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Difference between revisions of "2023 AMC 10A Problems/Problem 9"

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==Solution==
 
==Solution==
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Do careful casework by each month. In the month and the date, we need a <math>0</math>, a <math>3</math>, and two digits repeated. After the case work, we get <math>9</math>, meaning the answer <math>\boxed{\textbf{(E)}~9}</math>.
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Do careful casework by each month. In the month and the date, we need a <math>0</math>, a <math>3</math>, and two digits repeated (which have to be <math>1</math> and <math>2</math> after consideration). After the case work, we get <math>9</math>, meaning the answer <math>\boxed{\textbf{(E)}~9}</math>.
 
For those who are wondering, the numbers are:
 
For those who are wondering, the numbers are:
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20230113, 20230131, 20230223, 20230311, 20230322, 20231013, 20231031, 20231103, 20231130.
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<math>20230113</math>, <math>20230131</math>, <math>20230223</math>, <math>20230311</math>, <math>20230322</math>, <math>20231013</math>, <math>20231031</math>, <math>20231103</math>, <math>20231130</math>.
  
 
== Video Solution 1 by OmegaLearn ==
 
== Video Solution 1 by OmegaLearn ==

Revision as of 22:23, 9 November 2023

Problem

A digital display shows the current date as an $8$-digit integer consisting of a $4$-digit year, followed by a $2$-digit month, followed by a $2$-digit date within the month. For example, Arbor Day this year is displayed as 20230428. For how many dates in $2023$ will each digit appear an even number of times in the 8-digital display for that date?

$\textbf{(A)}~5\qquad\textbf{(B)}~6\qquad\textbf{(C)}~7\qquad\textbf{(D)}~8\qquad\textbf{(E)}~9$

Solution

Do careful casework by each month. In the month and the date, we need a $0$, a $3$, and two digits repeated (which have to be $1$ and $2$ after consideration). After the case work, we get $9$, meaning the answer $\boxed{\textbf{(E)}~9}$. For those who are wondering, the numbers are: $20230113$, $20230131$, $20230223$, $20230311$, $20230322$, $20231013$, $20231031$, $20231103$, $20231130$.

Video Solution 1 by OmegaLearn

https://youtu.be/xguAy0PV7EA

See Also

2023 AMC 10A (Problems • Answer Key • Resources)
Preceded by
Problem 8 		Followed by
Problem 10
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

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