MathDB

arcs and parallel sides

Source: Tournament of Towns, Fall 2002, Junior A Level, P3

May 17, 2014

combinatorics proposedcombinatorics

Problem Statement

The vertices of a

50\text{-gon}

divide a circumference into

50

arcs, whose lengths are

1,2,\ldots 50

in some order. It is known that any two opposite arcs (corresponding to opposite sides) differ by

25

. Prove that the polygon has two parallel sides.