AMC 8 1992 Problem 15

AMC8 1992 年第 15 题

余数与同余★★★☆☆

What is the

1992^\text{nd}

letter in this sequence?

\text{ABCDEDCBAABCDEDCBAABCDEDCBAABCDEDC}\cdots

此序列中的第 1992 个字母是什么？

正确答案 · Correct Answer

解析 · Solution

Solution 1

The sequence consists of repeated strings of 9 letters,

\text{ABCDEDCBA}

. When 1992 is divided by 9, the remainder is 3, and so the 1992nd letter in the sequence is the 3rd letter of the smaller string,

\text{(C)\ \text{C}}

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