Question 15
Let $P$ be a regular 100-gon. An Aussie triangulation is formed by dividing $P$ into a set $T$ of non-overlapping triangles such that:
- there are exactly 2025 different points, including the 100 vertices of $P$, that are a vertex of at least one triangle in $T$, and
- no three of these 2025 points are collinear.
A quokkalateral is a convex quadrilateral that consists of two triangles in T sharing a common side. Two quokkalaterals may share a triangle in T.
Determine the minimum number of quokkalaterals among all Aussie triangulations.
- there are exactly 2025 different points, including the 100 vertices of $P$, that are a vertex of at least one triangle in $T$, and
- no three of these 2025 points are collinear.
A quokkalateral is a convex quadrilateral that consists of two triangles in T sharing a common side. Two quokkalaterals may share a triangle in T.
Determine the minimum number of quokkalaterals among all Aussie triangulations.