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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

a

e b

c

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 6×4 = 24 to the total.

Team c: Add 5×4 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:

(7×4) + (6×4) + (5×4) + (4×4) + (3×4) + (2×4) + (1×4) + (0×4) = (7+6+...+0)4 = 28×4 = 112

112 games were played

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