AMC8 2009

AMC8 2009 · Q22

AMC8 2009 · Q22. It mainly tests Basic counting (rules of product/sum), Base representation.

How many whole numbers between 1 and 1000 do not contain the digit 1?

1 到 1000 之间有多少个不含数字 1 的整数？

(A) 512 512

(B) 648 648

(D) 728 728

(E) 800 800

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): There are 8 one-digit positive integers, excluding 1. There are $8\cdot 9=72$ two-digit integers that do not contain the digit 1. There are $8\cdot 9\cdot 9=648$ three-digit integers that do not contain the digit 1. There are $8+72+648=728$ integers between 1 and 1000 that do not contain the digit 1.

答案（D）：除去 1 之外，有 8 个一位正整数。有 $8\cdot 9=72$ 个不包含数字 1 的两位整数。有 $8\cdot 9\cdot 9=648$ 个不包含数字 1 的三位整数。因此，在 1 到 1000 之间不包含数字 1 的整数共有 $8+72+648=728$ 个。

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