### Brain Teasers

# Pizza Puzzle

Amy was eating a pizza, and the pizza is cut into 8 pieces. Because this is mathematics, and mathematics is exact, we will say that eating a 1/8 of a pizza takes exactly 2 minutes.

Now, Amy starts eating, but 2 minutes later, Barney comes, and he wants pizza too. So they both eat some more pizza, until, 2 minutes later, Chris arrives and he wants some pizza too! So they all eat pizza, until, 2 minutes later, Dean arrives, and he wants pizza as well! Now, there is not enough pizza for all of them to share with the way it is cut, so they'll have to cut the pizza into 4 pieces. Now, cutting 1 straight line (No matter how long or short) takes 1 minute, and (because there are 4 people) it takes them 4 times less of the amount of time to cut one straight line. What is the shortest amount of time they can achieve this? (Cutting the pizza, not eating the pizza)

Now, Amy starts eating, but 2 minutes later, Barney comes, and he wants pizza too. So they both eat some more pizza, until, 2 minutes later, Chris arrives and he wants some pizza too! So they all eat pizza, until, 2 minutes later, Dean arrives, and he wants pizza as well! Now, there is not enough pizza for all of them to share with the way it is cut, so they'll have to cut the pizza into 4 pieces. Now, cutting 1 straight line (No matter how long or short) takes 1 minute, and (because there are 4 people) it takes them 4 times less of the amount of time to cut one straight line. What is the shortest amount of time they can achieve this? (Cutting the pizza, not eating the pizza)

### Hint

How many 1/8s of a pizza are left?Think about the way they can place what is left of the pizza.### Answer

15 seconds.If Amy starts eating one slice, and two minutes later, Barney comes, that means that she ate 1 slice (1/8 of the pizza). Then when Barney and Amy continue eating until Chris comes, they would've eaten 2 slices together, making 3 slices eaten altogether. And when Amy, Barney, and Chris continue eating until Dean comes, they eat 3 slices combined, and altogether, 6 slices, leaving 2 slices uneaten. If they place the 2 slices opposite each other, then they can cut 1 straight line to cut both of the two pieces in half, and then they have 4/16 or 4 halves of a slice.

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