20th International Mathematical Olympiad 1978 Problems & Solutions

A1.  m and n are positive integers with m < n. The last three decimal digits of 1978m are the same as the last three decimal digits of 1978n. Find m and n such that m + n has the least possible value. A2.  P is a point inside a sphere. Three mutually perpendicular rays from P intersect the sphere at points U, V and W. Q denotes the vertex diagonally opposite P in the