AMC 8 2009 Problem 22
AMC8 2009 年第 22 题
基本计数原理★★★☆☆
How many whole numbers between 1 and 1000 do not contain the digit 1?
1 和 1000 之间有多少个整数不含有数字 1？
的值是
- A.512
- B.648
- C.720
- D.728
- E.800
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
There are 8 8 one-digit positive integers, excluding 1 1. There are 8 ⋅ 9 = 72 8⋅9=72 two-digit integers that do not contain the digit 1 1. There are 8 ⋅ 9 ⋅ 9 = 648 8⋅9⋅9=648 three-digit integers that do not contain the digit 1 1. There are 8 + 72 + 648 = 728 8+72+648=728 integers between 1 1 and 1000 1000 that do not contain the digit 1 1. OR OR Think of each number between 1 1 and 1000 1000 as a three-digit number. For example, think of 2 2 as 002 002 and 27 27 as 027 027. There are 9 3 = 729 9 3 =729 three-digit numbers that do not use the digit 1 1. Because 000 000 does not represent a whole number between 1 1 and 1000 1000, the total is 728 728. Answer: 𝐷 D .
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