# Math Help - Basketball game problem

1. ## Basketball game problem

Sorry for the lame title, couldn't thinnk of a better one xD
Anyways, can anyone please tell me how to solve this problem:

At a basketball tournament involving 8 teams, each team played 4 games with each of the other teams. How many games were played at this tournament?

The mark scheme says: since each team 4 games with other teams, 8*4= 32 games are played by each team. each game involved two teams, hence 32*(8/2)=128 games were played.

hmmm, so, if each team plays 4 games with each other team, but not itself (which is rediculous) , shouldn't it be 4*7=28 games each team, also, why do we divide the number of teams by two? I know it says there is two teams each match, but what effect why do we divide it by two?
Please help me, I am just confused, I just need a good explanation to remove this confusion.....

2. ## Re: Basketball game problem

Originally Posted by IBstudent
At a basketball tournament involving 8 teams, each team played 4 games with each of the other teams. How many games were played at this tournament?
I am a bit concerned about the wording used in this question. I am woefully ignorant of sports. A tournament in which each team plays each other team four times seems a bit much. But let’s say that is correct.
It can be modeled as an multi-graph on eight vertices in which there are four edges between any two vertices.
$\binom{8}{2}=28$, so there are 28 pairing of teams.
Four edges, games, for each pair: $112$.

3. ## Re: Basketball game problem

Thanks.... but the answer is supposed to be 128, which is weird. The question is actually a multiple choice question that includes your answer, it also includes another answer which I thought was correct....
I wonder how they can guess the wrong answers that we might have so accurately!

4. ## Re: Basketball game problem

Originally Posted by IBstudent
Thanks.... but the answer is supposed to be 128, which is weird. The question is actually a multiple choice question that includes your answer, it also includes another answer which I thought was correct....I wonder how they can guess the wrong answers that we might have so accurately!
The key is simply wrong.
If we both are correct and the question means each team each plays other team four times it is impossible for the answer to be 128. I delayed in posting an answer trying to find a reading of the question which gives 128. There is none. Then I decided that the fact there were 28 parings made it likely that the 128 is a natural typo.