Problem:
Let denote the sum of the digits of the positive integer . For example, and . For how many two-digit values of is
Answer Choices:
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Solution:
Let . Since , we have . Thus if , then or . The values of for which are , and , and the values of for which are , and . There are values in all.
Answer: .
The problems and solutions on this page are the property of the MAA's American Mathematics Competitions