IMO Shortlist 1990 problem 28


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2. travnja 2012.
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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.
Izvor: Međunarodna matematička olimpijada, shortlist 1990