G6

Part of 2021 IMO Shortlist

Problems(1)

Fitting an Equilateral Triangle in an Equilateral n-gon

Source: 2021 ISL G6

Find all integers

n\geq 3

for which every convex equilateral

n

-gon of side length

1

contains an equilateral triangle of side length

1

. (Here, polygons contain their boundaries.)