Mathematical Formula

[dwil]

What is the formula for determining the total number of matches played by X teams who play each other once?

[jake-the-peg]

x(x-1)/2

[jim360]

(1/2)*X*(X-1)

You can see this by counting. 1 team won't have a match, two teams will play each other once, 3 teams will have 3 matches (AB, AC, BC), 4 will need 6: (AB, CD, AC, BD, AD, BC), and so on... meaning that the number of matches needed is determined by the series of triangular numbers, which has the formula above.

[sandyRoe]

I didn't know the answer here, but was thinking if there were 10 teams in a league would there be 45 matches?

[Old_Geezer]

1+2+3+4+.....+(x-2)+(x-1)

[Old_Geezer]

Which is probably factorial (x-1) ?

[dwil]

Thanks all. Most of you win the coconut but jake's the easiest one to do.

[ToraToraTora]

talk about make hard work of it jim/og, jake is spot on, nothing more needed! Sandy, yes 10x9/2.

[jim360]

All I added was explaining where the result came from -- why should that be making hard work of it? Ideally should make it easier, really, to see the derivation or at least some hint of it.

[ToraToraTora]

or another way to take the 6 nations as an example. there are 6 teams each has five matches and there are 3 per week for 5 weeks.