2024 AMC 8 Problems/Problem 4: Difference between revisions
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==Problem== | ==Problem 4== | ||
When Yunji added all the integers from <math>1</math> to <math>9</math>, she mistakenly left out a number. Her incorrect sum turned out to be a square number. What number did Yunji leave out? | When Yunji added all the integers from <math>1</math> to <math>9</math>, she mistakenly left out a number. Her incorrect sum turned out to be a square number. What number did Yunji leave out? | ||
<math>\textbf{(A) } 5\qquad\textbf{(B) } 6\qquad\textbf{(C) } 7\qquad\textbf{(D) } 8\qquad\textbf{(E) } 9</math> | <math>\textbf{(A) } 5\qquad\textbf{(B) } 6\qquad\textbf{(C) } 7\qquad\textbf{(D) } 8\qquad\textbf{(E) } 9</math> | ||
==Solution 1= | ==Solution== | ||
Adding numbers 1 through 9 gives us 45. This was her expected sum, but what she got was a perfect square. Since she got that perfect square sum by forgetting a number, that sum is less than 45. The square number right under 45 is 36. So 45 - 36 = 9. So the solution is E[9]. | |||
~That_One_Dude | |||
== Video Solution 1 (Detailed Explanation) 🚀⚡📊 == | |||
Youtube Link ⬇️ | |||
https://youtu.be/5mCSOiqX8sA | |||
~ ChillGuyDoesMath :) | |||
==Video Solution by Central Valley Math Circle (Goes through the full thought process)== | |||
https://youtu.be/dMX5_MXVkYs | |||
~mr_mathman | |||
== Video by MathTalks_Now == | |||
https://www.youtube.com/watch?v=crn37TRMLv4 | |||
-rc1219 | |||
==Video Solution by Math-X (First fully understand the problem!!!)== | |||
https://youtu.be/BaE00H2SHQM?si=tzbzeCdEfXqROciK&t=907 | |||
~Math-X | |||
==Video Solution (A Clever Explanation You’ll Get Instantly)== | |||
https://youtu.be/5ZIFnqymdDQ?si=bxVKQiul4AjzVUgC&t=331 | |||
~hsnacademy | |||
==Video Solution 1 (Simple and Fast) by Parshwa== | ==Video Solution 1 (Simple and Fast) by Parshwa== | ||
| Line 36: | Line 62: | ||
==Video Solution by Intersigation== | ==Video Solution by Intersigation== | ||
https://youtu.be/ktzijuZtDas&t=232 | https://youtu.be/ktzijuZtDas&t=232 | ||
==Video Solution by Daily Dose of Math (Understandable, Logical, and Speedy)== | |||
https://youtube/bSP | |||
qeNO11M?si=HIzlxPjMfvGM5lxR | |||
~Thesmartgreekmathdude | |||
==Video Solution by WhyMath== | |||
https://youtu.be/PCvkqxz0f0I | |||
== Video solution by TheNeuralMathAcademy == | |||
https://youtu.be/f63MY1T2MgI&t=285s | |||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2024|num-b=3|num-a=5}} | {{AMC8 box|year=2024|num-b=3|num-a=5}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
[[Category:Introductory Combinatorics Problems]] | |||
Latest revision as of 20:58, 20 August 2025
Problem 4
When Yunji added all the integers from 
to 
, she mistakenly left out a number. Her incorrect sum turned out to be a square number. What number did Yunji leave out?
Solution
Adding numbers 1 through 9 gives us 45. This was her expected sum, but what she got was a perfect square. Since she got that perfect square sum by forgetting a number, that sum is less than 45. The square number right under 45 is 36. So 45 - 36 = 9. So the solution is E[9].
~That_One_Dude
Video Solution 1 (Detailed Explanation) 🚀⚡📊
Youtube Link ⬇️
~ ChillGuyDoesMath :)
Video Solution by Central Valley Math Circle (Goes through the full thought process)
~mr_mathman
Video by MathTalks_Now
https://www.youtube.com/watch?v=crn37TRMLv4
-rc1219
Video Solution by Math-X (First fully understand the problem!!!)
https://youtu.be/BaE00H2SHQM?si=tzbzeCdEfXqROciK&t=907
~Math-X
Video Solution (A Clever Explanation You’ll Get Instantly)
https://youtu.be/5ZIFnqymdDQ?si=bxVKQiul4AjzVUgC&t=331
~hsnacademy
Video Solution 1 (Simple and Fast) by Parshwa
Video Solution 2 (easy to digest) by Power Solve
https://youtu.be/HE7JjZQ6xCk?si=sTC7YNSmfEOMe4Sn&t=179
Video Solution by Math-X (First fully understand the problem!!!)
https://youtu.be/BaE00H2SHQM?si=9ZUxEGmGam7il9xr&t=907
~Math-X
Video Solution by NiuniuMaths (Easy to understand!)
https://www.youtube.com/watch?v=Ylw-kJkSpq8
~NiuniuMaths
Video Solution 2 by SpreadTheMathLove
https://www.youtube.com/watch?v=L83DxusGkSY
Video Solution by CosineMethod [🔥Fast and Easy🔥]
Video Solution by Intersigation
https://youtu.be/ktzijuZtDas&t=232
Video Solution by Daily Dose of Math (Understandable, Logical, and Speedy)
https://youtube/bSP qeNO11M?si=HIzlxPjMfvGM5lxR
~Thesmartgreekmathdude
Video Solution by WhyMath
Video solution by TheNeuralMathAcademy
https://youtu.be/f63MY1T2MgI&t=285s
See Also
| 2024 AMC 8 (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 AJHSME/AMC 8 Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing
