8 players compete in a tournament, every one 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 the different score the player placing second gets the same score as the total of four bottom players

1. the total of the player placing second. was
2. the total score of the top four players was

The bottom 4 played 6 games amongst themselves, so their scores must total at least 6.
Hence the number 2 player scored at least 6. The maximum score possible is 7, so if the
number 2 player scored more than 6, then he must have scored 6 1/2 and the top player 7.
But then the top player must have won all his games, and hence the number 2 player lost at
least one game and could not have scored 6 1/2. Hence the number 2 player scored exactly 6,
and the bottom 4 players lost all their games with the top 4 players. In particular, the number
3 player won against the number 7 player.

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