Eight players competed at a recent chess tournament. Knowing that:
Each player played all the others, exactly once.
Winning earns you 1 point; drawing, ½ point; and losing, 0 points.
Everybody ended with a different number of points.
The one who ended 2nd earned as many points as the four bottom players put together.
What was the result of the game between the player who ended 3rd and the player who ended 7th?
The first thing you have to realize is you can have fractional points, so there are 15 possible scores, instead of just 8.
The top two people must have at least one loss between them since they played one game. This means the place 2 had at most 6 points. The last 4 people must have at least 6 points between them since they played 6 games.
Since the bottom four people had at least and at most 6 wins, they can't have any more wins, which includes games by place 7, which means place 3 must have won that game.
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Posted by Gamer
on 2005-11-16 17:00:56 |
Two important parts
