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## Pick-A-Pizza

Logic Grid puzzles come with a handy interactive grid that will help you solve the puzzle based on the given clues.

 Puzzle ID: #37354 Fun: (2.73) Difficulty: (3.34) Category: Logic-Grid Submitted By: camrae27 Corrected By: MarcM1098

There is a new pizza place in town called Pick-A-Pizza. They have five wheels that, for just a few dollars, you can spin to decide the pizza chef, crust, cheese, meat topping, and veggie topping. When the wheels stop spinning, you have your pizza order! There have only been five customers so far, and each time, a different chef, a different crust (crisp, Greek, Sicilian, thin, or whole wheat), a different cheese (Gorgonzola, mozzarella, Parmesan, provolone, or Romano), a different meat topping (bacon, chicken, meatball, pepperoni, or sausage), and a different veggie topping (broccoli, mushrooms, olives, onions, or peppers) have been chosen. From the information provided, can you determine the crust, cheese, meat and veggie toppings on the pizza made by each chef?

1. The pizza topped with onions (which wasn't made by Nunzio) didn't have a Greek crust. Alfredo's pizza didn't have a whole wheat crust and wasn't topped with pepperoni. No pizza had both olives and mozzarella.

2. Mario didn't make the bacon pizza (whose crust was neither crisp nor thin). The sausage-topped pizza (which didn't have a whole wheat crust) didn't include peppers. Luigi's pizza (which didn't have a crisp crust) wasn't topped with broccoli.

3. Alfredo's pizza (which didn't include chicken) didn't have a Sicilian crust. Neither the pizza with a whole wheat crust (which wasn't topped with onions) nor Nunzio's pizza was topped with provolone cheese. Neither the pie topped with broccoli nor the pepperoni pizza was the one that had a crisp crust.

4. Neither Giuseppe's pizza nor the sausage pizza was the one topped with onions. The Sicilian pizza (which wasn't Luigi's) wasn't topped with peppers. Alfredo's pizza (which didn't include olives) wasn't topped with provolone cheese.

5. Mario didn't make the pepperoni pizza. The sausage pizza (which wasn't made by Nunzio) wasn't topped with mushrooms. The broccoli pizza was neither the one with a thin crust nor the one topped with mozzarella.

6. The meatball pizza (which wasn't topped with onions) didn't have a crisp crust. The olive pizza wasn't topped with Romano. Luigi's pizza (which didn't have a thin crust) wasn't topped with provolone.

7. The pizza with a Greek crust wasn't topped with broccoli. The bacon pizza had neither Parmesan nor Romano cheeses. There were no peppers on the thin crust pizza.

Alfredo, Thin, Romano, Meatball, Mushrooms
Giuseppe, Whole Wheat, Mozzarella, Pepperoni, Peppers
Luigi, Greek, Parmesan, Sausage, Olives
Mario, Crisp, Provolone, Chicken, Onions
Nunzio, Sicilian, Gorgonzola, Bacon, Broccoli

The hints are not necessary to solve the puzzle. Here is an explanation of the first hint:

Luigi's crust is not crisp (clue 2), Sicilian (clue 4), or thin (clue 6), so it must be Greek or whole wheat. However, onions are not on the pizza with a Greek crust (clue 1) or a whole wheat crust (clue 3), so Luigi cannot have onions on his pizza.

That leaves only Mario or Alfredo who can have onions. Assuming Alfredo has onions leads to a contradiction: Alfredo did not use chicken (clue 3) or pepperoni (clue 1), and onions are not with meatballs (clue 6) or sausage (clue 4), so if Alfredo has onions, he must also have bacon. Alfredo does not have a Sicilian crust (clue 3) or a whole wheat crust (clue 1), and onions are not on the pizza with a Greek crust (clue 1), so he must have a crisp crust or a thin crust. However, bacon is not on the pizza with a crisp crust or a thin crust (clue 2), so Alfredo cannot have bacon. This is a contradiction, so the assumption that Alfredo has onions is false. Thus Mario has onions.

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