AMC8 2012
AMC8 2012 · Q14
AMC8 2012 · Q14. It mainly tests Basic counting (rules of product/sum).
In the BIG N, a middle school football conference, each team plays every other team exactly once. If a total of 21 conference games were played during the 2012 season, how many teams were members of the BIG N conference?
在 BIG N 中学足球联盟中，每支队伍与其他每支队伍正好比赛一次。2012 赛季总共进行了 21 场联盟比赛，BIG N 联盟有多少支队伍？
(A)
6
6
(B)
7
7
(C)
8
8
(D)
9
9
(E)
10
10
Answer
Correct choice: (B)
正确答案：（B）
Solution
This problem is very similar to a handshake problem. We use the formula $\frac{n(n-1)}{2}$ to usually find the number of games played (or handshakes). Now we have to use the formula in reverse.
So we have the equation $\frac{n(n-1)}{2} = 21$. Solving, we find that the number of teams in the BIG N conference is $\boxed{\textbf{(B)}\ 7}$.
这类似于握手问题。使用公式 $\frac{n(n-1)}{2}$ 求比赛数（或握手数）。反过来解方程 $\frac{n(n-1)}{2} = 21$，得出 BIG N 联盟队伍数为 $\boxed{\textbf{(B)}\ 7}$。
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