28. A Set of Football Matches is to Be Organized
a set of football matches is to be organized in a round robin fashion i.e every participating teams plays a match against every other team once if 45 matches are totally played ,how many teams participated?
Submitted by tartle · Added 17 January 2013 · Updated 2 July 2026
Solution:
In a round robin format, the number of matches played is given by the formula n(n-1)/2, where n is the number of teams. Setting this equal to 45 gives the equation n(n-1) = 90. Solving this quadratic equation, we find that n = 10, so there are 10 teams participating.
Comments (3)
Nine
n(n-1)/2=45
n=10
1 team only : 0 matches
2 teams : 1 match
3 teams : 3 matches
4: 6
5: 10
6: 15
7: 21
8: 28
9: 36
10: 45
So the answer is 10
(The sequence is 1,3,6,10,15,21,36,45... increasing by 1,2,3,4,5... etc)
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