22nd International Mathematical Olympiad 1981 Problems & Solutions

A1.  P is a point inside the triangle ABC. D, E, F are the feet of the perpendiculars from P to the lines BC, CA, AB respectively. Find all P which minimise:         BC/PD + CA/PE + AB/PF. A2.  Take r such that 1 ≤ r ≤ n, and consider all subsets of r elements of the set {1, 2, ... , n}. Each subset has a smallest element. Let F(n,r) be the arithmetic mean of these smallest