AMC 8 1985 Problem 15

AMC8 1985 年第 15 题

基本计数原理★★★☆☆

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

100 到 400 之间有多少个整数包含数字 2？

A.100
B.120
C.138
D.140
E.148

正确答案 · Correct Answer

解析 · Solution

Solution 1

All 100 integers from 200 to 299 start with 2.

Of the integers from 100 to 400 not starting with 2, 20 have a second digit of 2:

\{120, 121, 122, \cdots, 129, 320, 321, 322, \cdots, 329\}

, while 20 have a third digit of 2:

\{102, 112, 122, \cdots, 192, 302, 312, 322, \cdots, 392\}

. Of these, 122 and 322 have both a second and third digit of 2, so a total of 20 + 20 - 2 = 38 integers between 100 and 400 not starting with 2 contain the digit 2.

Therefore, a total of 100 + 38 = 138 integers between 100 and 400 contain the digit 2.

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