Question 96
Let $n \ge 3$ be an integer. For a convex $n$-gon $A_1A_2\dots A_n$ we consider a line $g$ through $A_1$ that does not contain any other point of the $n$-gon. Let $h$ be the orthogonal to $g$ through $A_1$. We orthogonally project the $n$-gon onto $h$. For $j = 1, \dots, n$ let $B_j$ denote the image of $A_j$. The line $g$ is called valid if the points $B_j$ are disjoint.
We consider all convex $n$-gons and all valid lines $g$. How many different orderings of the points $B_1, \dots, B_n$ do exist?
G. Baron, Vienna
We consider all convex $n$-gons and all valid lines $g$. How many different orderings of the points $B_1, \dots, B_n$ do exist?
G. Baron, Vienna