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Problem 211

AMC 10/12, early questions

Algebra Difficulty 3.8 Find the answer AMC 10 A · United States

The number $2024$ is written as the sum of not necessarily distinct two-digit numbers. What is the least number of two-digit numbers needed to write this sum?

Your answer

Official solution

In order to minimize the number of terms in the sum, the greatest two-digit number, $99$ , should be used as many times as possible. Because $20 \cdot 99 = 1980$ , the minimum number of terms is greater than $20$ . On the other hand, $2024 = 20 \cdot 99 + 44$ , so the least number of two-digit numbers needed is $21$ .

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