Difference between revisions of "2021 Fall AMC 12B Problems/Problem 1"
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==Problem== | ==Problem== | ||
− | What is the value of <math>1234+2341+3412+4123 | + | What is the value of <math>1234 + 2341 + 3412 + 4123</math> |
<math>\textbf{(A)}\: 10{,}000\qquad\textbf{(B)} \: 10{,}010\qquad\textbf{(C)} \: 10{,}110\qquad\textbf{(D)} \: 11{,}000\qquad\textbf{(E)} \: 11{,}110</math> | <math>\textbf{(A)}\: 10{,}000\qquad\textbf{(B)} \: 10{,}010\qquad\textbf{(C)} \: 10{,}110\qquad\textbf{(D)} \: 11{,}000\qquad\textbf{(E)} \: 11{,}110</math> | ||
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~stjwyl | ~stjwyl | ||
+ | |||
+ | == Solution 4 (Brute Force)== | ||
+ | We can simply add the numbers. <math>1234 + 2341 + 3412 + 4123 = 11110 \implies \boxed{\textbf{(E)}}</math>. | ||
+ | |||
+ | Note: Although this would not take terribly long, it is not recommended to do this in a real contest. | ||
+ | |||
+ | ~ [https://artofproblemsolving.com/wiki/index.php/User:Cxsmi cxsmi] | ||
==Video Solution by Interstigation== | ==Video Solution by Interstigation== | ||
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https://youtu.be/I9lSM0hO39M | https://youtu.be/I9lSM0hO39M | ||
− | ~Education, the Study of | + | ~Education, the Study of Everything |
==Video Solution by WhyMath== | ==Video Solution by WhyMath== | ||
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~savannahsolver | ~savannahsolver | ||
+ | ==Video Solution by TheBeautyofMath== | ||
+ | For AMC 10: https://youtu.be/lC7naDZ1Eu4 | ||
+ | |||
+ | For AMC 12: https://youtu.be/yaE5aAmeesc | ||
+ | |||
+ | ~IceMatrix | ||
+ | |||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2021 Fall|ab=B|before=First Problem|num-a=2}} | {{AMC10 box|year=2021 Fall|ab=B|before=First Problem|num-a=2}} | ||
{{AMC12 box|year=2021 Fall|ab=B|before=First Problem|num-a=2}} | {{AMC12 box|year=2021 Fall|ab=B|before=First Problem|num-a=2}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 00:48, 30 January 2024
- The following problem is from both the 2021 Fall AMC 10B #1 and 2021 Fall AMC 12B #1, so both problems redirect to this page.
Contents
Problem
What is the value of
Solution 1
We see that and each appear in the ones, tens, hundreds, and thousands digit exactly once. Since , we find that the sum is equal to Note that it is equally valid to manually add all four numbers together to get the answer.
~kingofpineapplz
Solution 2
We have ~Steven Chen (www.professorchenedu.com)
Solution 3
We see that the units digit must be , since is . But every digit from there, will be a since we have that each time afterwards, we must carry the from the previous sum. The answer choice that satisfies these conditions is .
~stjwyl
Solution 4 (Brute Force)
We can simply add the numbers. .
Note: Although this would not take terribly long, it is not recommended to do this in a real contest.
~ cxsmi
Video Solution by Interstigation
Video Solution
~Education, the Study of Everything
Video Solution by WhyMath
~savannahsolver
Video Solution by TheBeautyofMath
For AMC 10: https://youtu.be/lC7naDZ1Eu4
For AMC 12: https://youtu.be/yaE5aAmeesc
~IceMatrix
See Also
2021 Fall AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
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 |
2021 Fall AMC 12B (Problems • Answer Key • Resources) | |
Preceded by First Problem |
Followed by Problem 2 |
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.