Question

$100$ 到 $400$ 之间有多少个整数含有数字 $2$ ？

How many whole numbers between $100$ and $400$ contain the digit $2?$

$100$

$120$

$138$

$140$

$148$

答案：C

知识点：数字容斥原理分类讨论

难度评级：1050

解答：

从 $200$ 到 $299$ 的 $100$ 个数全部含有 $2$ 。

在 $100$ 到 $199$ 中，十位是 $2$ 的有 $10$ 个，个位是 $2$ 的有 $10$ 个，但 $122$ 被重复计算了一次，所以有 $10 + 10 - 1 = 19$ 个。 $300$ 到 $399$ 同样有 $19$ 个。

总数是 $100 + 19 + 19 = 138$ 。

所以正确答案是 C。

All $100$ numbers from $200$ to $299$ contain a $2.$

Among $100$ to $199,$ there are $10$ with a $2$ in the tens place and $10$ with a $2$ in the units place, but $122$ is counted twice, giving $10 + 10 - 1 = 19.$ The range $300$ to $399$ similarly contributes $19.$

The total is $100 + 19 + 19 = 138.$

Thus, the correct answer is C .

1985 AMC 8 第 15 题

答案：C

难度评级：1050

解答：

其他年份的第 15 题