Solution to the Pizza Problem

Jared Bukarau, a good friend from college, created this video of this pizza problem. I solved it very quickly, but it got me thinking. So I decided to expand and generalize the problem. Here are some possible solutions:

Discoveries:

·         The number of pieces you create will always be 6 more than the number of intersections.

·         If you are allowed to make 5 straight cuts, you can cut any number of pieces between 6 and 16.

o   6 is the minimum, because there are no intersections.

o   The highest number of intersections will be (5 x 4)/2 = 10 because each of the 5 lines intersect with the 4 other lines, but this would double count the number of intersections, so you would need to divide by 2. So the maximum number of pieces is 10 + 6 = 16 pieces. (Although, some pieces are pretty small).

Generalization:

·         If we generalize this problem to n cuts. You will always create n + 1 pieces more than the number of intersections.

·         You can cut any number of pieces between n + 1 and  pieces.

o   Note: is the maximum number of intersections with n lines.