Question

学生 Arn、Bob、Cyd、Dan、Eve 和 Fon 按这个顺序围成一圈。他们开始报数：Arn 先报，然后 Bob，以此类推。当一个数含有数字 $7$ （例如 $47$ ）或者是 $7$ 的倍数时，报到这个数的人离开圆圈，报数继续。最后留在圆圈里的是谁？

Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in that order in a circle. They start counting: Arn first, then Bob, and so forth. When the number contains a $7$ as a digit (such as $47$ ) or is a multiple of $7$ that person leaves the circle and the counting continues. Who is the last one present in the circle?

$\text{Arn}$

$\text{Bob}$

$\text{Cyd}$

$\text{Dan}$

$\text{Eve}$

答案：D

知识点：整除性数字过程模拟

难度评级：1070

小提示：

只模拟会让人离开的那些数

Simulate only the numbers that cause someone to leave.

大提示：

每次有人离开后仍按原来的顺序继续报数，下一个数由圆圈中下一位还在的人报出

Keep the counting order after each person leaves; the next number goes to the next person still in the circle.

视频讲解：

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文字解答：

最先会让人离开的五个数是 $7,14,17,21,27$ 。只跟踪这些轮次即可。

Arn 报到 $7$ ，Cyd 报到 $14$ ，Fon 报到 $17$ ，Bob 报到 $21$ ，Eve 报到 $27$ 。

Dan 是唯一留在圆圈里的学生，所以正确答案是 D。

The first five removal numbers are $7,14,17,21,27.$ Tracking only those turns gives:

Arn says $7$ , Cyd says $14$ , Fon says $17$ , Bob says $21$ , and Eve says $27$ .

Dan is the only student remaining, so D is the correct answer.

2018 AMC 8 第 3 题