Problem

Source: (2022-) 2023 XVI 16th Dürer Math Competition Finals Day 2 E15

Tags: geometry, combinatorics, combinatorial geometry



Csongi bought a $12$-sided convex polygon-shaped pizza. The pizza has no interior point with three or more distinct diagonals passing through it. Áron wants to cut the pizza along $3$ diagonals so that exactly $6$ pieces of pizza are created. In how many ways can he do this? Two ways of slicing are different if one of them has a cut line that the other does not have.