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Challenging Chess Championship (Posted on 2005-11-16) Difficulty: 3 of 5
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?

    See The Solution Submitted by Old Original Oskar!    
    Rating: 3.3333 (6 votes)

    Comments: ( Back to comment list | You must be logged in to post comments.)
    Solution Solution | Comment 10 of 13 |

    There are only 3 possible cases:

    Case 1: 7th Rank defeats 3rd Rank
    Case 2: 7th Rank draws with 3rd Rank
    Case 3: 7th Rank loses to 3rd Rank

    Before going into each of the cases, please note that:

    The total points are 28. If 1st Rank has 7 points (he wins all his games),
    then automatically 2nd Rank lost at least 1 game and hence has only 6 points max.
    If 1st Rank has 6.5 points, then since all the players have a different score the second

    Rank can only have max 6 points.

    So, the max sum of the bottom 4 players is 6 points.

    Now, there are 4 players at the bottom of the table and they all played with each other.

    Hence 6 games were played between them and hence 6 points were shared between them. Hence

    the sum of their points will at least be 6 points.

    Now, this automatically eliminates case 1 and case 2 as both these cases will give the 7th

    Ranked player either 1 point or 0.5 point which will make the sum of the points of the last

    4 players beyond 6 points.

    Hence, only case 3 is possible i.e......7th Rank loses to 3rd Rank.

     

    -Kalam


      Posted by Kalam on 2005-11-17 04:12:40
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