# Puzzles/Logic puzzles/Pizzas/Solution

< Puzzles‎ | Logic puzzles‎ | Pizzas

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

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.