2024 AMC 10A Problems/Problem 4
Contents
[hide]Problem
The number 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?
Solution 1
Since we want the least number of two-digit numbers, we maximize the two-digit numbers by choosing as many s as possible. Since we choose twenty s and one for a total of two-digit numbers.
~MRENTHUSIASM
Solution 2
We claim the answer is . This can be achieved by adding twenty 's and a . To prove that the answer cannot be less than or equal to , we note that the maximum value of the sum of or less two digit numbers is , which is smaller than , so we are done. Thus, the answer is
~andliu766
See also
2024 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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All AMC 10 Problems and Solutions |
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