A league of two halves
“Football season’s started again, then,” said David Kickham.
“Yup,” replied Robby Fouler. “I’ve just been sorting out the fixture list for the Tackleham league. A right palaver, I’ll tell you. Every team plays every other team once. There’s too many teams to have a home game and an away game.”
“How many teams are there in the league?” asked David.
“I don’t entirely recall,” confessed Robby. “I do know that there are three more teams this season than there were last season.”
David thought for a moment. “Well, then—how many matches do they play altogether? We can work out how many teams there are if you can tell me that.”
“Well, that’s kind of difficult too, you know… I’m, not too good with numbers.
I remember that it’s twice as many as it was last year.” Robby paused, and shook his head. “No, sorry, not quite. It’d be twice as many if there was one more fixture.”
“Twice as many as last year, less one, then,” said David.
“Then I can tell you how many teams there are this year.”
What is the number of teams?
Scroll down for the answer
There are 11 teams.
If there are n teams, then the number of games is: n x (n – 1) 2
There were n – 3 teams last year, and this year there were twice as many games as last year, minus one.
So n x (n – 1) = [2 x (n – 3) x (n -4)] – 1 2 2
Or n2 – 13n + 22 = 0. So (n-2) x (n-11) = 0. Therefore n = 2 or 11. But n = 2 would give -1 teams last year, so n = 11.
The winner was NA McPhail, Windermere