Question

Jo 和 Blair 轮流从 $1$ 开始数，每次比对方上一轮说到的最后一个数多说一个数。Jo 先说“一”，所以 Blair 接着说“一、二”。然后 Jo 说“一、二、三”，依此类推。说出的第 $53$ 个数是什么？

Jo and Blair take turns counting from $1$ to one more than the last number said by the other person. Jo starts by saying "1", so Blair follows by saying "1, 2". Jo then says "1, 2, 3", and so on. What is the $53$ rd number said?

$2$

$3$

$5$

$6$

$8$

答案：E

知识点：三角形数

难度评级：1380

解答：

到数到 $n$ 的那一轮结束时，共说了 $1 + 2 + \cdots + n = \tfrac12 n(n+1)$ 个数。当 $n = 9$ 时，这个总数为 $45$ 。下一轮从 $1, 2, \ldots$ 开始，所以第 $53$ 个数是这一轮的第 $8$ 个数，即 $8$ 。正确答案是 E。

After the turn that counts up to $n,$ exactly $1 + 2 + \cdots + n = \tfrac12 n(n+1)$ numbers have been said. For $n = 9$ that is $45.$ The next turn starts $1, 2, \ldots,$ so the $53$ rd number is the $8$ th number of that turn, namely $8.$ Thus, the correct answer is E.

2013 AMC 12B 第 7 题

答案：E

难度评级：1380

解答：

其他年份的第 7 题