Question

几名学生围坐在一张大圆桌旁。他们传递一个装有 $100$ 颗糖的袋子。每个人拿到袋子后取一颗糖，然后把袋子传给下一个人。如果 Chris 拿了第一颗和最后一颗糖，那么桌旁学生人数可能是

Several students are seated at a large circular table. They pass around a bag containing $100$ pieces of candy. Each person receives the bag, takes one piece of candy, and then passes the bag to the next person. If Chris takes the first and the last piece of candy, then the number of students at the table could be

$10$

$11$

$19$

$20$

$25$

答案：B

知识点：整除性因数

难度评级：1140

解答：

Chris 拿第一颗糖，然后袋子一圈圈传递，直到 Chris 拿到最后一颗，也就是第 $100$ 颗。第一次和最后一次之间相隔 $99$ 次取糖。

因此 Chris 第一次之后的 $99$ 次取糖必须正好经过若干整圈后回到 Chris。这说明学生人数必须整除 $99$ ；选项中只有 $11$ 符合。

所以正确答案是 B。

Chris takes the first piece, and then the bag goes around until Chris takes the last ( $100$ th) piece. So the $99$ pieces after Chris's first must be exactly a whole number of trips around the table back to Chris.

This means the number of students divides $99$ . Among the choices, only $11$ divides $99$ .

Thus, the correct answer is B .

1990 AMC 8 第 22 题

答案：B

难度评级：1140

解答：

其他年份的第 22 题