AMC 8 1993 Problem 22
AMC8 1993 年第 22 题
基本计数原理★★★☆☆
Pat Peano has a collection of numbers to label the pages of his scrapbook. He has an infinite number of 0's, 1's, 3's, 4's, 5's, 6's, 7's, 8's and 9's, but only twenty-two 2's. How far can he number the pages of his scrapbook with these digits?
Pat Peano 有一批数字用于给他的剪贴簿页码编号。他有无限多个 0、1、3、4、5、6、7、8 和 9，但只有二十二个 2。用这些数字他最多能将剪贴簿页码编到多少？
- A.22
- B.99
- C.112
- D.119
- E.199
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
There is 1 two in the one-digit numbers.
The number of two-digit numbers with a two in the tens place is 10 and the number with a two in the ones place is 9. Thus the digit two is used 10+9=19 times for the two digit numbers.
Now, Pat Peano only has 22-1-19=2 remaining twos. You must subtract 1 because 22 is counted twice. The last numbers with a two that he can write are 102 and 112. He can continue numbering the last couple pages without a two until 120, with the last number he writes being .
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