AMC 8 1989 Problem 22

AMC8 1989 年第 22 题

余数与同余★★★☆☆

The digits 1, 9, 8, 9 are "cycled" separately as shown and put together in a numbered list. What is the

7\text{th}

number in the list?

数字 1、9、8、9 分别如图所示"循环"排列，并合在一起形成一个编号列表。列表中的第 7 个数是什么？

正确答案 · Correct Answer

解析 · Solution

Solution 1

Every

4\text{th}

line includes 1989 while every

6\text{th}

line includes

\text{AJHSME}

. Therefore, a line has

\text{AJSHME 1989}

if and only if its number is divisible by both 4 and 6. Therefore, the number of the first such line is

\text{lcm}(4,6)=12

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