2023 AMC 12A Problems/Problem 7

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

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

2023 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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2023 AMC 12A Problems/Problem 7

Contents

Problem

Solution

Video Solution 1 by OmegaLearn

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