1990 AMC 8 第 22 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
22.
几名学生围坐在一张大圆桌旁。他们传递一个装有 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 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
小提示：
Chris 拿了第 颗和第 颗，所以在 Chris 第一次拿糖后，剩下的 次传递取糖必须刚好回到 Chris
Chris takes piece and piece , so after Chris’s first piece, the remaining pieces bring the bag exactly back to Chris
大提示：
学生人数必须整除 。
The number of students must divide evenly
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 颗。第一次和最后一次之间相隔 次取糖。
因此 Chris 第一次之后的取糖过程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 ；选项中只有 能整除 。
所以正确答案是 B。
Chris takes the first piece, and then the bag goes around until Chris takes the last (th) piece. So the 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 . Among the choices, only divides .
Thus, the correct answer is B .
其他年份的第 22 题
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