MathNet 2022-part-05 — 197 problems (EN–VI) Question 98

Determine all positive integers $n \ge 3$ with the following property: every convex $n$-gon all of whose sides have length $1$ contains, in the region it bounds, an equilateral triangle of side length $1$.

(Note: the region bounded by a convex polygon consists of its interior and its boundary.)