Problem 6

Given a polygon $P$, let $f(P)$ denote the number of lines of reflection symmetries of $P$. For example, if $P$ is a square, then $f(P)=4$, and if $P$ is rectangle that is not a square, then $f(P)=2$. For how many different values $n$ does there exist a $2024$-gon $P$ with $f(P)=n$?

A square and a rectangle (which is not a square) with the 4, respectively 2, lines of symmetries illustrated.

To deter guessing without thinking, we ask that you also solve the following simple arithmetic problem before checking your answer:

What is 6 × 3 + 4?

This problem was first solved on Wed 21st February at 4:16:33pm