Difference between revisions of "2021 Fall AMC 10B Problems/Problem 1"
(Created page with "==Problem== 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})...") |
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<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> | ||
| + | |||
| + | == 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 find that the sum is equal to <math>10\cdot(1+10+100+1000)=\boxed{(E)11,110}</math> | ||
| + | |||
| + | ~kingofpineapplz | ||
Revision as of 21:31, 22 November 2021
Problem
What is the value of 
Solution 1
We see that 
and 
each appear once in the ones, tens, hundreds, and thousands digit of some number. Since 
,
we find that the sum is equal to 
~kingofpineapplz
