1. x and y are positive reals such that x3 + y3 + (x + y)3 + 30xy = 2000. Show that x + y = 10.
2. Find all positive integers n such that n3 + 33 is a perfect square.
3. ABC is a triangle. E, F are points on the side BC such that the semicircle diameter EF touches AB at Q and AC at P. Show that the intersection of EP and FQ lies on the altitude from A.
4. n girls and 2n boys played a tennis tournament. Every player played every other player. The boys won 7/5 times as many matches as the girls (and there were no draws). Find n.
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Junior Balkan Mathematical Olympiad Problems
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