Puzzles/Logic puzzles/Pizzas/Solution

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Puzzles | Logic puzzles | Pizzas | Solution


Aaron - green pepper, onions and sausage
Betty - green pepper, mushrooms and onions
Charlie - mushrooms, pepperoni and sausage
Debbie - green pepper, pepperoni and sausage
Eric - mushrooms, onions and pepperoni

Reasoning[edit]

We are informed that B and D had green pepper, B and C had mushrooms, D and E had pepperoni and A and C had sausage, all marked with a Y.

          | A | B | C | D | E 
Green Pep |   | Y |   | Y |   
Mushrooms |   | Y | Y |   |   
Onions    |   |   |   |   |   
Pepperoni |   |   |   | Y | Y 
Sausage   | Y |   | Y |   |

We are also informed that the pairs B and D, B and C, D and E, and A and C, didn't share anything, except what is already marked with a Y. This eliminates the possibilities marked with an N.

          | A | B | C | D | E 
Green Pep |   | Y | N | Y | N 
Mushrooms | N | Y | Y | N |   
Onions    |   |   |   |   |   
Pepperoni |   | N |   | Y | Y 
Sausage   | Y | N | Y |   |

Knowing everyone had 3 toppings allows us to place another Y.

          | A | B | C | D | E 
Green Pep |   | Y | N | Y | N 
Mushrooms | N | Y | Y | N |   
Onions    |   | Y |   |   |   
Pepperoni |   | N |   | Y | Y 
Sausage   | Y | N | Y |   |

And we know B didn't share with C or D.

          | A | B | C | D | E 
Green Pep |   | Y | N | Y | N 
Mushrooms | N | Y | Y | N |   
Onions    |   | Y | N | N |   
Pepperoni |   | N |   | Y | Y 
Sausage   | Y | N | Y |   |

Allowing us to place 2 more Ys.

          | A | B | C | D | E 
Green Pep |   | Y | N | Y | N 
Mushrooms | N | Y | Y | N |   
Onions    |   | Y | N | N |   
Pepperoni |   | N | Y | Y | Y 
Sausage   | Y | N | Y | Y |

D didn't share with E, A didn't share with C.

          | A | B | C | D | E 
Green Pep |   | Y | N | Y | N 
Mushrooms | N | Y | Y | N |   
Onions    |   | Y | N | N |   
Pepperoni | N | N | Y | Y | Y 
Sausage   | Y | N | Y | Y | N

This allows us to place the remaining 4 Ys.

          | A | B | C | D | E 
Green Pep | Y | Y | N | Y | N 
Mushrooms | N | Y | Y | N | Y 
Onions    | Y | Y | N | N | Y 
Pepperoni | N | N | Y | Y | Y 
Sausage   | Y | N | Y | Y | N

Surprisingly, no one chose green pepper, onions and pepperoni.