Let $R$ be a unit square region and $n \geq 4$ an integer. A point $X$ in the interior of $R$ is called n-ray partitional if there are $n$ rays emanating from $X$ that divide $R$ into $n$ triangles of equal area. How many points are $100$-ray partitional but not $60$-ray partitional?(AMC 10A 2011/25)
It, as well as Sols 1 and 2 state that 4 of the rays must intersect the vertices of the square. Sol 3 does not make that assumption. (I understood the rest of the video solution. )
Can anyone justify why this statement is true?
If there are no rays that intersect a vertex, then that vertex will be part of a quadrilateral, not a triangle.
Solution 3 implicitly makes that assumption by assuming that each side forms an integral number of triangles