2024 AMC 10A Problems/Problem 4
- The following problem is from both the 2024 AMC 10A #4 and 2024 AMC 12A #3, so both problems redirect to this page.
Contents
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
Solution 3 (Same as solution 1 but Using 100=99+1)
. Since 
, 
. Therefore a total of two-digit numbers are needed.
~woh123
Video Solution by Pi Academy
https://youtu.be/GPoTfGAf8bc?si=JYDhLVzfHUbXa3DW
Video Solution by Daily Dose of Math
~Thesmartgreekmathdude
Video Solution by FrankTutor
Video Solution 1 by Power Solve
https://youtu.be/j-37jvqzhrg?si=rWQoAYu7QsZP8ty4&t=407
Video Solution by SpreadTheMathLove
https://www.youtube.com/watch?v=6SQ74nt3ynw
See also
| 2024 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
| 2024 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 2 |
Followed by Problem 4 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
