Maths question

[Pixelchic]

More maths than sport I think...

If a football tournament has 45 matches,and every team played all the other teams only once,how many teams took part?

Thanks

[turnerjmw]

Ten, I should think

[Pixelchic]

Well I was thinking if there were 7 teams, they would play 6 matches each so that would be 42???
Likewise if there were 8 teams, 7 matches each it would be 56???
Am I right or is there a catch?

[Jumbuck]

Pixelchic - A vs B is the same as B vs A in this instance so halve your answer.

[turnerjmw]

It's 9+8+7+6+5+4+3+2+1 = 45
So A v B, A v C, A v D, A v E, A v F, A v G, A v H, A v I, A v J = 9
B v C, B v D, B v E, B v F, B v G, B v H, B v I, B v J = 8 etc down to I v J = 1

[beejay1124]

10
-
10 x 9-----divided by 1 x 2
= 45

[jake-the-peg]

The number of matches N is given by n(n-1)/2 and n is the number of teams

So if there were 3 teams you'd have 3x2 /2 = 3 matches etc.

so 45=n(n-1)/2
90=n(n-1)

n²-n-90=0

solving with the quadratic formula gives 10

(And they say what's the point of algebra!!!)

[Pixelchic]

So obvious when you know. Knew I was missing something. Thanks guys :)

[tamborine]

divisional squared - 7 x 7 = 49 - 45 = 4 (ds 2). It would be 6.2 (due to cancellations)