IMO Shortlist 2006
IMO Shortlist 2006
... a regular 2006- gon is called odd if its endpoints divide the boundary into two parts, each composed of an odd number of sides. Sides are also regarded as odd diagonals. Suppose the 2006- gon has ... happen, it just suffices to select a vertex of the 2006- gon and draw a broken line joining every second vertex, starting from the selected one. Since 2006 is even, the line closes. This alrea...
Ngày tải lên: 02/06/2014, 16:35
IMO Shortlist 2004
... ABM. Duˇsan Djuki´c Vladimir Jankovi´c Ivan Mati´c Nikola Petrovi´c IMO Shortlist 2004 From the book The IMO Compendium, www .imo. org.yu Springer Berlin Heidelberg NewYork Hong Kong London Milan ... even. Find all positive integers n such that n has an alternate multiple. 1.1.2 Shortlisted Problems 1. A1 (KOR) IMO4 Let n ≥ 3 be an integer and t 1 , t 2 , . . . , t n positive real nu...
Ngày tải lên: 02/06/2014, 16:34
IMO Shortlist 2007
... line, and we get the contradiction again. 48 th International Mathematical Olympiad Vietnam 2007 Shortlisted Problems with Solutions 29 Solution 2. Again, we suppose the contrary. Consider an arbitrary
Ngày tải lên: 02/06/2014, 16:36
IMO Shortlist 2008
... extreme shortage of easy and appr opriate submissions forced the Problem Selection Committee to shortlist a simplified variant. The same one-dimensional Claim is used in both versions. Original ... element of S b is b + 1, a contradiction. 49 th International Mathematical Olympiad Spain 2008 Shortlisted Problems with Solutions Geometry G1. In an acute-angled triangle ABC, point H is the
Ngày tải lên: 02/06/2014, 16:37
IMO Shortlist 2009
... Geometry Problem Shortlist 50th IMO 2009 Geometry G1 BEL (Belgium) Let ABC be a triangle with AB = AC. The angle bisectors ... respectively. Let the triangle XY Z be equilateral. Prove that ABC is equilateral too. 8 50th IMO 2009 Problem Shortlist Geometry G8 BGR (Bulgaria) Let ABCD be a circumscribed quadrilateral. Let g be ... respectively. Show that the orthocenter of I 1 I 2 I 3...
Ngày tải lên: 02/06/2014, 16:41
IMO Shortlist 2010
... 1, j is a TL-block, thus the 51 st International Mathematical Olympiad Astana, Kazakhstan 2010 Shortlisted Problems with Solutions 29 i 1 th row is a n L-row. Now, choosing the ith row to be
Ngày tải lên: 02/06/2014, 16:42
