A spherical planet is surrounded by 25 point asteroids. Prove, that at any given moment there will be a point on the surface of the planet from which an astronomer will not be able to see more than 11 asteroids.
An area of airspace contains clouds. It turns out that the area can be divided by 10 aeroplanes into regions such that each region contains no more than one cloud. What is the largest number of clouds an aircraft can fly through whilst holding a straight line course.