6

Part of 1991 Romania Team Selection Test

Problems(1)

here is a regular n-gon whose all vertices lie on the considered arcs

Source: Romania IMO TST 1991 p6

n \ge 3

be an integer. A finite number of disjoint arcs with the total sum of length

1 -\frac{1}{n}

are given on a circle of perimeter

1

. Prove that there is a regular

n

-gon whose all vertices lie on the considered arcs

combinatoricscombinatorial geometry