### Brain Teasers

# Pizza Pieces

What is the largest number of pieces you can form with n straight cuts of a pizza?

The pieces do not need to be of equal size.

The pieces do not need to be of equal size.

### Answer

The answer is n*(n+1)/2 + 1.With every cut you should cut through every previous cut. As long as you keep doing this you will always be able to do so again with your next cut. The number of additional pieces formed on cut x will always be x. The sum of all integers from 1 to n is n*(n+1)/2. So the sum of additional pieces cut will be n*(n+1)/2.

Finally add 1 because we start with 1 piece: n*(n+1)/2 + 1.

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