IMO Shortlist 2002 problem C1


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2. travnja 2012.
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Let n be a positive integer. Each point (x,y) in the plane, where x and y are non-negative integers with x+y<n, is coloured red or blue, subject to the following condition: if a point (x,y) is red, then so are all points (x',y') with x'\leq x and y'\leq y. Let A be the number of ways to choose n blue points with distinct x-coordinates, and let B be the number of ways to choose n blue points with distinct y-coordinates. Prove that A=B.
Izvor: Međunarodna matematička olimpijada, shortlist 2002