It is impossible to draw a closed broken line
Source: IMO ShortList 1990, Problem 28 (USS 3)
August 15, 2008
analytic geometryvectornumber theoryrational numberIMO Shortlist
Problem Statement
Prove that on the coordinate plane it is impossible to draw a closed broken line such that
(i) the coordinates of each vertex are rational;
(ii) the length each of its edges is 1;
(iii) the line has an odd number of vertices.