A Series of Hard Problems (1 of 3)
Let ( a 1 , b 1 ) , ( a 2 , b 2 ) , . . . , ( a n , b n ) be the vertices of a convex polygon which contains the origin in its interior. Is it possible to prove that there exist positive real numbers x and y such that - ( ( a 1 , b 1 ) x a 1 y b 1 + ( a 2 , b 2 ) x a 2 y b 2 + . . . + ( a n , b n ) x a n y b n = ( 0 , 0 )
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