How a Simple Pizza Stumped Mathematicians for 11 Years

If you still have nightmares about the Pythagorean theorem from your school days, discussing the laws of geometry over dinner at an Italian restaurant is probably the last thing you’d do. However, for a mathematician, everyday occasions are perfect opportunities to delve into solving unusual puzzles…

One thing is for sure, Rick Mabry and Paul Deiermann might have been irked by the pizza cutter for a while. These two American researchers took on a challenge issued in 1994 by Mathematics Magazine to demonstrate a peculiar proposition about fairly dividing a pizza. To put it simply: imagine your server awkwardly divides your four-cheese (or pepperoni, if you prefer) pizza. They ensure the slices intersect at one point, but not at the center. If there are two of you at the table, and each of you alternately picks adjacent slices, who ends up eating more pizza by the end?

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If you’re stumped, don’t worry: our mathematicians took a whole 11 years to solve this puzzle in all its complexity, through extensive algebraic calculations and combinatorial analysis (quite a feat…). If you’re curious about the solution, here’s the short of it: it all depends on the lines of cuts and the number of slices.

If at least one cut passes through the center or if the number of slices is even, it’s simple: each diner will eat exactly the same amount of pizza in any scenario. The situation gets tricky when the cutter never goes through the center and divides the pizza into an odd number of slices. For a pizza cut into 3, 7, 11, 15… slices, the person who picks the slice with the center will have more to eat. Conversely, for a pizza cut 5, 9, 13, 17 times, it’s precisely the opposite: you should let your neighbor take the slice containing the center to avoid being short-changed.

Confused? Since the “pizza theorem” isn’t on the menu at trattorias yet, there’s no risk of a pop quiz: you can order your margherita in peace.