3rd All Russian Mathematical Olympiad Problems 1963

3rd All Russian Mathematical Olympiad Problems 19631.  Given 5 circles. Every 4 have a common point. Prove that there is a point common to all 5. 2.  8 players compete in a tournament. Everyone plays everyone else just once. The winner of a game gets 1, the loser 0, or each gets 1/2 if the game is drawn. The final result is that everyone gets a different score