Problem:
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?
Answer Choices:
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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 , the minimum number of terms is greater than 20 . On the other hand, , so the least number of two-digit numbers needed is .
The problems on this page are the property of the MAA's American Mathematics Competitions