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IQ Question on teams and matches

  1. Dec 12, 2011 #1
    1. The problem statement, all variables and given/known data

    There are 11 teams playing in a round robin way. Winning a match gives one point and loosing a match gives none. There is no draw in the entire series. If the difference between maximum and minimum score is 8 and there are exactly 3 teams whose scores are same. Find out the score of the team which is ranked fourth according to scores if the teams scored equally are ranked the same.



    2. Relevant equations

    I don't have any.


    3. My attempt

    I arranged the scores from 9 to 1. and guessed that the answer is 6.
     
  2. jcsd
  3. Dec 12, 2011 #2
    In each round, there are how many possible points that could be won? Multiply this by the total number of rounds, and you will see the total number of points that can be won over the competition, and this might help you arrange the scores.
     
  4. Dec 12, 2011 #3
    I think the question says that the only repeated score is that where three teams are tied on a score, and otherwise different teams have different scores. Combine this with the spread of 8 points (three possibilities) and the total number of points available to establish all the individual team point scores.
     
  5. Dec 13, 2011 #4
    Please give me the solution. I have my exams on the 18th and I am frustrated. I don't have time to think.
     
  6. Dec 13, 2011 #5

    SammyS

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    Will we also be with when you take your exam ?

    Can you explain how you arrived at your answer?
     
    Last edited: Dec 13, 2011
  7. Dec 13, 2011 #6

    eumyang

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    I used daveb's suggestion, combined with your attempt, to come up with a solution. I hope that you aren't required to use any specific method, because I just used the ol' guess-and-check. So I would read daveb's post again and think about it.
     
  8. Dec 13, 2011 #7
    There are how many total points to be won, across all teams? Call this P.

    There are THREE options initially to investigate for a range of 8 points: 2 to 10, 1 to 9 and 0 to 8.

    Ignoring the repeated scores, there must be a team with every possible (integer) points value in range (no drawn matches, so only integers).

    Still ignoring the repeat scores, these give a total points score of X, Y or Z

    Therefore the two other teams (who are tied for points with one of these) must have (P-X)/2 or (P-Y)/2 or (P-Z)/2 points

    Which of these options is feasible?
     
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