese, Hotdog Crust, c), (Cheese, Hotdog Crust, e), (Cheese, f, g)
  4. From Gabriel and the facts we know, (Cheese, Hotdog Crust, Pepperoni), (Cheese, Hotdog Crust, Pepperoni), (Cheese, f, g)
  5. Then from Samuel, (Cheese, Hotdog Crust, Pepperoni), (Cheese, Hotdog Crust, Pepperoni), (Cheese, Ham, Pineapple)
  6. Compute for the total cost. $13!
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Al Z3B
Dec 26, 2018

To satisfy Ian: every pizza have 3 topping so we infer that we will have 9 kinds of topping and we have to find out number of every kind of 5 kinds we have. To satisfy Nathne we need 2 hot dogs . To satisfy himself we need 3 additional cheese To satisfy Gabriel we need 2 pepperoni To satisfy Samuel all pizzas must contain all kinds of toppings so We need 1 ham 1 pineapple So total cost will be
2* 2.5+2* 2+3*.75+.5+1.25=13

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