Difference between revisions of "2024 AMC 8 Problems/Problem 4"

(Solution 1)
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==Solution 1==
 
==Solution 1==
  
Calulate the sum of the digits from <math>1-9</math> is <math>1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45</math>. Thus, one of the answer choices (that are equal to Yunju's digits) subtracted from her sum of <math>45</math> must equal a square.  
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Calulate the sum of the digits from <math>1-9</math>, which is <math>1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45</math>. Thus, one of the answer choices (that are equal to Yunju's digits) subtracted from her sum of <math>45</math> must equal a square.  
  
 
Note that <math>45 - 9 = 36 = 6^2</math> works.
 
Note that <math>45 - 9 = 36 = 6^2</math> works.

Revision as of 22:47, 17 February 2024

Problem

When Yunji added all the integers from $1$ to $9$, she mistakenly left out a number. Her incorrect sum turned out to be a square number. What number did Yunji leave out?

Solution 1

Calulate the sum of the digits from $1-9$, which is $1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45$. Thus, one of the answer choices (that are equal to Yunju's digits) subtracted from her sum of $45$ must equal a square.

Note that $45 - 9 = 36 = 6^2$ works.

Solution 2

The sum of digits 1-9 is 45, 45-9=36 36=6^2 Therefore, the solution is that the integer she forgot was 9.

Video Solution 1 (Simple and Fast) by Parshwa

https://youtu.be/Qrf4GTDjjXs

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🔥]

noooooooooooooooooooooooooooooooooooooo!!!!!!!!!!!!!!!!!!

Video Solution by Intersigation

https://youtu.be/ktzijuZtDas&t=232

See Also

2024 AMC 8 (ProblemsAnswer KeyResources)
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

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