Hello guys, this puzzle is created by me, I hope you like it. If something is unclear about it, let me know.
Star Lord has landed on a deserted planet with one space policeman. He is moving around the planet, painting a line along his path, claiming any land which is surrounded by paint (the part containing less unclaimed area). The policeman is trying to restrict the total land claimed by Star Lord as much as possible. If he encounters him, Star Lord gets arrested and can not continue painting anymore. Can you prove that the policeman has a strategy, which prevents Star Lord from claiming more than 50% of the planet's surface? If there are two policemen on the planet, can you prove that they have a strategy, which prevents Star Lord from claiming more than 25% of the surface?
Remark: We assume that Star Lord and the policemen are moving with the same speed, take decisions in real time and are fully aware of everybody's locations. Their initial positions are arbitrary and the planet is a perfect sphere.
Recently I started developing a website about various puzzles - www.puzzlereview.com, you can check it out if you are interested. I keep updating it regularly and will be happy to hear some fresh ideas.