Advanced Math/Math


Ok so here is the 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?" someone on this site already asked this question and the answer was to draw a diagram like this
         e      b
         g      d
         f   e

And draw lines from the letters to the other letters in the circle. I understand that part, but then the person said that I should get 28 lines total and then multiply 28 by 4. But why would team a, for example, have 7 lines drawn from it if they only played 4 games? shouldn't they only have 4 lines? and why do you multiply 28 by 4?

"But why would team a, for example, have 7 lines drawn from it if they only played 4 games? shouldn't they only have 4 lines?"
I think you misunderstood the question. Team a did not play only 4 games. They played 4 games with Team b, 4 games with Team c, etc., for a total of 28 games.

A diagram with showing all 28 lines would be unnecessarily cluttered, so draw just the 7 lines between a and the other teams, then multiply 7 by 4 to get 28 games.

Team b also played against 7 teams, but you've already accounted for Team a, so b's games add 64 = 24 to the total.
Team c: Add 54 to the total
The last set of games, Team h, are already accounted for, so nothing is added to the total.

Now add up the games:
(74) + (64) + (54) + (44) + (34) + (24) + (14) + (04) = (7+6+...+0)4 = 284 = 112
112 games were played

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Janet Yang


I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.


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