How many matches should these teams win?

Probability Level 2

There are 8 teams that are participating in a cricket tournament.

During the round-robin league stage, each team plays two times against each of the other teams.

A team earns two points when it wins a match, but does not earn any point when it loses a match.

At the end of the round-robin league, all teams have scored the same number of points.

How many matches did each team win?


The answer is 7.

Srinivasa Gopal by Srinivasa Gopal , 53, India

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2 solutions

Srinivasa Gopal
Oct 31, 2020

Total number of matches = 2 * 8C2 = 56

Total sum of match points that all the teams can score = 112

If all the teams have scored an identical number of points, points scored by each team = 112/8 = 14

In the event that all teams have scored an identical number of points, the number of wins by any team = Points scored /No of points for a win = 14/2 = 7

2 Helpful 3 Interesting 2 Brilliant 0 Confused
Hongqi Wang
Oct 31, 2020

  • "each team plays two times against each of the other teams", that means each team play 2 × ( 8 − 1 ) = 14 2 \times (8 - 1) = 14

  • "all teams have scored the same number of points.", then the losts and wins of each team are the same, so each team wins 14 / 2 = 7 14 / 2 = 7

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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