2021 Fall AMC 10B Problems/Problem 1

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 once in the ones, tens, hundreds, and thousands digit of some number. 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

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2021 Fall AMC 10B Problems/Problem 1

Problem

Solution 1