Question

从 $1$ 到 $1000$ 之间，有多少个整数不含数字 $1$ ？

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

$512$

$648$

$720$

$728$

$800$

可以按位数分类。

不含数字 $1$ 的一位数有 $8$ 个。

不含数字 $1$ 的两位数有 $8 \cdot 9 = 72$ 个。

不含数字 $1$ 的三位数有 $8 \cdot 9 \cdot 9 = 648$ 个。

因此不含数字 $1$ 的数共有个。 $8 + 72 + 648 = 728$

所以正确答案是 D。

We can case on the number of digits.

There are $8$ one digit numbers excluding $1.$

There are $8 \cdot 9 = 72$ two digit numbers that lack the digit $1.$

There are $8 \cdot 9 \cdot 9 = 648$ three digit numbers that do not include $1.$

This yields a total of $8 + 72 + 648 = 728$ numbers that do not contain the digit $1.$

Thus, D is the correct answer.