Math Gold Medalist

Lor

2023 AMC 12A

Problem 7

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?

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

Calendar

Casework

Priority: The Most Limited Case

Number of days in each month(2023):

January:31

Februrary:28

March:31

April:30

May:31

June:30

July:31

August:31

September:30

October:31

November:30

December:31

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   Solution