In the 'Barkclays English Premier league' the total of the points of all teams is $420$ .There were $2$ points for a win,1 point for a draw and no point for lose.If each team played twice against each team,Then what was the number of the leagues participated in the competition?
I solved this in 5 minutes.You guys are smarter than me.Surely you will solve in a minute or something.
Beginners Problem 002
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sakibtanvir
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nafistiham
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Re: Beginners Problem 002
If one knows about combination.there is nothing to
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
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sakibtanvir
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Re: Beginners Problem 002
My solution was like that:
The answer is 21. 
An amount of certain opposition is a great help to a man.Kites rise against,not with,the wind.
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nafistiham
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Re: Beginners Problem 002
notice that in each match a total of $2$ points was achieved no matter what happened.so
\[n(n-1) \cdot 2 = 420\]
\[\rightarrow n(n-1)=210\]
\[\rightarrow n=15\]
\[n(n-1) \cdot 2 = 420\]
\[\rightarrow n(n-1)=210\]
\[\rightarrow n=15\]
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
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sakibtanvir
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Re: Beginners Problem 002
But the draw should be considered also. 
An amount of certain opposition is a great help to a man.Kites rise against,not with,the wind.
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nafistiham
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Re: Beginners Problem 002
suppose team a and team b are playing.there are $3$ cases. a wins, a loses or a draws. whatever happens the total point of a and b after this match will be $2$. that's what i am trying to say.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
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sakibtanvir
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Re: Beginners Problem 002
Ohhooooooo,sorryyyyy 
An amount of certain opposition is a great help to a man.Kites rise against,not with,the wind.