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

(Problem)
(Solution 1)
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== Solution 1 ==
 
== Solution 1 ==
We see that <math>1, 2, 3,</math> and <math>4</math> each appear once in the ones, tens, hundreds, and thousands digit of some number. Since <math>1+2+3+4=10</math>,
+
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 <math>10\cdot(1+10+100+1000)=\boxed{(E)11,110}</math>
 
we find that the sum is equal to <math>10\cdot(1+10+100+1000)=\boxed{(E)11,110}</math>
  
 
~kingofpineapplz
 
~kingofpineapplz

Revision as of 20:32, 22 November 2021

Problem

What is the value of $1234+2341+3412+4123?$

$(\textbf{A})\: 10{,}000\qquad(\textbf{B}) \: 10{,}010\qquad(\textbf{C}) \: 10{,}110\qquad(\textbf{D}) \: 11{,}000\qquad(\textbf{E}) \: 11{,}110$

Solution 1

We see that $1, 2, 3,$ and $4$ each appear in the ones, tens, hundreds, and thousands digit exactly once. Since $1+2+3+4=10$, we find that the sum is equal to $10\cdot(1+10+100+1000)=\boxed{(E)11,110}$

~kingofpineapplz