There are 1000 students in a colony who play one or more game among Hockey, Golf, Badminton, Polo and Chess. 225 students play Badminton but not Hockey. 500 people play Hockey. 325 students played exactly three games and 225 students played exactly four games. All those students who play Golf do not play Polo. No student plays Golf alone. The number of students who play Polo, Badminton and Chess but not the other two is half the number of students who do not play Hockey but play Golf. Exactly 175 students play Hockey and at most one more game. All those students who play Chess also play Badminton.