Difference between revisions of "2021 Fall AMC 10B Problems/Problem 1"

Latest revision as of 22:20, 23 November 2021

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-==Problem==
+#REDIRECT [[2021_Fall_AMC_12B_Problems/Problem_1]]
-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>
-== Solution 1 ==
-We see that <math>1, 2, 3,</math> and <math>4</math> each appear in the ones, tens, hundreds, and thousands digit exactly once. Since <math>1+2+3+4=10</math>, we find that the sum is equal to <cmath>10\cdot(1+10+100+1000)=\boxed{(\textbf{E})11,110}.</cmath>
-Note: it is equally valid to manually add all 4 numbers together to get the answer.
-~kingofpineapplz