25th All Russian Mathematical Olympiad Problems 1999

1.  The digits of n strictly increase from left to right. Find the sum of the digits of 9n. 2.  Each edge of a finite connected graph is colored with one of N colors in such a way that there is just one edge of each color at each point. One edge of each color but one is deleted. Show that the graph remains connected. 3.  ABC is a triangle. A' is the

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