Several teams take part in a competition, each of which must play one game with all the other teams. How many teams took part in the competition if they played 45 games in all?
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let the total no.of team=n
as they playing with a single league tournament (one game with ohter)
therefore
n(n-1)/2=total no.match
n(n-1)/2=45
n^2-n-90=0
by solving we get
n=10
its similar to the hand shake problem formula is N(N+1)/2
here n(n+1)/2=45
n(n+1)=90
put n=9
then 9(9+1)=90
so nine teams play the game
n(n-1)/2=45
n^2-n=90
n^2-n-90=0
n=10