22nd All Russian Mathematical Olympiad Problems 1996

1.  Can a majority of the numbers from 1 to a million be represented as the sum of a square and a (non-negative) cube? 2.  Non-intersecting circles of equal radius are drawn centered on each vertex of a triangle. From each vertex a tangent is drawn to the other circles which intersects the opposite side of the triangle. The six resulting lines enclose a

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