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A bit of geometry, combinatorics, and number theory

Source: German TST, IMO ShortList 2003, combinatorics problem 3

May 18, 2004
geometrycombinatorial geometrypolygonExtremal combinatoricsright angleanglesIMO Shortlist

Problem Statement

Let n≥5n \geq 5 be a given integer. Determine the greatest integer kk for which there exists a polygon with nn vertices (convex or not, with non-selfintersecting boundary) having kk internal right angles.
Proposed by Juozas Juvencijus Macys, Lithuania
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